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School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 1 (Version 1) Solutions June 11, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 1 (Version 2) Solutions June 11, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 2 (Version 2) Solutions June 23, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 3 (Version 2) Solutions July 7, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use co
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 4 (Version 1) Solutions July 16, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: CALCULUS
! " # $ $ % & % % $ ' % # $ $ $ ' () * + , $ - . -$ . $ -. $ / / 0 ! $ $ / / / $ / $
School: Kennesaw
Course: CALCULUS
! " #$ % ! "& % % % % ' (% & ) ! #$ # * $ % % !" ' #& $ !" + #$, ) !" ! & &% % ' !" " ! " " & %" ! %" -% " " % ./ 2 y 1 -3 -2 -1 0 -1 -2 1 x 2 3 " 0.2 1.2 0 0.1 x 1.3 1.4 -0.2 -0.1 0 0.1 x 0.2 -0.2 -0.1 -0.2 " " . ( " " " " % " " % . " +& " "
School: Kennesaw
Course: CALCULUS
! "# # $ # # 20 15 10 5 -4 -3 -2 -1 0 -5 -10 1 2 x 3 4 % & '( & ! # $ # )" '( * # # & '( !
School: Kennesaw
James Garfields Proof of the Pythagorean Theorem College Trigonometry (MATH 1112) Kennesaw State University The Pythagorean Theorem states that for any right triangle with sides of length a and b and hypotenuse of length c, it is true that . There are man
School: Kennesaw
Course: Elemenary Statistics
B&W CONFIRMINGS 58 Chapter 2 Frequency Distributions and Graphs Exercises 23 1. Do Students Need Summer Development? For 108 randomly selected college applicants, the following frequency distribution for entrance exam scores was obtained. Construct a hist
School: Kennesaw
Course: College Algebra
Math 1111 Fall 2013 Sample Practice Problems This is not an all inclusive list of problems that might be on the test. In addition to these problems, please review your notes, the homework and the pretest problems in MML. Given the line 9x-3y = 12, write i
School: Kennesaw
Course: CALCULUS
Chelsea Spear MATH 1190 Castle 24 January 2008 Many mathematical concepts are intertwined throughout our everyday lives. Whether calculating the tip for a waiter at a fancy restaurant, managing the checkbook, or just meeting the challenge of learning
School: Kennesaw
Course: Calculus 1
Lecture 8, September 14, 2011 1. 2. 3. Answer questions Quiz 3 Sections 2.5 and 2.6 2.5 Derivatives of Trigonometric Functions Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a The proof is on page 103. s o n E d u c a C o p y i g h 2 0
School: Kennesaw
Course: Calculus 1
Lecture 24 , November 28, 2011 Task 1: questions Task 2: Sections 4.6 and 4.7 C o p y i g h 2 0 0 7 P e a 4.6 Indefinite Integrals and the Substitution Rule s o n E d u c a Let us first work on a simple problem Example 1 on page 287. C o p y i g h 2 0 0
School: Kennesaw
Course: Calculus 1
Lecture 23, November 21 2011 Task 1: questions Task 2: A quiz Task 3: Sections 4.5 and 4.6 4.5 The Fundamental Theorem of Calculus Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u
School: Kennesaw
Course: Calculus 1
Lecture 22, November 16, 2011 Task 1: questions Task 2: A quiz Task 3: Sections 4.4 and 4.5 4.4 The Definite Integral Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a This int
School: Kennesaw
Course: Calculus 1
Lecture 21, November 14, 2011 Task 1: Sections 4.3 and 4.4 4.3 Sigma Notation and Limits of Finite Sums Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 1 (Version 1) Solutions June 11, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 1 (Version 2) Solutions June 11, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 2 (Version 2) Solutions June 23, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 3 (Version 2) Solutions July 7, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use co
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 4 (Version 1) Solutions July 16, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
1.2 Gaussian and Gauss-Jordan Elimination 1. Denition: A matrix is a rectangular array of numbers. The numbers in the array are called the entries in the matrix. A general m n matrix can be written as A= a11 a12 a1n a21 a22 a2n . . . . . . . . . am1 am2 a
School: Kennesaw
Course: LINEAR ALGEBRA I
Chapter 1. Systems of Linear Equations 1.1 Introduction to Systems of Linear Equations 1. Linear Equations. Def: A linear equation in n variables x1 , x2 , ., xn is an equation that can be written in the form a1 x1 + a2 x2 + + an xn = b where b and the co
School: Kennesaw
Course: LINEAR ALGEBRA I
Chapter 2. Matrices 2.1 Operations with Matrices 1. Operations: Let A = [aij ]mn and B = [bij ]mn , and c is a number, then 1. A = B if and only if aij = bij for all i, j. 2. Let C = [cij ]mn = A B, then cij = aij bij . 3. Let C = [cij ]mn = cA, then cij
School: Kennesaw
Course: LINEAR ALGEBRA I
2.2 Properties of Matrix Operations 1. Properties of Matrix Operations: Assuming that the sizes of the matrices are such that the indicated operations can be performed, then the following rules of matrix arithmetic are valid. A+B =B+A (Commutative law)
School: Kennesaw
Course: LINEAR ALGEBRA I
2.3 The Inverse of a Matrix 1. Inverses: If A is a square matrix, and if a matrix B of the same size can be found such that AB = BA = I, then A is said to be invertible and B is called an inverse of A, denoted by A1 . If no such matrix B exists, then A is
School: Kennesaw
Course: LINEAR ALGEBRA I
2.4 Elenmentary Matrices 1. Denition: An n n matrix is called an elenmentary matrix if it can be obtained from the n n identity matrix In by performing a single elementary row operation. 2. Row operation by matrix multiplication: Let E be the elementary m
School: Kennesaw
Course: ELEMENTARY STATISTICS
DataLabI HannahLeighCrawford Categorical Data: Choose 2 categorical variables a. Construct a contingency table b. Create a bar chart or a pie chart c. Discuss any unusual features revealed by the display of the variable. Describe patterns found. Hint:youm
School: Kennesaw
Course: LINEAR ALGEBRA I
MATH 3260/01 Linear Algebra Summer 2014 Instructor: Dr. Liancheng Wang Office: MS 223A E-mail: lwang5@kennesaw.edu Phone: 678-797-2139 Office Hours: 12:00-2:00 pm, MW, or by appointment Text: Elementary Linear Algebra, 7th edition, by Ron Larson, BROOKS/C
School: Kennesaw
MATH1112CollegeTrigonometry CourseSyllabusSpring2014 Instructor: MonicaDoriney Time/location:M5:00 6:15 PM and 6:30 7:45 PM Mathematics and Statistics - Room108 Email: mdoriney@kennesaw.edu Office/hours:Varioustimesavailable,byappointment CourseDescriptio
School: Kennesaw
Course: College Algebra
MATH 1111: College Algebra Fall Semester 2013 Instructor Lori Joseph CRN 83606 Days MWF Time 11:00 am 11:50 am Course Num/Sec MATH 1111/32 Location Science 213 A Course in the General Education Program Program Description: The General Education Program at
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
MATH 3310 Differential Equations, Spring 2010 Instructor: Dr. Liancheng Wang Office: Sci. & Math. 511 E-mail: lwang5@kennesaw.edu Phone: 678-797-2139 Office Hours: 2:00-3:15 pm, 5:00-6:00 pm, T TH, or by appointment Text: A First Course of Differential Eq
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 1 (Version 1) Solutions June 11, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 1 (Version 2) Solutions June 11, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 2 (Version 2) Solutions June 23, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 3 (Version 2) Solutions July 7, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use co
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 4 (Version 1) Solutions July 16, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 2 (Version 1) Solutions June 23, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 3 (Version 1) Solutions July 7, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use co
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 4 (Version 2) Solutions July 16, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: College Algebra
S. F. Ellermeyer MATH 1111 Exam 3 (Version 1) Solutions July 9, 2008 Name Instructions. You may not use any books or notes on this exam. You may use a calculator. You must show all of your work in order to receive credit! Write in complete sentences where
School: Kennesaw
Course: College Algebra
S. F. Ellermeyer MATH 1111 Exam 2 (Version 1) Solutions June 25, 2008 Name Instructions. You may not use any books or notes on this exam. You may use a calculator. You must show all of your work in order to receive credit! Write in complete sentences wher
School: Kennesaw
Course: College Algebra
S. F. Ellermeyer MATH 1111 Exam 1 (Version 2) Solutions June 11, 2008 Name Instructions. You may not use any books or notes on this exam. You may use a calculator. You must show all of your work in order to receive credit! Also, write in complete sentence
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 2 (Version 1) Solutions February 27, 2014 S. F. Ellermeyer Name Instructions for Problems 14: In each of Problems 14, a definite integral (with answer) is given. For each integral, show how to evaluate the integral (using the integration st
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 2 (Version 2) Solutions February 27, 2014 S. F. Ellermeyer Name Instructions for Problems 14: In each of Problems 14, a definite integral (with answer) is given. For each integral, show how to evaluate the integral (using the integration st
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 3 (Version 2) Solutions March 25, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 3 (Version 1) Solutions March 25, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 4 (Version 2) Solutions April 24, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 4 (Version 1) Solutions April 24, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 3 (Practice Version) Solutions March 25, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 1 (Version 1) Solutions January 23, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 1 (Version 2) Solutions January 23, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 3 (Practice Version) March 25, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doing
School: Kennesaw
MATH 2390 Exam 3 Solutions April 8, 2014 S. F. Ellermeyer Name Instructions. Remember that writing and correct use of notation are very important. Write in complete sentences. 1. Prove that if a, b and c are any integers such that a|b and b|c, then a|c. P
School: Kennesaw
MATH 2390 Exam 1 Solutions January 30, 2014 S. F. Ellermeyer Name Instructions. Remember that writing and correct use of notation are very important. Write in complete sentences. 1. Let the universal set be Z (the set of all integers). The set S x Z | |x|
School: Kennesaw
MATH 2390 Exam 2 Solutions March 4, 2014 S. F. Ellermeyer Name Instructions. Remember that writing and correct use of notation are very important. Write in complete sentences where appropriate. 1. Let P and Q be statements. Complete each of the following
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 2 (Version 2) Solutions September 11, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 2 (Version 1) Solutions September 11, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 5 (Version 2) Solutions October 9, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are do
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 5 (Version 1) Solutions October 9, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are do
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 8 (Version 2) Solutions November 18, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 6 (Version 2) Solutions October 21, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
MATH 2203 Exam 1 (Version 2) Solutions September 4, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
MATH 2203 Exam 1 (Version 1) Solutions September 4, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
MATH 2203 (Calculus III) - Quiz 1 Solutions August 26, 2014 S. F. Ellermeyer Name Instructions. This is a takehome quiz. It is due to be handed in to me by Friday, August 29 at noon. You may work on this quiz alone or in a group of one or two other people
School: Kennesaw
MATH 2203 (Calculus III) - Quiz 2 Solutions September 9, 2014 S. F. Ellermeyer Name Instructions. This is a takehome quiz. It is due to be handed in to me by Friday, September 12 at noon. You may work on this quiz alone or in a group of one or two other p
School: Kennesaw
Course: ELEMENTARY STATISTICS
Section 2.4 Graphs Can Be Misleading Objectives 1. 2. 3. Understand how improper positioning of the vertical scale can be misleading Understand the area principle for constructing statistical graphs Understand how three-dimensional graphs can be misleadin
School: Kennesaw
Course: CALCULUS
M A T H 1 190 M U L T I PL E C H O I C E C h o o s e t h e D e ter m in e N Qu i z 5 f r o m t h e gr a p h al t er nat i ve t h a t b e s t o n e h e t he r th e f u w n c tio n has an y a co m ple te s the bso l u te Na k p a m e s ta te m en t ex tr e
School: Kennesaw
Course: CALCULUS
No Nam 4 1 to 4 4 Qu i z 7 c a l c t 1l a t o r a l l o w e d D Ch o o s e t h e M W T I P L E C H O I CE f i n d th e m o st 6 al t er nat i ve t h a t b e s t h co m lll w B1U c ? \ cL p l et e s th e s t a t e n h 1e n t o r a n s w e r s t e o e n oy
School: Kennesaw
Course: CALCULUS
/ _ M U L H PL E CH O I CE D e te r m in e Nam Test T H 11 90 fr o Ch o o the gra ph m w ae the o al t er nat i ve t h a t b e e t n e h e t h e r t h e D1n c ti o n h aa an y a co m M e p lete s the b so l u t e st a te m e n RN L o r a n s w ers t e x t
School: Kennesaw
Course: CALCULUS
L Qu i z 6 M A T TI 1 190 No 1 Fin d the f u n c t io n t h e p o i n t P( 1 2 J c al c u l a to r a l lo w e d ho s e de Dv a t i v c i s w 2, 24) f (x ) ' (4 p o i n t s ) 4x + 2 = an d ( w ho s e g r a ph p a s s e s thr o u gh d f r o m a 12 i n c
School: Kennesaw
Course: CALCULUS
M A T H 1 190 C a l c u l u s Qu iz 1 M U L T I PL E C H O I C E C h o o s e t h e o n e 2 al t er nat i ve t h a t b e e t Nam co m Bh c n c e ple te s th e sta te m e n t o r a n sw e rs th e q u e et io n ti o n i s to b e a h i ft e d G iv t d i r e c
School: Kennesaw
Course: CALCULUS
E x t r a C r e d i t Qu i z P a r t 1 L o o k in g a y o u r T e st 3 at ) L is t t he b) On w a n sw e r pr o b lem hic h o t h e pr o b l e m t he f o l lo be r num f t h o s e l i st e d n um As h v j >o her n be r an o f an in g : y p r o b le m s p
School: Kennesaw
Course: CALCULUS
M A T H 1 19 0 1 Th e s lo o pe N f t h e l i n e t a n g e n t t o th e gr a ph ( ]) 2 If x y + y 2 + 4 0, " = f 3 2 + 5 ln y - > A 12 a t ( 2 , 1) i s 5 ' t o 5 12 2 Qu i z 4 : :t he n . 2 , the v a lu e o f is 2 ( +in ) ; 3 Fin d the a w If x - 9 9 s
School: Kennesaw
Course: CALCULUS
Te st 1 M A M 1 190 + ) A i 1m r B) e = 4 2 ) 20 2 ]; i n d t h e l i m i t , i f i t A o v D) 7 2 0 Lt 1 th e pr o b le m 3 ) I f : (x ) >r @ ' ' 4 u So l v A: h J ) /r al l f vw f id e 25 x . ex ) Do es 5x . 6 a n 37 . d = (x ( ) 1 ) 20\ 2 $ n o ) . 23
School: Kennesaw
Course: CALCULUS
(3 4 8 1 TD Qu l z M A T H I 19 0 Si 1n p 1i f y a l l F in d N 3 a n sw e r s a s m u c h a s 8 am e p o s sib l e n x e v ' c ( y 0 s . vY j u , l/ oj a , y - (2 x 3 Scanned by CamScanner ' )? , - s in 2 (3 x 4 ) . . (A ) Zr (D ) ir ' 2T e t b ( 3 ' e
School: Kennesaw
Course: CALCULUS
MAm 1 19 O N. . j . Ala B h (B r m M U L T I P L E C1 I OI C C i r c l e t h e l e t t e r 21 f th e r sc t r o o n e al t er nat i ve t h a t b e s t " ' 5 , - 13 t7 o L c c L t t B t7 . ds ; B c o t t + 13 " - pletes the co m B + co t 7_ sc et a t e m e
School: Kennesaw
Course: CALCULUS
Scanned by CamScanner 3 M u l tiple C ho ic e : R e m f( ) x x = 3 k ! (2 p o i n t s ) c t io n Sh o w t h a t t h e D m w or 4 sho w be r t o em e ithe r is ev er 9 ! ( F in d 5 a eac 1i m X (2 h lim it 2 2 + x 7x + r p o in ts ea ch ) Sh o w y o
School: Kennesaw
Course: LINEAR ALGEBRA I
MATH 3260/01 Linear Algebra Summer 2014 Instructor: Dr. Liancheng Wang Office: MS 223A E-mail: lwang5@kennesaw.edu Phone: 678-797-2139 Office Hours: 12:00-2:00 pm, MW, or by appointment Text: Elementary Linear Algebra, 7th edition, by Ron Larson, BROOKS/C
School: Kennesaw
Course: LINEAR ALGEBRA I
1.2 Gaussian and Gauss-Jordan Elimination 1. Denition: A matrix is a rectangular array of numbers. The numbers in the array are called the entries in the matrix. A general m n matrix can be written as A= a11 a12 a1n a21 a22 a2n . . . . . . . . . am1 am2 a
School: Kennesaw
Course: LINEAR ALGEBRA I
Chapter 1. Systems of Linear Equations 1.1 Introduction to Systems of Linear Equations 1. Linear Equations. Def: A linear equation in n variables x1 , x2 , ., xn is an equation that can be written in the form a1 x1 + a2 x2 + + an xn = b where b and the co
School: Kennesaw
Course: LINEAR ALGEBRA I
Chapter 2. Matrices 2.1 Operations with Matrices 1. Operations: Let A = [aij ]mn and B = [bij ]mn , and c is a number, then 1. A = B if and only if aij = bij for all i, j. 2. Let C = [cij ]mn = A B, then cij = aij bij . 3. Let C = [cij ]mn = cA, then cij
School: Kennesaw
Course: LINEAR ALGEBRA I
2.2 Properties of Matrix Operations 1. Properties of Matrix Operations: Assuming that the sizes of the matrices are such that the indicated operations can be performed, then the following rules of matrix arithmetic are valid. A+B =B+A (Commutative law)
School: Kennesaw
Course: LINEAR ALGEBRA I
2.3 The Inverse of a Matrix 1. Inverses: If A is a square matrix, and if a matrix B of the same size can be found such that AB = BA = I, then A is said to be invertible and B is called an inverse of A, denoted by A1 . If no such matrix B exists, then A is
School: Kennesaw
Course: LINEAR ALGEBRA I
2.4 Elenmentary Matrices 1. Denition: An n n matrix is called an elenmentary matrix if it can be obtained from the n n identity matrix In by performing a single elementary row operation. 2. Row operation by matrix multiplication: Let E be the elementary m
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 3 Determinants 3.1 The Determinant of a Matrix 1. The determinant of a 2 2 matrix. The determinant of a 2 2 matrix a b A= c d is given det(A) = |A| = ad bc. Def: Minors and Cofactors. Let A = (aij )nn be an matrix, then the minor of entry aij is denot
School: Kennesaw
Course: LINEAR ALGEBRA I
3.2 Determinants and Elementary Operations Theorem: Let A = (aij )nn be an matrix. If a multiple of one row (column) of A is added to another row (column) to produce a matrix B, then det(A)=det(B). If two rows (columns) of A are interchanged to produce
School: Kennesaw
Course: LINEAR ALGEBRA I
3.3 Properties of the Determinants Theorem: If A and B are nn matrices, then det(AB) = (det(A)(det(B) Theorem: If A is an n n matrix and c is a scalar, then det(cA) = cn det(A). Theorem: A square matrix A is invertible if and only if detA = 0. Theorem: If
School: Kennesaw
Course: LINEAR ALGEBRA I
3.4 Applications the Determinants 1. The Adjoint of a Matrix: cofactor of aij , then the matrix C11 C 21 A= . . . Cn1 If A is an n n matrix and Cij is the C12 C1n C22 C2n . . . . . . Cn2 Cnn is called the matrix of cofactors from A. The transpose of thi
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 4 Vector Spaces 4.1 Vectors in Rn 1. Vectors in the plane. A vector in the plane is represented geometrically by a directed line segment whose initial point is the origin and whose terminal point is the point (x1 , x2 ). This vector is represented by
School: Kennesaw
Course: CALCULUS
! " # $ $ % & % % $ ' % # $ $ $ ' () * + , $ - . -$ . $ -. $ / / 0 ! $ $ / / / $ / $
School: Kennesaw
Course: CALCULUS
! " #$ % ! "& % % % % ' (% & ) ! #$ # * $ % % !" ' #& $ !" + #$, ) !" ! & &% % ' !" " ! " " & %" ! %" -% " " % ./ 2 y 1 -3 -2 -1 0 -1 -2 1 x 2 3 " 0.2 1.2 0 0.1 x 1.3 1.4 -0.2 -0.1 0 0.1 x 0.2 -0.2 -0.1 -0.2 " " . ( " " " " % " " % . " +& " "
School: Kennesaw
Course: CALCULUS
! "# # $ # # 20 15 10 5 -4 -3 -2 -1 0 -5 -10 1 2 x 3 4 % & '( & ! # $ # )" '( * # # & '( !
School: Kennesaw
James Garfields Proof of the Pythagorean Theorem College Trigonometry (MATH 1112) Kennesaw State University The Pythagorean Theorem states that for any right triangle with sides of length a and b and hypotenuse of length c, it is true that . There are man
School: Kennesaw
Course: Elemenary Statistics
B&W CONFIRMINGS 58 Chapter 2 Frequency Distributions and Graphs Exercises 23 1. Do Students Need Summer Development? For 108 randomly selected college applicants, the following frequency distribution for entrance exam scores was obtained. Construct a hist
School: Kennesaw
Course: College Algebra
Math 1111 Fall 2013 Sample Practice Problems This is not an all inclusive list of problems that might be on the test. In addition to these problems, please review your notes, the homework and the pretest problems in MML. Given the line 9x-3y = 12, write i
School: Kennesaw
Course: College Algebra
Math 1111 Fully answer all questions on this sheet or on your own paper, using graph paper when necessary. Make sure your name is on all pages and that problem numbers are clearly marked. There are extra graphs at the end of the test. For questions 1-4, s
School: Kennesaw
Course: College Algebra
Rational Expressions Section R.6 (p. 35-43) MATH 1111 A rational expression is the quotient of two polynomials. Skills Determine the domain of a rational expression. Simplify rational expressions. The Domain of Rational Expressions Multiply, divide, add,
School: Kennesaw
Course: College Algebra
The Basics of Equation Solving Section R.5 (p. 30-34) MATH 1111 An equation is a statement that two expressions are equal. Skills Solve linear equations. Solve quadratic equations. Solve a formula for a given variable. To solve an equation in one variable
School: Kennesaw
Chapter R: Functions, Graphs, and Models_ Section Objectives: Defining a function and its domain/range Linear functions Quadratic functions The graph of an equation is a drawing that represents all ordered pairs that are solutions of the equation. Exam
School: Kennesaw
Section 5.2: Applications of Models Section Objectives: Perform computations involving interest compounded continuously and continuous money flow. Calculate the total consumption of a natural resource. Find the present value of an investment. Growth Fo
School: Kennesaw
Sec 5.1: An Econ Application: Consumer & Producer Surplus Section Objectives: Given demand and supply functions, find the consumer surplus and the producer surplus at the equilibrium point. DEFINITION Suppose that consumer surplus describes the demand fu
School: Kennesaw
Section 4.4: Properties of Definite Integrals Section Objectives: Use the properties of definite integrals to find the area between curves. Solve applied problems involving definite integrals. Determine the average value of a function. THEOREM 5 For Fo
School: Kennesaw
Section 4.3: Area and Definite Integrals Section Objectives: Find the area under a curve over a given closed interval. Evaluate a definite integral. Interpret an area below the horizontal axis. Solve applied problems involving definite integrals. DEFI
School: Kennesaw
Section 4.2: Antiderivatives as Areas Section Objectives: Find the area under a graph to solve real-world problems Use rectangles to approximate the area under a graph. Example 1: A vehicle travels at 50 mi/hr for 2 hours. How far has the vehicle travel
School: Kennesaw
Section 4.1: Antidifferentiation Section Objectives: Find an antiderivative of a function. Evaluate indefinite integrals using the basic integration formulas. Use initial conditions, or boundary conditions, to determine an antiderivative. THEOREM 1 The
School: Kennesaw
Section 3.6: An Economics Application: Elasticity of Demand Section Objectives: Find the elasticity of a demand function. Find the maximum of a total-revenue function. Characterize demand in terms of elasticity. DEFINITION The elasticity of demand () i
School: Kennesaw
Section 3.4: Applications: Decay Section Objectives: Find a function that satisfies Convert between decay rate and half-life. Solve applied problems involving exponential decay. The equation , where , shows to be decreasing as a function of time, and t
School: Kennesaw
Section 3.3: Uninhibited and Limited Growth Models Section Objectives: Find functions that satisfy Convert between growth rate and doubling time. Solve application problems using exponential growth and limited growth models. RECALL Example: Differentia
School: Kennesaw
Section 3.2: Logarithmic Functions Section Objectives: Convert between logarithmic and exponential equations. Solve exponential equations. Solve problems involving exponential and logarithmic functions. Differentiate functions involving natural logari
School: Kennesaw
Section 3.1: Exponential Functions Section Objectives: Graph exponential functions. Differentiate exponential functions. DEFINITION An exponential function Where is given by is any real number, () and . The number Example 1: Graph ( ) DEFINITION: ( We c
School: Kennesaw
Section 2.6: Marginals and Differentials Section Objectives: Find marginal cost, revenue, and profit. Find and Use differentials for approximations. DEFINITION Let and represent, respectively, the total cost, revenue, and profit from the production and
School: Kennesaw
Section 2.5: Max-Min Problems; Business & Econ Applications Section Objectives: Solve maximum and minimum problems using calculus. A Strategy for Solving Maximum-Minimum Problems: 1. Read the problem carefully. If relevant, make a drawing. 2. Make a list
School: Kennesaw
Section 2.4: Using Derivatives to Find Absolute Max & Min Section Objectives: Find absolute extrema using Maximum-Minimum Principle 1. Find absolute extrema using Maximum-Minimum Principle 2. DEFINITION: Suppose that is an is an is a function with domai
School: Kennesaw
Sec. 2.3: Graph Sketching: Asymptotes & Rational Functions Section Objectives: Find limits involving infinity. Determine the asymptotes of a functions graph. Graph rational functions. DEFINITION: A rational function is a function that can be described
School: Kennesaw
Section 2.2: Using Second Derivatives to Find Max & Min Values and Sketch Graphs Section Objectives: Find the relative extrema of a function using the Second-Derivative Test. Sketch the graph of a continuous function. Suppose that is a function whose de
School: Kennesaw
Section 2.1: Using Derivatives to Find Max & Min Values & Sketch Graphs Section Objectives: Find relative extrema of a continuous function using the First-Derivative Test. Sketch graphs of continuous functions. A function is increasing over if, for ever
School: Kennesaw
Section 1.8: Higher Order Derivatives Section Objectives: Find derivatives of higher order. Given a formula for distance, find velocity and acceleration. Higher Order Derivatives () Consider the function given by . Its derivative, ( ) is given by () . T
School: Kennesaw
Section 1.7: The Chain Rule Section Objectives: Find the composition of two functions. Differentiate using the Extended Power Rule or the Chain Rule. THEOREM 7: The Extended Power Rule Suppose that is a differentiable function of . Then, for any real nu
School: Kennesaw
Section 1.6: Differentiation Techniques: The Product and Quotient Rules Section Objectives: Differentiate using the Product and the Quotient Rules. Use the Quotient Rule to differentiate the average cost, revenue, and profit functions. THEOREM 5: The Pr
School: Kennesaw
Section 1.5: Differentiation Techniques: The Power & SumDifference Rules Section Objectives: Differentiate using the Power Rule or the Sum-Difference Rule. Differentiate a constant or a constant times a function. Determine points at which a tangent lin
School: Kennesaw
Sec 1.4: Differentiation Using Limits of Difference Quotients Section Objectives: Find derivatives and values of derivatives Find equations of tangent lines The slope of the tangent line at is This limit is also the For a function function of its define
School: Kennesaw
Section 1.3: Average Rates of Change _ Section Objectives: Compute an average rate of change. Find a simplified difference quotient. An The average rate of change of is the slope of a line between with respect to , as changes from ratio of the change in
School: Kennesaw
Section 1.2: Algebraic Limits and Continuity_ Section Objectives: Develop and use the Limit Principles to calculate limits. Determine whether a function is continuous at a point. LIMIT PROPERTIES () If and we have the following: () L1 The limit of a con
School: Kennesaw
Section 1.1: Limits: A Numerical and Graphical Approach _ Section Objective: Find limits of functions, if they exist, using numerical or graphical methods. DEFINITON: () The of a function , as approaches , is written This means that as the values of appr
School: Kennesaw
Course: Calculus 1
Review of Test 1 This test covers limit, continuity, differentiation, and some applications of differentiation. Review Sections 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, and 2.7. A Compute limits (rules, the squeeze theorem, and limits i
School: Kennesaw
Course: Calculus 1
Review for Final Sections: 1.3, 1.4, 1.5, 1.6, 1.7, 1.8 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12, 2.13 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 4.1, 4.2, 4.3, 4.4., 4.5, 4.6, 4.7 Limits and continuity Derivatives Applications of derivatives
School: Kennesaw
Course: ELEMENTARY STATISTICS
Chapter 2 Describing distributions with numbers Measure of center The measure you use depends on the shape of the data. If the data is mound shaped and symmetric we use the mean. X= Add up the data value = x/n Total # of data values Advantage - Familiar -
School: Kennesaw
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Chapter 7. The laplace Transform 7.2 Inverse Transforms and Transforms of Derivatives 1. Inverse Transforms: Let F (s) be a Laplace transform of a function f , i.e. F (s) = Lcfw_f (t), we then say f (t) is the inverse Laplace transform of F (s) and write
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Chapter 7. The laplace Transform 7.1 Denition of the Laplace Transform 1. Review of Integral with Innite Intervals: Let f be a function dened on [a, ), then a f (t)dt = lim b a b f (t)dt provided that the limit exists and nite. 2. Laplace Transform: Let
School: Kennesaw
Course: CALCULUS
Chelsea Spear MATH 1190 Castle 24 January 2008 Many mathematical concepts are intertwined throughout our everyday lives. Whether calculating the tip for a waiter at a fancy restaurant, managing the checkbook, or just meeting the challenge of learning
School: Kennesaw
Course: Calculus 1
Lecture 8, September 14, 2011 1. 2. 3. Answer questions Quiz 3 Sections 2.5 and 2.6 2.5 Derivatives of Trigonometric Functions Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a The proof is on page 103. s o n E d u c a C o p y i g h 2 0
School: Kennesaw
Course: Calculus 1
Lecture 24 , November 28, 2011 Task 1: questions Task 2: Sections 4.6 and 4.7 C o p y i g h 2 0 0 7 P e a 4.6 Indefinite Integrals and the Substitution Rule s o n E d u c a Let us first work on a simple problem Example 1 on page 287. C o p y i g h 2 0 0
School: Kennesaw
Course: Calculus 1
Lecture 23, November 21 2011 Task 1: questions Task 2: A quiz Task 3: Sections 4.5 and 4.6 4.5 The Fundamental Theorem of Calculus Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u
School: Kennesaw
Course: Calculus 1
Lecture 22, November 16, 2011 Task 1: questions Task 2: A quiz Task 3: Sections 4.4 and 4.5 4.4 The Definite Integral Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a This int
School: Kennesaw
Course: Calculus 1
Lecture 21, November 14, 2011 Task 1: Sections 4.3 and 4.4 4.3 Sigma Notation and Limits of Finite Sums Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7
School: Kennesaw
Course: Calculus 1
Lecture 20, November 9, 2011 Task 1: Questions? Task 2: A Quiz Task 3: Sections 4.1 and 4.2 Chapter 4 Integration Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a 4.1 Antiderivatives s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E
School: Kennesaw
Course: Calculus 1
Lecture 19, November 7, 2011 3.6 Applied Optimization 3.7 Indeterminate Forms and L' Hopital's Rule Copyright 2007 Pearson Education, Inc. 3.6 Copyright 2007 Pearson Education, Inc. C o p y i g h Work on Example 1on page 209 2 0 0 7 P e a s o n E d u c a
School: Kennesaw
Course: Calculus 1
Lecture 18, November 2, 2011 Task 1: Section 3.5 Task 2: Section 3.6 Copyright 2007 Pearson Education, Inc. C o p y i g h Section 3.5 Parametrizations of plane curves 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g
School: Kennesaw
Course: Calculus 1
Lecture 17, October 24, 2011 Task 1: Section 3.4 Task 2: Section 3.5 Copyright 2007 Pearson Education, Inc. 3.4 Concavity and Curve Sketching Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a
School: Kennesaw
Course: Calculus 1
Lecture 16, October 19, 2011 Task 1: Section 3.3 Monotonic Functions and the First Derivative Test Task 2: Section 3.4 Concavity and Curve Sketching Inc. Copyright 2007 Pearson Education, 3.3 Monotonic Functions and the First Derivative Test Copyright 200
School: Kennesaw
Course: Calculus 1
Lecture 15, October 17, 2011 Section 3.2 The Mean Value Theorem Copyright 2007 Pearson Education, Inc. C o p y i g h Review 2 0 0 7 P e a This is a very important result. Its proof is on page 178-179. s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E
School: Kennesaw
Course: Calculus 1
Lecture 14, October 12, 2011 Task 1: any questions on HW Task 2: a quiz Task 3: Section 3.1 3.1 Extreme Values of Functions Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C
School: Kennesaw
Course: Calculus 1
Lecture 13, October 10, 2011 Task 1: any questions on HW Task 2: Finish up Section 1.12 2.12 Related Rates Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0
School: Kennesaw
Course: Calculus 1
Lecture 12, October 5, 2011 Task 1: questions Task 2: Quiz Task 3: Section 2.11 Section 2.11 Inverse Trigonometric Functions Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C
School: Kennesaw
Course: Calculus 1
Lecture 11, October 3, 2011 Task 1: Sections 2.9-2.10 2.9 - 2.10 Derivatives of Inverse Functions and Logarithms Copyright 2007 Pearson Education, Inc. C o p y i g h Inverses When we go from an output of a function back to its input or inputs, we get an i
School: Kennesaw
Course: Calculus 1
Lecture 10, September 28, 2011 Task 1: Discuss Test 1 Task 2: Section 2.8 2.8 Implicit Differentiation Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a Work on Example 1 on page 121 C o p y i g h Work on Example 2 on pag
School: Kennesaw
Course: Calculus 1
Lecture 9, September 19, 2011 Task 1: Any questions? Task 2: Section 2.7 2.7 The Chain Rule Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n
School: Kennesaw
Course: Calculus 1
Lecture 7, September 12, 2011 1. 2. Answer questions Section 2.3 and 2.4 2.3 Differentiation Rules for Polynomials, Exponentials, Products, and Quotients Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2
School: Kennesaw
Course: Calculus 1
Lecture 6, September 7, 2011 2.1 Tangents and Derivatives at a Point Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h Work on Example 1 on page 72 2 0 0 7 P e a
School: Kennesaw
Course: Calculus 1
Lecture 5, August 31, 2011 C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h 2 0 0 7 P e a s o n E d u c a Wor
School: Kennesaw
Course: Calculus 1
Lecture 4, Fall 2011 (Sections 1.6 and 1.7) Task 1: a quiz Task 2: Finish up Section 1.6 Task 3: Section 1.7 An important limit (Section 1.6) Copyright 2007 Pearson Education, Inc. C o p y i g h 2 0 0 7 P e a s o n E d u c a C o p y i g h An important li
School: Kennesaw
Course: Calculus 1
Lecture 3, Fall 2011 (Sections 1.5, 1.6) 1.5 The Precise Definition of a Limit Copyright 2007 Pearson Education, Inc. C o p y i g h Work on Example 1 on page 34. Let f(x)=2x-1. We will work on |f(x)-7|<2 to get |x-4|<1. 2 0 0 7 P e a s o n E d u c a C o
School: Kennesaw
Course: Calculus 1
Lecture 2, August 22, 2011 Copyright 2007 Pearson Education, Inc. 1.4 Limit of a Function and Limits Laws Copyright 2007 Pearson Education, Inc. Limit of a function and limit laws Let f(x) be defined on an open interval about a, except possibly at a itsel
School: Kennesaw
Course: Calculus 1
Math 1190/01 Welcome to my class! Lecture 1, August 17, 2011 Copyright 2007 Pearson Education, Inc. 1.3 Rates of Change and Tangents to Curves Copyright 2007 Pearson Education, Inc. It assumes negligible air resistance to slow the object down, and that gr
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 1 (Version 1) Solutions June 11, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 1 (Version 2) Solutions June 11, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 2 (Version 2) Solutions June 23, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 3 (Version 2) Solutions July 7, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use co
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 4 (Version 1) Solutions July 16, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 2 (Version 1) Solutions June 23, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 3 (Version 1) Solutions July 7, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use co
School: Kennesaw
Course: LINEAR ALGEBRA I
S. F. Ellermeyer MATH 3260 Exam 4 (Version 2) Solutions July 16, 2008 Name Instructions. Remember to include all important details of your work. You will not get full credit (or perhaps even any partial credit) if I see gaps in your reasoning. Also, use c
School: Kennesaw
Course: College Algebra
S. F. Ellermeyer MATH 1111 Exam 3 (Version 1) Solutions July 9, 2008 Name Instructions. You may not use any books or notes on this exam. You may use a calculator. You must show all of your work in order to receive credit! Write in complete sentences where
School: Kennesaw
Course: College Algebra
S. F. Ellermeyer MATH 1111 Exam 2 (Version 1) Solutions June 25, 2008 Name Instructions. You may not use any books or notes on this exam. You may use a calculator. You must show all of your work in order to receive credit! Write in complete sentences wher
School: Kennesaw
Course: College Algebra
S. F. Ellermeyer MATH 1111 Exam 1 (Version 2) Solutions June 11, 2008 Name Instructions. You may not use any books or notes on this exam. You may use a calculator. You must show all of your work in order to receive credit! Also, write in complete sentence
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 2 (Version 1) Solutions February 27, 2014 S. F. Ellermeyer Name Instructions for Problems 14: In each of Problems 14, a definite integral (with answer) is given. For each integral, show how to evaluate the integral (using the integration st
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 2 (Version 2) Solutions February 27, 2014 S. F. Ellermeyer Name Instructions for Problems 14: In each of Problems 14, a definite integral (with answer) is given. For each integral, show how to evaluate the integral (using the integration st
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 3 (Version 2) Solutions March 25, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 3 (Version 1) Solutions March 25, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 4 (Version 2) Solutions April 24, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 4 (Version 1) Solutions April 24, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doi
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 3 (Practice Version) Solutions March 25, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 1 (Version 1) Solutions January 23, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 1 (Version 2) Solutions January 23, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
Course: CALCULUS 2
MATH 2202 Exam 3 (Practice Version) March 25, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doing
School: Kennesaw
MATH 2390 Exam 3 Solutions April 8, 2014 S. F. Ellermeyer Name Instructions. Remember that writing and correct use of notation are very important. Write in complete sentences. 1. Prove that if a, b and c are any integers such that a|b and b|c, then a|c. P
School: Kennesaw
MATH 2390 Exam 1 Solutions January 30, 2014 S. F. Ellermeyer Name Instructions. Remember that writing and correct use of notation are very important. Write in complete sentences. 1. Let the universal set be Z (the set of all integers). The set S x Z | |x|
School: Kennesaw
MATH 2390 Exam 2 Solutions March 4, 2014 S. F. Ellermeyer Name Instructions. Remember that writing and correct use of notation are very important. Write in complete sentences where appropriate. 1. Let P and Q be statements. Complete each of the following
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 2 (Version 2) Solutions September 11, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 2 (Version 1) Solutions September 11, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 5 (Version 2) Solutions October 9, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are do
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 5 (Version 1) Solutions October 9, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are do
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 8 (Version 2) Solutions November 18, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
Course: Calculus III
MATH 2203 Exam 6 (Version 2) Solutions October 21, 2013 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
MATH 2203 Exam 1 (Version 2) Solutions September 4, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
MATH 2203 Exam 1 (Version 1) Solutions September 4, 2014 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
MATH 2203 (Calculus III) - Quiz 1 Solutions August 26, 2014 S. F. Ellermeyer Name Instructions. This is a takehome quiz. It is due to be handed in to me by Friday, August 29 at noon. You may work on this quiz alone or in a group of one or two other people
School: Kennesaw
MATH 2203 (Calculus III) - Quiz 2 Solutions September 9, 2014 S. F. Ellermeyer Name Instructions. This is a takehome quiz. It is due to be handed in to me by Friday, September 12 at noon. You may work on this quiz alone or in a group of one or two other p
School: Kennesaw
Course: CALCULUS
M A T H 1 190 M U L T I PL E C H O I C E C h o o s e t h e D e ter m in e N Qu i z 5 f r o m t h e gr a p h al t er nat i ve t h a t b e s t o n e h e t he r th e f u w n c tio n has an y a co m ple te s the bso l u te Na k p a m e s ta te m en t ex tr e
School: Kennesaw
Course: CALCULUS
No Nam 4 1 to 4 4 Qu i z 7 c a l c t 1l a t o r a l l o w e d D Ch o o s e t h e M W T I P L E C H O I CE f i n d th e m o st 6 al t er nat i ve t h a t b e s t h co m lll w B1U c ? \ cL p l et e s th e s t a t e n h 1e n t o r a n s w e r s t e o e n oy
School: Kennesaw
Course: CALCULUS
/ _ M U L H PL E CH O I CE D e te r m in e Nam Test T H 11 90 fr o Ch o o the gra ph m w ae the o al t er nat i ve t h a t b e e t n e h e t h e r t h e D1n c ti o n h aa an y a co m M e p lete s the b so l u t e st a te m e n RN L o r a n s w ers t e x t
School: Kennesaw
Course: CALCULUS
L Qu i z 6 M A T TI 1 190 No 1 Fin d the f u n c t io n t h e p o i n t P( 1 2 J c al c u l a to r a l lo w e d ho s e de Dv a t i v c i s w 2, 24) f (x ) ' (4 p o i n t s ) 4x + 2 = an d ( w ho s e g r a ph p a s s e s thr o u gh d f r o m a 12 i n c
School: Kennesaw
Course: CALCULUS
M A T H 1 190 C a l c u l u s Qu iz 1 M U L T I PL E C H O I C E C h o o s e t h e o n e 2 al t er nat i ve t h a t b e e t Nam co m Bh c n c e ple te s th e sta te m e n t o r a n sw e rs th e q u e et io n ti o n i s to b e a h i ft e d G iv t d i r e c
School: Kennesaw
Course: CALCULUS
E x t r a C r e d i t Qu i z P a r t 1 L o o k in g a y o u r T e st 3 at ) L is t t he b) On w a n sw e r pr o b lem hic h o t h e pr o b l e m t he f o l lo be r num f t h o s e l i st e d n um As h v j >o her n be r an o f an in g : y p r o b le m s p
School: Kennesaw
Course: CALCULUS
M A T H 1 19 0 1 Th e s lo o pe N f t h e l i n e t a n g e n t t o th e gr a ph ( ]) 2 If x y + y 2 + 4 0, " = f 3 2 + 5 ln y - > A 12 a t ( 2 , 1) i s 5 ' t o 5 12 2 Qu i z 4 : :t he n . 2 , the v a lu e o f is 2 ( +in ) ; 3 Fin d the a w If x - 9 9 s
School: Kennesaw
Course: CALCULUS
Te st 1 M A M 1 190 + ) A i 1m r B) e = 4 2 ) 20 2 ]; i n d t h e l i m i t , i f i t A o v D) 7 2 0 Lt 1 th e pr o b le m 3 ) I f : (x ) >r @ ' ' 4 u So l v A: h J ) /r al l f vw f id e 25 x . ex ) Do es 5x . 6 a n 37 . d = (x ( ) 1 ) 20\ 2 $ n o ) . 23
School: Kennesaw
Course: CALCULUS
(3 4 8 1 TD Qu l z M A T H I 19 0 Si 1n p 1i f y a l l F in d N 3 a n sw e r s a s m u c h a s 8 am e p o s sib l e n x e v ' c ( y 0 s . vY j u , l/ oj a , y - (2 x 3 Scanned by CamScanner ' )? , - s in 2 (3 x 4 ) . . (A ) Zr (D ) ir ' 2T e t b ( 3 ' e
School: Kennesaw
Course: CALCULUS
MAm 1 19 O N. . j . Ala B h (B r m M U L T I P L E C1 I OI C C i r c l e t h e l e t t e r 21 f th e r sc t r o o n e al t er nat i ve t h a t b e s t " ' 5 , - 13 t7 o L c c L t t B t7 . ds ; B c o t t + 13 " - pletes the co m B + co t 7_ sc et a t e m e
School: Kennesaw
Course: CALCULUS
Scanned by CamScanner 3 M u l tiple C ho ic e : R e m f( ) x x = 3 k ! (2 p o i n t s ) c t io n Sh o w t h a t t h e D m w or 4 sho w be r t o em e ithe r is ev er 9 ! ( F in d 5 a eac 1i m X (2 h lim it 2 2 + x 7x + r p o in ts ea ch ) Sh o w y o
School: Kennesaw
Course: CALCULUS
S. F. Ellermeyer MATH 1190 Exam 1 (Version 1) Solutions September 7, 2007 Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 3 (Version 2) Solutions October 31, 2007 Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 4 (Version 1) Solutions November 28, 2007 Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 2 (Version 2) Solutions September 28, 2007 Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 4 (Version 1) Solutions April 5, 2004 Name Instructions. This exam contains six problems, but only ve of them will be graded. You may choose any ve to do. Please write DONT GRADE on the one that you dont want me to grade. I
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 1 January 28, 2004 Answers and Solutions Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are d
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 2 (Version 2) Solutions February 18, 2004 Name 1. The position of a particle that is moving in a straight line is given by the function s = 2t3 t + 1 where t is measured in seconds and s is measured in meters. Find the velo
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 3 (Version 2) Solutions March 15, 2004 Name Instructions. This exam contains six problems, but only ve of them will be graded. You may choose any ve to do. Please write DONT GRADE on the one that you dont want me to grade.
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 1 (Version 2) January 28, 2004 Answers and Solutions Name Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know wh
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 3 (Version 1) Solutions March 15, 2004 Name Instructions. This exam contains six problems, but only ve of them will be graded. You may choose any ve to do. Please write DONT GRADE on the one that you dont want me to grade.
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 4 (Version 2) Solutions April 5, 2004 Name Instructions. This exam contains six problems, but only ve of them will be graded. You may choose any ve to do. Please write DONT GRADE on the one that you dont want me to grade. I
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 5 (Version 2) Solutions April 23, 2004 Name Instructions. This exam contains six problems, but only ve of them will be graded. You may choose any ve to do. Please write DONT GRADE on the one that you dont want me to grade.
School: Kennesaw
Course: Calculus I
MATH 1190 Final Exam 4 (Version 1) Solutions April 30, 2004 S. F. Ellermeyer Name Instructions. This exam contains twelve problems, but only ten of them will be graded. You may choose any ten to do. Please write DONT GRADE on the two that you dont want me
School: Kennesaw
Course: Calculus I
S. F. Ellermeyer MATH 1190 Exam 5 (Version 1) Solutions April 23, 2004 Name Instructions. This exam contains six problems, but only ve of them will be graded. You may choose any ve to do. Please write DONT GRADE on the one that you dont want me to grade.
School: Kennesaw
Course: LINEAR ALGEBRA I
1.2 Gaussian and Gauss-Jordan Elimination 1. Denition: A matrix is a rectangular array of numbers. The numbers in the array are called the entries in the matrix. A general m n matrix can be written as A= a11 a12 a1n a21 a22 a2n . . . . . . . . . am1 am2 a
School: Kennesaw
Course: LINEAR ALGEBRA I
Chapter 1. Systems of Linear Equations 1.1 Introduction to Systems of Linear Equations 1. Linear Equations. Def: A linear equation in n variables x1 , x2 , ., xn is an equation that can be written in the form a1 x1 + a2 x2 + + an xn = b where b and the co
School: Kennesaw
Course: LINEAR ALGEBRA I
Chapter 2. Matrices 2.1 Operations with Matrices 1. Operations: Let A = [aij ]mn and B = [bij ]mn , and c is a number, then 1. A = B if and only if aij = bij for all i, j. 2. Let C = [cij ]mn = A B, then cij = aij bij . 3. Let C = [cij ]mn = cA, then cij
School: Kennesaw
Course: LINEAR ALGEBRA I
2.2 Properties of Matrix Operations 1. Properties of Matrix Operations: Assuming that the sizes of the matrices are such that the indicated operations can be performed, then the following rules of matrix arithmetic are valid. A+B =B+A (Commutative law)
School: Kennesaw
Course: LINEAR ALGEBRA I
2.3 The Inverse of a Matrix 1. Inverses: If A is a square matrix, and if a matrix B of the same size can be found such that AB = BA = I, then A is said to be invertible and B is called an inverse of A, denoted by A1 . If no such matrix B exists, then A is
School: Kennesaw
Course: LINEAR ALGEBRA I
2.4 Elenmentary Matrices 1. Denition: An n n matrix is called an elenmentary matrix if it can be obtained from the n n identity matrix In by performing a single elementary row operation. 2. Row operation by matrix multiplication: Let E be the elementary m
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 3 Determinants 3.1 The Determinant of a Matrix 1. The determinant of a 2 2 matrix. The determinant of a 2 2 matrix a b A= c d is given det(A) = |A| = ad bc. Def: Minors and Cofactors. Let A = (aij )nn be an matrix, then the minor of entry aij is denot
School: Kennesaw
Course: LINEAR ALGEBRA I
3.2 Determinants and Elementary Operations Theorem: Let A = (aij )nn be an matrix. If a multiple of one row (column) of A is added to another row (column) to produce a matrix B, then det(A)=det(B). If two rows (columns) of A are interchanged to produce
School: Kennesaw
Course: LINEAR ALGEBRA I
3.3 Properties of the Determinants Theorem: If A and B are nn matrices, then det(AB) = (det(A)(det(B) Theorem: If A is an n n matrix and c is a scalar, then det(cA) = cn det(A). Theorem: A square matrix A is invertible if and only if detA = 0. Theorem: If
School: Kennesaw
Course: LINEAR ALGEBRA I
3.4 Applications the Determinants 1. The Adjoint of a Matrix: cofactor of aij , then the matrix C11 C 21 A= . . . Cn1 If A is an n n matrix and Cij is the C12 C1n C22 C2n . . . . . . Cn2 Cnn is called the matrix of cofactors from A. The transpose of thi
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 4 Vector Spaces 4.1 Vectors in Rn 1. Vectors in the plane. A vector in the plane is represented geometrically by a directed line segment whose initial point is the origin and whose terminal point is the point (x1 , x2 ). This vector is represented by
School: Kennesaw
Course: LINEAR ALGEBRA I
4.2 Vector Spaces 1. Real Vector Spaces. Def: Let V be a set on which two operations (vector addition and scalar multiplication) are dened. If the following axioms are satised by all objects u, v and w in V and all scalars k and m, then we call V a vector
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 4 General Vector Spaces 4.7 Coordinates and Change of Basis 1. Coordinates Relative to a Basis: If B = cfw_u1 , u2 , , un is an ordered basis for a vector space V , and x = c1 u1 + c2 u2 + + cn un is the expression for a vector x in terms of the basi
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 4 General Vector Spaces 4.6 Rank of a Matrix and systems of Linear Equations Def: For an m n matrix A= a11 a12 a1n a21 a22 a2n . . . . . . . . . am1 am2 amn the vectors r1 = [a11 a12 a1n ] r2 = [a21 a22 a2n ] . . . rm = [am1 am2 amn ] in Rn that ar
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 6 Linear Transformations 6.1 Introduction to Linear Transformations 1. Def: If V and W are vector spaces, and if T is a function with domain V and codomain W , then we say f is a transformation from V to W or that f maps V to W , which we denote by wr
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 6 Linear Transformations 6.3 Matrices for Linear Transformations 1. Standard Matrix for a Linear Transformation: Let T be a linear transformation from Rn to Rm and let e1 , e2 , ., en be the standard basis for Rn . If the images of these vectors are T
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 7 Eigenvalues and Eigenvectors 7.1 Eigenvalues and Eigenvectors 1. Eigenvalues and Eigenvectors: If A is an n n matrix, then a nonzero vector x in Rn is called an eigenvector of A if Ax is a scalar multiple of x; that is, if Ax = x for some scalar . T
School: Kennesaw
Course: LINEAR ALGEBRA I
Ch. 4 Vector Spaces 4.5 Basis and Dimension 1. Basis. If V is a vector space and S = cfw_u1 , u2 , , ur is a set of vectors in V , then S is called a basis for V if the following two conditions hold: (a) S is linearly independent. (b) S spans V . Ex: 1.
School: Kennesaw
Course: CALCULUS
! " 3 2.5 2 1.5 1 0.5 0 1.2 1.8 1x 1.4 1.6 0.2 0.4 0.6 0.8 2 # $ $ ! " % 2.5 2 1.5 1 0.5 -0.8 -0.6 -0.4 -0.2 0
School: Kennesaw
Course: CALCULUS
! ! " ! ! # $ ! #$ % ! ! ! ! ! ! & ! '! ! ! ! ! ! ! ! ( ) ! ! ! ! ! ! ! ! !
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Math 3310 Section 4.6 Solutions Ryan Livingston Section 4.6 Page 193: 1-11 odd For Problems 1-8, Find the General Solution 1. y + y = sec t SOLUTION: We nd the homogeneous solution by rst dening y = et so that the auxiliary equation becomes 2 + 1 = 0 so =
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
MATH 3310 Exercises on Higher Order ODEs Exercises On Higher Order ODEs For exercises 1-6, (a) nd the characteristic equation (b) the eigenvalues and (c) the corresponding eigenvectors for the matrix Exercise 1 6 3 A= 2 1 SOLUTION: (a) To nd the eigenvalu
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Ryan Livingston Section 1.3 Pg. 22 Exercises 1-7 odd 1. (a) If we wanted to sketch a line that runs through the initial point (0, 2) that is in the direction of the eld, we would get If we recall that the ODE was dy = 2x + y dx with the initial condition
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Ryan Livingston Section 1.1 Pg. 5 Exercises 1-17 1. d2 y dx2 2x dy + 2y = 0 dx From the equation above, we can deduce that it is a second order ordinary dierential equation. We can also deduce that the equation must be linear. Lastly, we can see that the
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Ryan Livingston Section 1.4 Eulers Method pg. 28 1-11 odd 1. Use Eulers method to approximate the solution to the intital vlaue problem dy x = dx y y (0) = 4 at the points x = 0.1, 0.2, 0.3, 0.4 and 0.5 using steps of size 0.1 (h = 0.1) Given the inital c
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Ryan Livingston Section 2.1 pg 46 1-25 odd Determine wether or not the following equations are seperable 1. dy dx sin (x + y ) = 0 SOLUTION: The equation dy sin (x + y ) = 0 dx is not seperable becasue we cannot break up the x and y variables in the term
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Math 3310 Section 4.3 Solutions Ryan Livingston Section 4.3 Page 173: 1-29 For Problems 1-19, Find the General Solution 1. y + y = 0 SOLUTION: We dene y = ex so the auxiliary equation is then 2 + 1 = 0 we solve for and get = i so the general solution is g
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Math 3310 Section 4.4 Solutions Ryan Livingston Section 4.4 Page 182: 9-31 odd For Problems 9-25, Find the Particular Solution 9. y + 2y y = 10 SOLUTION: We begin by nding the homogeneous solution, so we dene y = ex so that the auxiliary equation is then
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
Math 3310 Section 4.7 Solutions Ryan Livingston Section 4.7 Page 200 For Problems 9-14, Find the General Solution to the Cauchy Euler Equation 9. t2 y + 2ty 6y = 0 SOLUTION: We suppose that y = tr and y = rtr1 and y = r (r 1) tr2 . If we make these substi
School: Kennesaw
Course: ELEMENTARY STATISTICS
1.13 The answer is part c. A bar graph can be drawn using A,B,C,D and F as lables for the bars and the frequency for the vertical height. A pie chart would require slices labeled with A,B,C,D and F and we would have to figure out the percent.
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
ODE Homework Assignment (A First Course of Differential Equations with Modeling Applications) By Dennis G. Zill 2.2 2.3 2.4 2.5 2.6 4.1 4.2 4.3 4.4 1-25 (odd) 1-29 (odd) 1-19 (odd), 21, 23, 27, 29, 31, 33 1-21 (odd), 23, 25 1, 2, 3 1, 3, 15, 17, 19, 21, 2
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
ODE Homework Assignment (A First Course of Differential Equations with Modeling Applications) By Dennis G. Zill 2.2 2.3 2.4 2.5 2.6 4.1 4.2 4.3 4.4 4.6 7.1 7.2 7.3 7.4 1-25 (odd) 1-29 (odd) 1-19 (odd), 21, 23, 27, 29, 31, 33 1-21 (odd), 23, 25 1, 2, 3 1,
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
4.1 Homework Homework 1, 3, 15, 17, 19, 21, 23, 25, 31, 33 - 56 -
School: Kennesaw
Solutions to Homework Problems from Section 7.3 of Stewart 1. Given that sin x 5/13 and that x is in quadrant I, we have 2 144 cos 2 x 1 sin 2 x 1 5 169 13 so 144 12 . 13 169 Since x is in quadrant I we know that cos x 0 so cos x 12/13. Fro
School: Kennesaw
Answer and Solutions to Section 4.5 Homework Problems S. F. Ellermeyer November 19, 2006 1. It has been shown in class that H = fR0 ; R1 ; R2 g is a subgroup of D3 . Since H is a group of order 3 and Z3 (under addition) is also a group of order 3, an
School: Kennesaw
Answers and Solutions to Selected Section 4.5 Homework Problems Problems 1, 5, 9, 10, 11, 14, 15, 17, 19, 20, 21, 23, 29, 30, 31, 32, 33, and 34. S. F. Ellermeyer 1. s 2t st 3t 1 1 0 9. 1 : s, t s 1 0 2 , 1 3 . t 2 1 3 : s, t . This is a su
School: Kennesaw
Course: ELEMENTARY STATISTICS
DataLabI HannahLeighCrawford Categorical Data: Choose 2 categorical variables a. Construct a contingency table b. Create a bar chart or a pie chart c. Discuss any unusual features revealed by the display of the variable. Describe patterns found. Hint:youm
School: Kennesaw
Course: LINEAR ALGEBRA I
MATH 3260/01 Linear Algebra Summer 2014 Instructor: Dr. Liancheng Wang Office: MS 223A E-mail: lwang5@kennesaw.edu Phone: 678-797-2139 Office Hours: 12:00-2:00 pm, MW, or by appointment Text: Elementary Linear Algebra, 7th edition, by Ron Larson, BROOKS/C
School: Kennesaw
MATH1112CollegeTrigonometry CourseSyllabusSpring2014 Instructor: MonicaDoriney Time/location:M5:00 6:15 PM and 6:30 7:45 PM Mathematics and Statistics - Room108 Email: mdoriney@kennesaw.edu Office/hours:Varioustimesavailable,byappointment CourseDescriptio
School: Kennesaw
Course: College Algebra
MATH 1111: College Algebra Fall Semester 2013 Instructor Lori Joseph CRN 83606 Days MWF Time 11:00 am 11:50 am Course Num/Sec MATH 1111/32 Location Science 213 A Course in the General Education Program Program Description: The General Education Program at
School: Kennesaw
Course: DIFFERENTIAL EQUATIONS
MATH 3310 Differential Equations, Spring 2010 Instructor: Dr. Liancheng Wang Office: Sci. & Math. 511 E-mail: lwang5@kennesaw.edu Phone: 678-797-2139 Office Hours: 2:00-3:15 pm, 5:00-6:00 pm, T TH, or by appointment Text: A First Course of Differential Eq