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School: Oregon State
Course: Discrete Mathematics II
Mth 232 Review Problems for Exam I These are some review problems for the first midterm. They are gathered from old exams (mostly by other instructors). These questions cover the material in chapter 6, sections 1-4, and chapter 7, sections 1, 3, and 4. 1.
School: Oregon State
Course: Mth 111
COMM 218 Interpersonal Communication Instructor: Angela Cordova Exam #2 Study Guide Befamiliarwiththefollowingconceptsfromyourbookandclass.Additionally,rememberthatthisisjust a guideandis notnecessarilyallencompassing.Inotherwords,justbecauseitdoesntappea
School: Oregon State
Course: ADVANCED CALCULUS
AdvancedCalculus ThisisMTH311,Sec1. Timeandplace: MWRF10:0010:50,MWRF:WNGR287. Instructor: PatrickDeLeenheer Office:296KidderHall OfficeHours:MWF12:0012:50orbyappointment. Email:deleenhp@math.oregonstate.edu URL:www.math.oregonstate.edu/~deleenhp Prerequi
School: Oregon State
Course: ADVANCED CALCULUS
2.4 # 8 If cfw_an is monotone and has a convergent subsequence, then cfw_an converges. Assume that cfw_an is monotonically increasing (if decreasing, similar argument). It suces to show that cfw_an is bounded above, by the Monotone Convergence Theorem
School: Oregon State
Course: ADVANCED CALCULUS
I I ) é P/IOUC (:3 (940/? 6L /7W1 thtqjja M4,-imm, ' M 31 6! 714/344 7 (/13 . / VIA/Jr MIN-6014. Maw/(m {/JIMK W3 (1) 3 m Wollwum ,aém/f me 0% rm aim/VS 0M_ W MM: 5442/ M Mm 504% Wm WM Wkwé beytee/ rm MM Mom 30 1:1 Ana M W 1/»: MM m 2- b; My. éwmh m aMé
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Chapter 3 A L TEX A LTEX is a markup language. It is essentially an upgrade of Donald Knuths landmark typesetting language called TEX [3]. In the late 1970s Knuth realized that printing technology had neared a point at which very sophisticated typesetting
School: Oregon State
Course: Introductory Applications Of Mathematical Software
IntroductiontoMATLAB DavidKoslicki OregonStateUniversity 3/20/2015 Contents Preliminary Basics HomeworkExercises Vectors HomeworkExercises Plotting HomeworkExercises Matrices HomeworkExercises Matrix/VectorandMatrix/MatrixOperations HomeworkExercises Flow
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Latex Lecture 1 \documentclass[12pt]cfw_article \usepackagecfw_amsmath,amsfonts,amsthm,amssymb \authorcfw_Author \titlecfw_Title \begincfw_document \maketitle Hello world! $\mathbbcfw_N$ \sectioncfw_My section \subsectioncfw_My subsection \subsubsectioncf
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Title Author March 21, 2015 Hello world! N 1 My section 1.1 1.1.1 My subsection My subsubsection My unumbered subsubsection These are centered formulas f (x) = x + 2 f (x) = x + 2 f (x) = x + 2 f (x) = x + 2 f (x) = x + 2 This is an inline formula f (x) =
School: Oregon State
Course: Mathematical Modeling3
Model of heterogeneous microscale in SOFI for Monte Carlo simulations Nathan L. Gibson May 21, 2007 Abstract We present a methodology for creating a simulated foam microstructure for use in forward simulations of wave equations to quantitatively anal
School: Oregon State
Course: Mth 111
COMM 218 Interpersonal Communication Instructor: Angela Cordova Exam #2 Study Guide Befamiliarwiththefollowingconceptsfromyourbookandclass.Additionally,rememberthatthisisjust a guideandis notnecessarilyallencompassing.Inotherwords,justbecauseitdoesntappea
School: Oregon State
Course: LINEAR ALGEBRA II
Quiz #3 r. . You 11:11! 20 111111111135. . L ff: .1' " '1 {r ,5. :- P102150 explain 111111 11(1): the answers. Kenna: 1. [5 1111-1) Find the eigenvalues and 1:1111'05111'11111i11g eigcuvectors 0f 1 11 {- A:[1 J 1 a _ _ a I _ r . -' F11 2 - 1 I - 1- a
School: Oregon State
Course: PROBABILITY I
Midterm for Math 463/563 Theory of Probability \ \ l l \ Bob Burton \I * 7 November, 2014 /-/: -~ /" I I, There are a total of problems of varying length. /; -_#_'_/ l 2 2 3 3' .a (D 6 5 8 g Ul B 6 5" \. 2/ '"'-.\ 6 /M .H q \ "/5 Ac- <3 U D l l\ 2/ Z
School: Oregon State
Course: ADVANCED CALCULUS
1'1 Math 312, Section 003 -~ Second midterm exam March 2, 2015 Show you: work on all problems. 1. Assume D C R and f1 : D > R for all integers n 21. (8.) Dene what it means for the sequence {fn 3:1 of functions to converge uniformly to a. function f on
School: Oregon State
Course: ADVANCED CALCULUS
Name blues; News; Math 312, Section 003 First midterm exam February 9, 2015 Show your work on all problems. 1. Assume F(;r) = si11(:1:2) for all real 1, and also assume F(}) = 2. Use ideas developed in class to find an expression for F(:1:) that is valid
School: Oregon State
Course: ADVANCED CALCULUS
2.4 # 8 If cfw_an is monotone and has a convergent subsequence, then cfw_an converges. Assume that cfw_an is monotonically increasing (if decreasing, similar argument). It suces to show that cfw_an is bounded above, by the Monotone Convergence Theorem
School: Oregon State
Course: ADVANCED CALCULUS
I I ) é P/IOUC (:3 (940/? 6L /7W1 thtqjja M4,-imm, ' M 31 6! 714/344 7 (/13 . / VIA/Jr MIN-6014. Maw/(m {/JIMK W3 (1) 3 m Wollwum ,aém/f me 0% rm aim/VS 0M_ W MM: 5442/ M Mm 504% Wm WM Wkwé beytee/ rm MM Mom 30 1:1 Ana M W 1/»: MM m 2- b; My. éwmh m aMé
School: Oregon State
Course: ADVANCED CALCULUS
3.5 # 7 a. Prove that f (x) = x, x [0, 1] is continuous, i.e. if cfw_xn is a sequence in [0, 1], and xn x0 in [0, 1] as n , then xn x0 . 2 cases: If x0 = 0, then: xn x0 1 | xn x0 | = | | |xn x0 | xn + x0 x0 By the comparison lemma, the result follows.
School: Oregon State
Course: ADVANCED CALCULUS
Homework assignments: HW assignments (collected): HWI: 1.1: #5 (Use Example 1.1) and #16; 1.2: #4a (use suggested problems 1.1#15 and 1.2 #3, but don't turn in the proofs of these) (due Mon Jan 13). Note the typo on p.1: a square is missing in the very la
School: Oregon State
Course: Multiple Variable Calculus
21141'12 Lab %231, Winter 2012 Insmlctor: Dr. Scarborough / -r_._._.._._v-f"/ GTA: (circle One) Veronika Vasylkivska Shers'oHV \ . . {/d') h Class Tlme: (Clrcle One) 1:00 Recitation Tirm:(CirCie One) 8:00 9.00 1000 1100 1:00 NAME (Print) E12 -; 5
School: Oregon State
Course: ADVANCED CALCULUS
AdvancedCalculus ThisisMTH311,Sec1. Timeandplace: MWRF10:0010:50,MWRF:WNGR287. Instructor: PatrickDeLeenheer Office:296KidderHall OfficeHours:MWF12:0012:50orbyappointment. Email:deleenhp@math.oregonstate.edu URL:www.math.oregonstate.edu/~deleenhp Prerequi
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Syllabus Introduction to Mathematical Software Math 321, 3 credits Spring Quarter, 2015 Prerequisite: MTH 252 and either MTH 341 or 306. Course Content: This course is designed to familiarize students with the
School: Oregon State
Course: Discrete Mathematics II
Mth 232 Review Problems for Exam I These are some review problems for the first midterm. They are gathered from old exams (mostly by other instructors). These questions cover the material in chapter 6, sections 1-4, and chapter 7, sections 1, 3, and 4. 1.
School: Oregon State
Course: Mth 111
COMM 218 Interpersonal Communication Instructor: Angela Cordova Exam #2 Study Guide Befamiliarwiththefollowingconceptsfromyourbookandclass.Additionally,rememberthatthisisjust a guideandis notnecessarilyallencompassing.Inotherwords,justbecauseitdoesntappea
School: Oregon State
Course: ADVANCED CALCULUS
AdvancedCalculus ThisisMTH311,Sec1. Timeandplace: MWRF10:0010:50,MWRF:WNGR287. Instructor: PatrickDeLeenheer Office:296KidderHall OfficeHours:MWF12:0012:50orbyappointment. Email:deleenhp@math.oregonstate.edu URL:www.math.oregonstate.edu/~deleenhp Prerequi
School: Oregon State
Course: ADVANCED CALCULUS
2.4 # 8 If cfw_an is monotone and has a convergent subsequence, then cfw_an converges. Assume that cfw_an is monotonically increasing (if decreasing, similar argument). It suces to show that cfw_an is bounded above, by the Monotone Convergence Theorem
School: Oregon State
Course: ADVANCED CALCULUS
I I ) é P/IOUC (:3 (940/? 6L /7W1 thtqjja M4,-imm, ' M 31 6! 714/344 7 (/13 . / VIA/Jr MIN-6014. Maw/(m {/JIMK W3 (1) 3 m Wollwum ,aém/f me 0% rm aim/VS 0M_ W MM: 5442/ M Mm 504% Wm WM Wkwé beytee/ rm MM Mom 30 1:1 Ana M W 1/»: MM m 2- b; My. éwmh m aMé
School: Oregon State
Course: ADVANCED CALCULUS
3.5 # 7 a. Prove that f (x) = x, x [0, 1] is continuous, i.e. if cfw_xn is a sequence in [0, 1], and xn x0 in [0, 1] as n , then xn x0 . 2 cases: If x0 = 0, then: xn x0 1 | xn x0 | = | | |xn x0 | xn + x0 x0 By the comparison lemma, the result follows.
School: Oregon State
Course: ADVANCED CALCULUS
Homework assignments: HW assignments (collected): HWI: 1.1: #5 (Use Example 1.1) and #16; 1.2: #4a (use suggested problems 1.1#15 and 1.2 #3, but don't turn in the proofs of these) (due Mon Jan 13). Note the typo on p.1: a square is missing in the very la
School: Oregon State
Course: ADVANCED CALCULUS
6.1 # 1 Let P = cfw_0, 1/4, 1/2, 1. For the following functions f : [0, 1] R, nd L(f, P ) and U (f, P ): a.f (x) = x. L(f, P ) U (f, P ) 1 1 1 1 1 5 0. + . + . = 4 4 4 2 2 16 1 1 1 1 1 11 . + . + 1. = 4 4 2 4 2 16 = = b.f (x) = 10. L(f, P ) = 10. 1 1 1 +
School: Oregon State
Course: LINEAR ALGEBRA II
Quiz #3 r. . You 11:11! 20 111111111135. . L ff: .1' " '1 {r ,5. :- P102150 explain 111111 11(1): the answers. Kenna: 1. [5 1111-1) Find the eigenvalues and 1:1111'05111'11111i11g eigcuvectors 0f 1 11 {- A:[1 J 1 a _ _ a I _ r . -' F11 2 - 1 I - 1- a
School: Oregon State
Course: PROBABILITY I
Midterm for Math 463/563 Theory of Probability \ \ l l \ Bob Burton \I * 7 November, 2014 /-/: -~ /" I I, There are a total of problems of varying length. /; -_#_'_/ l 2 2 3 3' .a (D 6 5 8 g Ul B 6 5" \. 2/ '"'-.\ 6 /M .H q \ "/5 Ac- <3 U D l l\ 2/ Z
School: Oregon State
Course: PROBABILITY I
_ r Slw/(' I; oil-.312. 1 3' "jl;r(_'qd>¢ -JL,.'5.,K PICK, {gli'H-!rr\l'! (/Fian'hf'vl'r INLC nag-{L} bol;~s_glt;)i I,( 74(57r'igqrf; +L / l/pgkilyookj - r+H_.;'1 bi +0; (Hf- II-Eff 1'wa wdtbwkj a? Hnw'ooru mde 96 I" a {H.(Irp vfgq a 5 f " _;.'A rsgc jk
School: Oregon State
Course: ADVANCED CALCULUS
Math 312, Section 003 Lab session for Wednesday, February 11, 2015 Turn in your write-up at the beginning of class on Friday, February 13. 1. Let f(a:) = e for all real a. (a) Let n be a. positive integer, and let 1),; be the Taylor polynomial of f of deg
School: Oregon State
Course: ADVANCED CALCULUS
[It Mf g, Math 312, Section 003 /l 7( Lab session for Wednesday, January 14, 2015 [ a L / Turn in your writeup at the beginning of class on Friday, January 16. 1. Let [(1,1)] be a closed bounded interval. Assume that f : [(1, b] > R is continuous on [(1,
School: Oregon State
Course: ADVANCED CALCULUS
r_ o L - lllw 00 (L3 Math 312, Section 003 Lab session for Wednesday, January 7, 2015 Turn in your write-up at the beginning of class on Friday, January 9. 1. (Problem 11, page 150.) For a partition P = {3:0, . . . , 23,1} of the interval [(1,1)], Show th
School: Oregon State
Course: ADVANCED CALCULUS
Math 312, Section 003 Lab session for Wednesday, January 28, 2015 Turn in your writeup at the beginning of class on Hiday, January 30. 1. Let u(:c,t) = %[f(r+ct)+f(:r-ct)] + (£3 for all real 3: and all t 2 0, where c is a positive constant, and f and g ar
School: Oregon State
Course: ADVANCED CALCULUS
.xi / l. 3c .R-J Math 312, Section 003 Lab session for Wednesday, February 18, 2015 Turn in your writeup at the beginning of class on Friday, February 20. 1. For every positive integer 71, let " 1 l 1 S: =1 e+. - n g k + 2 + n - 1 (61) Find a positive con
School: Oregon State
Course: ADVANCED CALCULUS
1'1 Math 312, Section 003 -~ Second midterm exam March 2, 2015 Show you: work on all problems. 1. Assume D C R and f1 : D > R for all integers n 21. (8.) Dene what it means for the sequence {fn 3:1 of functions to converge uniformly to a. function f on
School: Oregon State
Course: ADVANCED CALCULUS
Name blues; News; Math 312, Section 003 First midterm exam February 9, 2015 Show your work on all problems. 1. Assume F(;r) = si11(:1:2) for all real 1, and also assume F(}) = 2. Use ideas developed in class to find an expression for F(:1:) that is valid
School: Oregon State
Course: ADVANCED CALCULUS
Math 312, Section 003 Lab session for Wednesday, March 4, 2015 Turn in your writeup at the beginning of class on Friday, March 6. 1. Prove the following theorem, which is known as the Weierstrass Mtest. Theorem. Assume D C R, fk : D ) R for all k 2 1, a
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Chapter 3 A L TEX A LTEX is a markup language. It is essentially an upgrade of Donald Knuths landmark typesetting language called TEX [3]. In the late 1970s Knuth realized that printing technology had neared a point at which very sophisticated typesetting
School: Oregon State
Course: Introductory Applications Of Mathematical Software
IntroductiontoMATLAB DavidKoslicki OregonStateUniversity 3/20/2015 Contents Preliminary Basics HomeworkExercises Vectors HomeworkExercises Plotting HomeworkExercises Matrices HomeworkExercises Matrix/VectorandMatrix/MatrixOperations HomeworkExercises Flow
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Latex Lecture 1 \documentclass[12pt]cfw_article \usepackagecfw_amsmath,amsfonts,amsthm,amssymb \authorcfw_Author \titlecfw_Title \begincfw_document \maketitle Hello world! $\mathbbcfw_N$ \sectioncfw_My section \subsectioncfw_My subsection \subsubsectioncf
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Title Author March 21, 2015 Hello world! N 1 My section 1.1 1.1.1 My subsection My subsubsection My unumbered subsubsection These are centered formulas f (x) = x + 2 f (x) = x + 2 f (x) = x + 2 f (x) = x + 2 f (x) = x + 2 This is an inline formula f (x) =
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Latex Lecture 2: \documentclass[12pt]cfw_article \usepackagecfw_amsmath,amsfonts,amsthm,amssymb \authorcfw_Author \titlecfw_Title \usepackagecfw_graphicx \newtheoremcfw_definitioncfw_Definition[section] \newtheoremcfw_theoremcfw_Theorem[section] %\theorem
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Title Author March 21, 2015 1 Alignment f (x) = (x 1)(x + 1) = x2 1. A= u(x) = 2 1 2 0 4 0 x<0 1 x 0. Lists 1. item1 2. item2 3. item3 1. Enumerate (a) Lettered items (b) Lettered items 2. Itemize Bulleted items Bulleted items 1 (1) This is a test yup i
School: Oregon State
Course: INTRODUCTION TO MODERN ALGEBRA
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
Homework 3 Solutions 1) A metric on a set X is a function d : X X R such that For all x, y, z R, (a) d (x, y) 0, with d (x, y) = 0 if and only if x = y (b) d (x, y) = d (y, x) (c) d (x, z) d (x, y) + d (y, z) 2) If x = (x1 , . . . , xn ) and y = (y1 , . .
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
NAME: HW 3 and Midterm Review: Due Tuesday May 5 For this combined review and HW assignment, you may work with your classmates. For the exam, you may bring a 3x5 note card, but no calculator or wi device, and you will work individually. The Midterm Exam t
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
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School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
NOTES FOR MATH 4510, FALL 2010 DOMINGO TOLEDO 1. Metric Spaces The following denition introduces the most central concept in the course. Think of the plane with its usual distance function as you read the denition. Denition 1.1. A metric space (X, d) is a
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
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School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
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School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
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School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
Notes on Introductory Point-Set Topology Allen Hatcher Chapter 1. Basic Point-Set Topology . 1 Topological Spaces 1, Interior, Closure, and Boundary 5, Basis for a Topology 7, Metric Spaces 9, Subspaces 10, Continuity and Homeomorphisms 12, Product Spaces
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
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School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
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School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
adr Q 2 ( n+1};kach [Wm $M\ P" (32 I" éf' i?sz Limerwa) 3 59? 09qu mam «m M+Ww 9w? *0 6:1 69 (M d (Pi 6}\ 7-: {wath 6W" 0 W1 M TR?) W W "5 J . < it I/ \k E a. I \/ g c? :M UOMM «Ex-mum, We «saw hails Mi 3 . [A39 M903; 7?an Ma: aenerre 65% P wk MAJ); 2
School: Oregon State
Course: MATRIX AND POWER SERIES METHODS
Lesson 7 Eigenvalues and Eigenvectors Hoewoon Kim Oregon State University mth 306 Matrix and Power Series Methods Jan.30, 2015 Hoewoon Kim (Math Dep. at OSU) Lesson 7 Jan.30, 2015 1 / 10 Eigenvalue Problems Let A be an n m matrix. TA : Rm Rn , TA (x) = Ax
School: Oregon State
Course: MATRIX AND POWER SERIES METHODS
Lesson 6 Linear Transformations - Part I Hoewoon Kim Oregon State University mth 306 Matrix and Power Series Methods Jan.23, 2015 Hoewoon Kim (Math Dep. at OSU) Lesson 6 Jan.23, 2015 1 / 13 Linear Transformations We can treat matrix multiplication as a fu
School: Oregon State
Course: MATRIX AND POWER SERIES METHODS
Lesson 6 Linear Transformations - Part II Hoewoon Kim Oregon State University mth 306 Matrix and Power Series Methods Jan.28, 2015 Hoewoon Kim (Math Dep. at OSU) Lesson 6 Jan.28, 2015 1/7 Composition of Linear Transformations TA : Rm Rn , SB : Rn Rp where
School: Oregon State
Course: MATRIX AND POWER SERIES METHODS
Lesson 2 Vectors Hoewoon Kim Oregon State University mth 306 Matrix and Power Series Methods Jan. 7, 2015 Hoewoon Kim (Math Dep. at OSU) Lesson 2 Jan. 7, 2015 1/8 Vectors A vector has its magnitude and direction, but not necessarily position. Examples: We
School: Oregon State
Course: Mathematical Modeling3
Model of heterogeneous microscale in SOFI for Monte Carlo simulations Nathan L. Gibson May 21, 2007 Abstract We present a methodology for creating a simulated foam microstructure for use in forward simulations of wave equations to quantitatively anal
School: Oregon State
Course: Mth 111
COMM 218 Interpersonal Communication Instructor: Angela Cordova Exam #2 Study Guide Befamiliarwiththefollowingconceptsfromyourbookandclass.Additionally,rememberthatthisisjust a guideandis notnecessarilyallencompassing.Inotherwords,justbecauseitdoesntappea
School: Oregon State
Course: LINEAR ALGEBRA II
Quiz #3 r. . You 11:11! 20 111111111135. . L ff: .1' " '1 {r ,5. :- P102150 explain 111111 11(1): the answers. Kenna: 1. [5 1111-1) Find the eigenvalues and 1:1111'05111'11111i11g eigcuvectors 0f 1 11 {- A:[1 J 1 a _ _ a I _ r . -' F11 2 - 1 I - 1- a
School: Oregon State
Course: PROBABILITY I
Midterm for Math 463/563 Theory of Probability \ \ l l \ Bob Burton \I * 7 November, 2014 /-/: -~ /" I I, There are a total of problems of varying length. /; -_#_'_/ l 2 2 3 3' .a (D 6 5 8 g Ul B 6 5" \. 2/ '"'-.\ 6 /M .H q \ "/5 Ac- <3 U D l l\ 2/ Z
School: Oregon State
Course: ADVANCED CALCULUS
1'1 Math 312, Section 003 -~ Second midterm exam March 2, 2015 Show you: work on all problems. 1. Assume D C R and f1 : D > R for all integers n 21. (8.) Dene what it means for the sequence {fn 3:1 of functions to converge uniformly to a. function f on
School: Oregon State
Course: ADVANCED CALCULUS
Name blues; News; Math 312, Section 003 First midterm exam February 9, 2015 Show your work on all problems. 1. Assume F(;r) = si11(:1:2) for all real 1, and also assume F(}) = 2. Use ideas developed in class to find an expression for F(:1:) that is valid
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
NAME: MIdterm Exam100 pointsMay 7, 2015 You may use a 3x5 note card, but no calculator or wi device, and you will work individually. Each problem is worth 10 points. The exam will end promptly at 9:50am. Problem 1 Let (X, d) be a metric space. Let A X and
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
NAME: (athm ? Midterm Exam100 pointsuuMay 7, 2015 You may use a 3x5 note card, but no calculator or wi device, and you will work individually. Each problem is worth 10 points. The exam will end promptly at 9:50am. Problem 1 Let (X, d) be a metric space. L
School: Oregon State
Course: Introduction To Probability
MIDTERM II MATH 361, SPRING 2013 PROFESSOR OSSIANDER SHOW YOUR WORK COMPLETELY, COHERENTLY, AND LEGIBLY There are 6 problems on this exam, each with multiple parts. Each part of each problem is worth 4 points. ' Show your work completely to receive full
School: Oregon State
Course: Differential Calculus4
Math 251 , Fall 2008 Exam 2 Page 2 Scarborough MAKE SURE YOU ANSWERED PROBLEM I from page 1 Use the following tables for problems 2, 3, 4 and 5. Suppose that f and g are differentiable functions with the following values \l f - . - 2. Let hm: foo23
School: Oregon State
Course: ADVANCED CALCULUS
2.4 # 8 If cfw_an is monotone and has a convergent subsequence, then cfw_an converges. Assume that cfw_an is monotonically increasing (if decreasing, similar argument). It suces to show that cfw_an is bounded above, by the Monotone Convergence Theorem
School: Oregon State
Course: ADVANCED CALCULUS
I I ) é P/IOUC (:3 (940/? 6L /7W1 thtqjja M4,-imm, ' M 31 6! 714/344 7 (/13 . / VIA/Jr MIN-6014. Maw/(m {/JIMK W3 (1) 3 m Wollwum ,aém/f me 0% rm aim/VS 0M_ W MM: 5442/ M Mm 504% Wm WM Wkwé beytee/ rm MM Mom 30 1:1 Ana M W 1/»: MM m 2- b; My. éwmh m aMé
School: Oregon State
Course: ADVANCED CALCULUS
3.5 # 7 a. Prove that f (x) = x, x [0, 1] is continuous, i.e. if cfw_xn is a sequence in [0, 1], and xn x0 in [0, 1] as n , then xn x0 . 2 cases: If x0 = 0, then: xn x0 1 | xn x0 | = | | |xn x0 | xn + x0 x0 By the comparison lemma, the result follows.
School: Oregon State
Course: ADVANCED CALCULUS
Homework assignments: HW assignments (collected): HWI: 1.1: #5 (Use Example 1.1) and #16; 1.2: #4a (use suggested problems 1.1#15 and 1.2 #3, but don't turn in the proofs of these) (due Mon Jan 13). Note the typo on p.1: a square is missing in the very la
School: Oregon State
Course: ADVANCED CALCULUS
6.1 # 1 Let P = cfw_0, 1/4, 1/2, 1. For the following functions f : [0, 1] R, nd L(f, P ) and U (f, P ): a.f (x) = x. L(f, P ) U (f, P ) 1 1 1 1 1 5 0. + . + . = 4 4 4 2 2 16 1 1 1 1 1 11 . + . + 1. = 4 4 2 4 2 16 = = b.f (x) = 10. L(f, P ) = 10. 1 1 1 +
School: Oregon State
Course: PROBABILITY I
_ r Slw/(' I; oil-.312. 1 3' "jl;r(_'qd>¢ -JL,.'5.,K PICK, {gli'H-!rr\l'! (/Fian'hf'vl'r INLC nag-{L} bol;~s_glt;)i I,( 74(57r'igqrf; +L / l/pgkilyookj - r+H_.;'1 bi +0; (Hf- II-Eff 1'wa wdtbwkj a? Hnw'ooru mde 96 I" a {H.(Irp vfgq a 5 f " _;.'A rsgc jk
School: Oregon State
Course: ADVANCED CALCULUS
Math 312, Section 003 Lab session for Wednesday, February 11, 2015 Turn in your write-up at the beginning of class on Friday, February 13. 1. Let f(a:) = e for all real a. (a) Let n be a. positive integer, and let 1),; be the Taylor polynomial of f of deg
School: Oregon State
Course: ADVANCED CALCULUS
[It Mf g, Math 312, Section 003 /l 7( Lab session for Wednesday, January 14, 2015 [ a L / Turn in your writeup at the beginning of class on Friday, January 16. 1. Let [(1,1)] be a closed bounded interval. Assume that f : [(1, b] > R is continuous on [(1,
School: Oregon State
Course: ADVANCED CALCULUS
r_ o L - lllw 00 (L3 Math 312, Section 003 Lab session for Wednesday, January 7, 2015 Turn in your write-up at the beginning of class on Friday, January 9. 1. (Problem 11, page 150.) For a partition P = {3:0, . . . , 23,1} of the interval [(1,1)], Show th
School: Oregon State
Course: ADVANCED CALCULUS
Math 312, Section 003 Lab session for Wednesday, January 28, 2015 Turn in your writeup at the beginning of class on Hiday, January 30. 1. Let u(:c,t) = %[f(r+ct)+f(:r-ct)] + (£3 for all real 3: and all t 2 0, where c is a positive constant, and f and g ar
School: Oregon State
Course: ADVANCED CALCULUS
.xi / l. 3c .R-J Math 312, Section 003 Lab session for Wednesday, February 18, 2015 Turn in your writeup at the beginning of class on Friday, February 20. 1. For every positive integer 71, let " 1 l 1 S: =1 e+. - n g k + 2 + n - 1 (61) Find a positive con
School: Oregon State
Course: ADVANCED CALCULUS
Math 312, Section 003 Lab session for Wednesday, March 4, 2015 Turn in your writeup at the beginning of class on Friday, March 6. 1. Prove the following theorem, which is known as the Weierstrass Mtest. Theorem. Assume D C R, fk : D ) R for all k 2 1, a
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
p. 13-14: 1bdefg, 3, 4, 6 1b) The interval on the x-axis 0 x 1 1d) The whole x-axis 1e) The whole plane 1f) The graph of the equation xy = 1 1g) The points in the plane with integer coordinates 3) The statement in the problem is logically equivalent to th
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
HW 2, MTH 430, Due Thursday April 23 Problem 1 The purpose this (geometry) problem is to show that midpoints are unique in the Euclidean metric on Rn . We use the Euclidean metric, norm, and scalar (dot) product: d2 (x, y) = |x y| = (x y) (x y). 1 Given x
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
Homework 4 Solutions p. 16: 2ab, 4ab, 5ab 2a) Proof: Let U be an open subset of X and which lies inside a set A. Let x U . Then U is an open subset of A containing x, hence x int (A). Therefore, U int (A). 2b) Proof: Let C be a closed subset of X, and let
School: Oregon State
Course: METRIC SPACES AND TOPOLOGY
Homework 2 Solutions 1) Let Rn be equipped with the Euclidean metric. Let x, y Rn , and dene m = (Recall that a point M Rn is a midpoint of x and y if x M = y M = 1 2 1 2 (x + y). x y .) Observe that m is a midpoint of x and y (verication is left to the r
School: Oregon State
Course: INTRODUCTION TO CONTEMPORARY MATHEMATICS
ID NUMBER:_ NAME: _ SECTION:_ ASSIGNMENT Answer the questions for each exercise. If there is a need for computed answers, solve and write the correct answers from your computed values in the blanks provided. Exercise 1. Select the correct answer and write
School: Oregon State
Course: Multiple Variable Calculus
21141'12 Lab %231, Winter 2012 Insmlctor: Dr. Scarborough / -r_._._.._._v-f"/ GTA: (circle One) Veronika Vasylkivska Shers'oHV \ . . {/d') h Class Tlme: (Clrcle One) 1:00 Recitation Tirm:(CirCie One) 8:00 9.00 1000 1100 1:00 NAME (Print) E12 -; 5
School: Oregon State
Course: Applied Discrete Math
MLC Lab Visit - Lab 07 - Maple Mth 355 (a.k.a. Mth 399) Feb 19, 2003 Maple 7 Bent E. Petersen petersen@math.orst.edu There are 5 problems below. Problem solutions are due Feb 26, 2003. Email your solutions to me as Maple worksheet attachments. Your worksh
School: Oregon State
Course: Applied Discrete Math
MLC Lab Visit - Lab 06 - Maple Mth 355 (a.k.a. Mth 399) Feb 12, 2003 Maple 7 Bent E. Petersen petersen@math.orst.edu There are 3 problems below. Problem solutions are due Feb 19, 2003. Email your solutions to me as Maple worksheet attachments. Your worksh
School: Oregon State
Course: Applied Discrete Math
MLC Lab Visit - Lab 05 - Maple Mth 355 (a.k.a. Mth 399) Feb 05, 2003 Maple 7 Bent E. Petersen petersen@math.orst.edu There are 6 problems below. Problem solutions are due Feb 12, 2003. Email your solutions to me as Maple worksheet attachments. Your worksh
School: Oregon State
Course: Linear Algebra
Mth 341 Linear Algebra Spring 2000 MLC Computer Lab Visit 1 Bent Petersen Login Press the Ctrl-Alt-Delete keys simultaneously. You should get a login prompt. Enter your ORST user name and press the Tab key. Then enter your ORST password and press the Ente
School: Oregon State
Course: ADVANCED CALCULUS
AdvancedCalculus ThisisMTH311,Sec1. Timeandplace: MWRF10:0010:50,MWRF:WNGR287. Instructor: PatrickDeLeenheer Office:296KidderHall OfficeHours:MWF12:0012:50orbyappointment. Email:deleenhp@math.oregonstate.edu URL:www.math.oregonstate.edu/~deleenhp Prerequi
School: Oregon State
Course: Introductory Applications Of Mathematical Software
Syllabus Introduction to Mathematical Software Math 321, 3 credits Spring Quarter, 2015 Prerequisite: MTH 252 and either MTH 341 or 306. Course Content: This course is designed to familiarize students with the