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School: Georgia State
Course: Elementary Statistics
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 B C D E F G H I J Math 1070 Excel Project (Due: Friday, November 15, 2
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
Math 2211 Spring 2009 Test 1 Review Definition 2.2.1. The limit of a function. Let f be a function defined at least on an open interval (c-p,c+p) except possibly at c itself. We say that lim f ( x) = L x c if for each > 0, there exist > 0 such that if 0 <
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
2211 Spring 2009 Test 1 Name_ Show all necessary work in your blue book. No credit will be given for incorrect work or answers without work. Please use a new page for each problem. Please use pencil. When finished, place this question paper in your blue b
School: Georgia State
Course: Mathematical Models For Computer Science
MATH-3030, Summer-2012 Quiz #5 Your name: MATH-3030 Math Models for CS CRN 52440 Quiz 5 Sections C.13.5-C.13.6,C.14.1-C.14.2,C.15.4,C.16.2,C.16.4 Directions: Do the quiz on your own paper and attach to this quiz assignment sheet. Clearly show all your wor
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
B. 1 Proof of the Well-ordering Theorem We follow the pattern outlined in Exercises 2-7 on pp. 72-73 of the text. Then h: J-YE. be well-ordered sets; let ar;d E J Let Theorem B.1. the following are equivalent: of or a section E equals h(J) is order preser
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8 9
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
A.1 Set Theory and Logic: Fundamental Concepts Notes by Dr. J. Santos) A.1. Primitive Concepts. In mathematics, the notion of a set is a primitive notion. That is, we admit, as a starting point, the existence of certain objects (which we call sets), which
School: Georgia State
Course: MATH 2212
Plant Reproduction Biol 2108 Lab Moss Moss Life Cycle Moss Sporophyte (Sphagnum) Moss Young Gametophyte Moss Antheridial Head Moss Archegonial Head Moss Protonema Moss Capsule Fern Fern Young Sporophyte Fern Antheridia Fern Archegonia Fern Indusium Fern S
School: Georgia State
Course: MATH 2212
Protostomes Annelida Annelida Mollusca Arthropoda Platyhelminthes Evolutionary Relationships Amongst Animals Ecdysozoans & Lophotrochozoans In ancient times the protostomes split into 2 major clades that have been evolving independently ever since Lopho
School: Georgia State
Course: MATH 2212
Plant Growth & Hormones Seed Dormancy Seed dormancy may last for weeks, months, years, or even centuries. What are the advantages of dormancy? Germination Plant Hormones What is a hormone? Hormones Naturally occurring regulatory compounds Substances tha
School: Georgia State
Course: Elementary Statistics
January 23, 2008 [LECTURE 6] What you need to know What you need to remember 1. One notice In a normal distribution, , , is actually the mean, and is the standard deviation. One interesting & important property of normal distribution 1
School: Georgia State
Course: Elementary Statistics
January 18, 2008 [LECTURE 5] What you need to remember for today's lecture? 1. IQR and outliers The interquartile range (IQR) is the distance between the first and third quartiles (the length of the box in the boxplot) IQR = Q3 - Q1 An outlier
School: Georgia State
Course: Elementary Statistics
January 16, 2008 [LECTURE 4] What you need to remember from today's lecture I. Measure of spread: quartiles and standard deviation Quartiles are three numbers that describe the trend, or statistically, the spread of the data. The calculation
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
Math 2211 Spring 2009 Test 1 Review Definition 2.2.1. The limit of a function. Let f be a function defined at least on an open interval (c-p,c+p) except possibly at c itself. We say that lim f ( x) = L x c if for each > 0, there exist > 0 such that if 0 <
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
2211 Spring 2009 Test 1 Name_ Show all necessary work in your blue book. No credit will be given for incorrect work or answers without work. Please use a new page for each problem. Please use pencil. When finished, place this question paper in your blue b
School: Georgia State
Course: Mathematical Models For Computer Science
MATH-3030, Summer-2012 Quiz #5 Your name: MATH-3030 Math Models for CS CRN 52440 Quiz 5 Sections C.13.5-C.13.6,C.14.1-C.14.2,C.15.4,C.16.2,C.16.4 Directions: Do the quiz on your own paper and attach to this quiz assignment sheet. Clearly show all your wor
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Solutions 1. Evaluate the limit if it exists (or clearly state and prove that it doesnt exist if thats the case): x2 + 2x 15 =? x5 x+5 (x + 5)(x 3) x2 + 2x 15 = lim = lim (x 3) = 8. lim x5 x5 x5 x+5 x+5 1 1 +t lim 3 =? t3 3 +
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Solution of Problem Set 7 Assigned: October 30, 2008 Due: November 6, 2008 Problem 1: There are a number of ways to
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Solution of Problem Set 9 Assigned: November 20, 2008 Due: December 4, 2008 Problem 1: + x = + 1 x(ex )dx = ex (x )
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set : FIR Linear Filters Assigned: October 30, 2008 Due: November 6, 2008 Problem 1: Prove the linear phase
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 9 Assigned: November 20, 2008 Problem 1: Due: December 4, 2008 Given a waveform x(t) with a pdf of the
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set : FIR Linear Filters Assigned: November 6, 2008 Due: November 18, 2008 Problem 1: A Mini-project: An Au
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
Lab Report 5- KH 3650 ° What are the physiological factors that limit V02 max? Would these factors be different for a trained person from a sedentary person? The highest V02 recorded in absolute terms was 3.97[L/ min), in relative terms it was 53.3 [ml/kg
School: Georgia State
Course: COMPLEX ANALYSIS
Chapter 7 Notes - Inference for Single Samples You know already for a large sample, you can invoke the CLT so: X N (, 2 ). Also for a large sample, you can replace an unknown by s. You know how to do a hypothesis test for the mean, either: calculate z-
School: Georgia State
Course: COMPLEX ANALYSIS
Chapter 9 Notes, Part 1 - Inference for Proportion and Count Data We want to estimate the proportion p of a population that have a specic attribute, like what percent of houses in Cambridge have a mouse in the house? We are given X1 , . . . , Xp where Xi
School: Georgia State
Course: COMPLEX ANALYSIS
$ " !$ ( ' " & / + ', 0 " $ !' # - . 0 " ' 1 " ' / ! !' 02 1' 0 ! !' 03 1' & / ' $ ) $& 0 /' & / * # ' $& ! $ /& $ 0& $ /) $% $' % * ! % ! '
School: Georgia State
Course: COMPLEX ANALYSIS
Chapter 14 Nonparametric Statistics A.K.A. distribution-free statistics! Does not depend on the population tting any particular type of distribution (e.g, normal). Since these methods make fewer assumptions, they apply more broadly. at the expense of a le
School: Georgia State
Course: COMPLEX ANALYSIS
Chapter 11 : Multiple Linear Regression We have: height weight . . . age person 1: person 2: : x12 x22 x11 x21 . . x1k x2k amount of lemonade purchased y1 y2 where we assume Yi = 0 + for i = 1, . . . , n and i N (0, 1 xi1 2 + 2 xi2 + + k xik + i ). The xi
School: Georgia State
Course: MATH MODELS FOR COMPUTER SCI
SPRING 2015 MATH 3030 MW 3:00 - 4:15 PM, Langdale Hall 601 Instructor: Xiaojing Ye, xye@gsu.edu, COE 704, Phone: 413-6444. Oce Hours: MW 2:00-2:50 PM. Textbook: (Required) Advanced Engineering Mathematics, 10th edition by E. Kreyszig, Wiley 2011. (We cove
School: Georgia State
Course: Discrete Math
COURSE SYLLABUS MATH 2420DISCRETE MATHEMATICS SUMMER, 2015 (Math 2420 Section 005, CRN 50333) Day and Time: MW 4:45-7:15pm. Room: Langdale Hall 403 Instructor: Dr. Mariana Montiel Office: COE 708 Direct phone: (404) 413-6414 e-mail: mmontiel@gsu.edu Offic
School: Georgia State
Course: Calculus Of One Variable I
MATH-2211 Syllabus Course Syllabus MATH-2211 - Calculus of One Variable I Spring semester, 2015 Course: MATH-2211 Calculus of One Variable I (CRN: 10657) Text: Calculus: One and Several Variables, 10th Edition by Salas, Hille & Etgen; Wiley, 2007, ISBN 97
School: Georgia State
Course: Calculus Of One Variable II
MATH-2212 Syllabus Course Syllabus MATH-2212 - Calculus of One Variable II Summer semester, 2015 Course: MATH-2212 Calculus of One Variable II (CRN: 54003) Text: (Required) Calculus: One and Several Variables, 10th Edition by Salas, Hille & Etgen; Wiley,
School: Georgia State
Course: Mathematical Modeling
Georgia State University Department of Computer Information Systems Course Syllabus CIS8630 (CRN xxxxx) Business Computer Forensics and Incident Response Spring 2010 Instructors : Name Office Office Hours Office Phone Office Fax Email Richard Baskerville
School: Georgia State
Course: Mathematical Modeling
CIS 4140E Spring 2010 Implementing IT-Facilitated Business Processes Richard Welke, Ph.D. Director, Center for Process Innovation Professor, Computer Information Systems Robinson College of Business Georgia State University Proposed Catalog Description Im
School: Georgia State
Course: Elementary Statistics
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 B C D E F G H I J Math 1070 Excel Project (Due: Friday, November 15, 2
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
Math 2211 Spring 2009 Test 1 Review Definition 2.2.1. The limit of a function. Let f be a function defined at least on an open interval (c-p,c+p) except possibly at c itself. We say that lim f ( x) = L x c if for each > 0, there exist > 0 such that if 0 <
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
2211 Spring 2009 Test 1 Name_ Show all necessary work in your blue book. No credit will be given for incorrect work or answers without work. Please use a new page for each problem. Please use pencil. When finished, place this question paper in your blue b
School: Georgia State
Course: Mathematical Models For Computer Science
MATH-3030, Summer-2012 Quiz #5 Your name: MATH-3030 Math Models for CS CRN 52440 Quiz 5 Sections C.13.5-C.13.6,C.14.1-C.14.2,C.15.4,C.16.2,C.16.4 Directions: Do the quiz on your own paper and attach to this quiz assignment sheet. Clearly show all your wor
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Solutions 1. Evaluate the limit if it exists (or clearly state and prove that it doesnt exist if thats the case): x2 + 2x 15 =? x5 x+5 (x + 5)(x 3) x2 + 2x 15 = lim = lim (x 3) = 8. lim x5 x5 x5 x+5 x+5 1 1 +t lim 3 =? t3 3 +
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Name: MATH-2211 Calculus-I CRN 808 Test-1 Directions: Do the test on your own paper and attach it to this test sheet (or in your blue book and put the test sheet inside). Sign your name and the CRN number on the test sheet. Cl
School: Georgia State
Course: Math Modeling
Year 1965 1974 1979 1983 1985 1987 1990 1992 1993 1995 2000 TotalPop. AllMales AllFemales 42.4 51.9 33.9 37.1 43.1 32.1 33.5 37.5 29.9 32.1 35.1 29.5 30.1 32.6 27.9 28.8 31.2 26.5 25.5 28.4 22.8 26.5 28.6 24.6 25 27.7 22.5 24.7 27 22.6 23.3 25.7 21 Males
School: Georgia State
Course: Math Modeling
Test 1 study guide (Show all your work) Math 1101 Fall 11 No.: _ Name: _ 1. i). Consider the following table. s t 70 149 73 175 66 146 66 126 64 138 A) Is t a function of s ? B Is s a function of t ? ii). The following table gives values for a function f(
School: Georgia State
Course: Math Modeling
Name: Ryan Lees No.: Due Oct 25th in class. Semester Project 2 Regression Line The following table shows (for the years 1965 to 2000 and for people 18 and over) the total percentage of cigarette smokers, the percentage of males who are smokers, and the pe
School: Georgia State
Course: Geometry And Spatial Sense
. Activity Two Congruent Halves <f the figures that follow, draw a line from dot to dot to cut the figure in half in such a way that the two .-es are congruent. The dotted line illustrates how the first one can be done. -f Can you think of a way that coul
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
6.890: Algorithmic Lower Bounds Fall 2014 Prof. Erik Demaine Problem Set 4 Due: Wednesday, November 12th, 2014 Problem 1. Given a graph G = (V, E), a connected dominating set D V is a set of vertices such that the subgraph of G induced by D is connected,
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
B. 1 Proof of the Well-ordering Theorem We follow the pattern outlined in Exercises 2-7 on pp. 72-73 of the text. Then h: J-YE. be well-ordered sets; let ar;d E J Let Theorem B.1. the following are equivalent: of or a section E equals h(J) is order preser
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set : The Discrete Fourier Transform Assigned: October 16, 2008 Due: October 23, 2008 Problem 1: A 128 mill
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
2.092/2.093 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS I FALL 2009 Quiz #2-solution Instructor: TA: Prof. K. J. Bathe Seounghyun Ham Problem 1 (10 points): 1 x y 1 x f his = 1 (1 y ) ; hi = 1 1+ . 4 2 2 4 2 his, x = 1 x 1 (1 y ) ; his, y = 1 . 4 2 8
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Solution of Problem Set 7 Assigned: October 30, 2008 Due: November 6, 2008 Problem 1: There are a number of ways to
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Solution of Problem Set 9 Assigned: November 20, 2008 Due: December 4, 2008 Problem 1: + x = + 1 x(ex )dx = ex (x )
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set : FIR Linear Filters Assigned: October 30, 2008 Due: November 6, 2008 Problem 1: Prove the linear phase
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 9 Assigned: November 20, 2008 Problem 1: Due: December 4, 2008 Given a waveform x(t) with a pdf of the
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
2.092/2.093 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS I FALL 2009 Quiz #2 Instructor: TA: Prof. K. J. Bathe Seounghyun Ham Problem 1 (10 points): A planar (two-dimensional) analysis of a fluid-structure system is to be performed. The simple model shown
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set : FIR Linear Filters Assigned: November 6, 2008 Due: November 18, 2008 Problem 1: A Mini-project: An Au
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Solution of Problem Set 8: FIR Linear Filters Assigned: November 6, 2008 Due: November 18, 2008 Problem 1: The stan
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8 9
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
B. 1 Proof of the Well-ordering Theorem We follow the pattern outlined in Exercises 2-7 on pp. 72-73 of the text. Then h: J-YE. be well-ordered sets; let ar;d E J Let Theorem B.1. the following are equivalent: of or a section E equals h(J) is order preser
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
1 2 3 4 5 6 7 8 9
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
A.1 Set Theory and Logic: Fundamental Concepts Notes by Dr. J. Santos) A.1. Primitive Concepts. In mathematics, the notion of a set is a primitive notion. That is, we admit, as a starting point, the existence of certain objects (which we call sets), which
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
1 2 3 4 5 6 7 8 9
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
1 2 3 4 5 6 7 8 9
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
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School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
1 2 3 4 5 6 7 8
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
1 2 3 4 5 6 7 8 9 10
School: Georgia State
Course: RESEARCH
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School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
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School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
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School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
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School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
0 Wm {5mm Meier M Qvm Efcavex gD (06; as perfova m Llrh but can he smoo AQQXovonrov ~Po orer z [1950/1173] _~_ evevg comwx vyxeihrig +090 (9? q sphere, Ts V90»in as HAQ/ surce, o a uniciae convex 3D b009, MBEVOND Poo/HEW ~ Wm? \05 th'rhg argum 6911 + AQeK
School: Georgia State
Course: COMPLEX ANALYSIS
Basic Concepts of Inference Statistical nference is the process of making conclusions using data that is subject to random variation. Here are some basic denitions. Bias( ) := ( ) computed from data. , where is the true parameter value and is an estimate
School: Georgia State
Course: COMPLEX ANALYSIS
Central Limit Theorem (Convergence of the sample means distribution to the normal distribution) Let X1 , X2 , . . . , Xn be a random sample drawn from any distribution with a nite mean and variance 2 . As n ! 1, the distribution of: X p / n converges to t
School: Georgia State
Course: MATH 2212
Plant Reproduction Biol 2108 Lab Moss Moss Life Cycle Moss Sporophyte (Sphagnum) Moss Young Gametophyte Moss Antheridial Head Moss Archegonial Head Moss Protonema Moss Capsule Fern Fern Young Sporophyte Fern Antheridia Fern Archegonia Fern Indusium Fern S
School: Georgia State
Course: MATH 2212
Protostomes Annelida Annelida Mollusca Arthropoda Platyhelminthes Evolutionary Relationships Amongst Animals Ecdysozoans & Lophotrochozoans In ancient times the protostomes split into 2 major clades that have been evolving independently ever since Lopho
School: Georgia State
Course: MATH 2212
Plant Growth & Hormones Seed Dormancy Seed dormancy may last for weeks, months, years, or even centuries. What are the advantages of dormancy? Germination Plant Hormones What is a hormone? Hormones Naturally occurring regulatory compounds Substances tha
School: Georgia State
Course: Elementary Statistics
January 23, 2008 [LECTURE 6] What you need to know What you need to remember 1. One notice In a normal distribution, , , is actually the mean, and is the standard deviation. One interesting & important property of normal distribution 1
School: Georgia State
Course: Elementary Statistics
January 18, 2008 [LECTURE 5] What you need to remember for today's lecture? 1. IQR and outliers The interquartile range (IQR) is the distance between the first and third quartiles (the length of the box in the boxplot) IQR = Q3 - Q1 An outlier
School: Georgia State
Course: Elementary Statistics
January 16, 2008 [LECTURE 4] What you need to remember from today's lecture I. Measure of spread: quartiles and standard deviation Quartiles are three numbers that describe the trend, or statistically, the spread of the data. The calculation
School: Georgia State
Course: Elementary Statistics
January 14, 2008 [LECTURE 3] I. Stemplots: How to make a stemplot: 1) Separate each observation into a stem, consisting of all but the final (rightmost) digit, and a leaf, which is that remaining final digit. Stems may have as many digits as nee
School: Georgia State
Course: Elementary Statistics
January 11, 2008 [LECTURE 2] What you need to remember for today's class I. Histograms: The range of values that a variable can take is divided into equal-size intervals. The histogram shows the number of individual data points that fall in each
School: Georgia State
Course: Elementary Statistics
January 9, 2008 [OUTLINE OF LECTURE 1] What you need to know for today's lecture I. II. III. What is statistics, and what do statisticians do? Why statistics is useful in everyday life? What can you expect from statistics and statisticians? Wha
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
Math 2211 Spring 2009 Test 1 Review Definition 2.2.1. The limit of a function. Let f be a function defined at least on an open interval (c-p,c+p) except possibly at c itself. We say that lim f ( x) = L x c if for each > 0, there exist > 0 such that if 0 <
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
2211 Spring 2009 Test 1 Name_ Show all necessary work in your blue book. No credit will be given for incorrect work or answers without work. Please use a new page for each problem. Please use pencil. When finished, place this question paper in your blue b
School: Georgia State
Course: Mathematical Models For Computer Science
MATH-3030, Summer-2012 Quiz #5 Your name: MATH-3030 Math Models for CS CRN 52440 Quiz 5 Sections C.13.5-C.13.6,C.14.1-C.14.2,C.15.4,C.16.2,C.16.4 Directions: Do the quiz on your own paper and attach to this quiz assignment sheet. Clearly show all your wor
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Solutions 1. Evaluate the limit if it exists (or clearly state and prove that it doesnt exist if thats the case): x2 + 2x 15 =? x5 x+5 (x + 5)(x 3) x2 + 2x 15 = lim = lim (x 3) = 8. lim x5 x5 x5 x+5 x+5 1 1 +t lim 3 =? t3 3 +
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Name: MATH-2211 Calculus-I CRN 808 Test-1 Directions: Do the test on your own paper and attach it to this test sheet (or in your blue book and put the test sheet inside). Sign your name and the CRN number on the test sheet. Cl
School: Georgia State
Course: Math Modeling
Test 1 study guide (Show all your work) Math 1101 Fall 11 No.: _ Name: _ 1. i). Consider the following table. s t 70 149 73 175 66 146 66 126 64 138 A) Is t a function of s ? B Is s a function of t ? ii). The following table gives values for a function f(
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
6.890: Algorithmic Lower Bounds Fall 2014 Prof. Erik Demaine Problem Set 4 Due: Wednesday, November 12th, 2014 Problem 1. Given a graph G = (V, E), a connected dominating set D V is a set of vertices such that the subgraph of G induced by D is connected,
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set : The Discrete Fourier Transform Assigned: October 16, 2008 Due: October 23, 2008 Problem 1: A 128 mill
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
2.092/2.093 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS I FALL 2009 Quiz #2-solution Instructor: TA: Prof. K. J. Bathe Seounghyun Ham Problem 1 (10 points): 1 x y 1 x f his = 1 (1 y ) ; hi = 1 1+ . 4 2 2 4 2 his, x = 1 x 1 (1 y ) ; his, y = 1 . 4 2 8
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
2.092/2.093 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS I FALL 2009 Quiz #2 Instructor: TA: Prof. K. J. Bathe Seounghyun Ham Problem 1 (10 points): A planar (two-dimensional) analysis of a fluid-structure system is to be performed. The simple model shown
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.004 Dynamics and Control II Fall 2007 Quiz 1 Friday, October 5, 2007 Duration: 50min (11:0511:55am) A DC motor is connected to an opamp circuit in cascade as shown in Figure 1. T
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
2.092/2.093 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS I FALL 2009 Quiz #1 Instructor: TA: Prof. K. J. Bathe Seounghyun Ham Problem 1 (10 points): Consider the solution of the problem shown below. A rod is spinning in steady-state at rad/sec. The rod is
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
2.092/2.093 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS I FALL 2009 Quiz #1-solution Instructor: TA: Prof. K. J. Bathe Seounghyun Ham Problem 1 (10 points): a) x (1) u (1) (x)=H U= 1 60 x 60 0 U x x (2) u (2) (x)=H U= 0 1U 100 100 where U= [ U1 U2 T U
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Solution of Problem Set 5: The Discrete Fourier Transform Assigned: October 16, 2008 Due: October 23, 2008 Problem
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
6.001, Spring Semester, 20057Qu1'z I 7 Sample Solutions 2 Part 1: (20 points) For each of the following expressions or sequences of expressions, state the value returned as the result of evaluating the nal expression in each set, or indicate that the eval
School: Georgia State
Course: RESEARCH
18.305 Exam 2, December 6, 04. Closed Book. 1. Find, for R ; 1, the leading term for each of the following integrals: 2 4 2 a. X e ?Rx +x dx. 15 points. 1 K 4 2 b. X e iRx +x dx. 15 points. ?K c. X K ?K e iR sinh x dx. bonus 20 points. 2. Consider the di
School: Georgia State
Course: RESEARCH
NAME: Sample Solutions Part 1: (25 points) Question 1: (define (rotate-left cycle) (cdr cycle) Question 2: (define (rotate-right cycle) (define (aux where start) (if (eq? (cdr where) start) where (aux (cdr where) start) (aux cycle cycle) (Question_3: (def
School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
18.305 Exam 1, October 18, 04. Closed Book. Problem: Consider the differential equation y + x 4 y : 0. (a) Locate and classify the singular points, finite or infinite, of this differential equation. (10%) (b) Find the WKB solutions of this equation. For w
School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 2 Assigned: Sept. 18, 2008 Due: Sept. 25, 2008 Problem 1: A waveform f (t) with a real even spectrum F
School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Solution of Problem Set 2 Assigned: Sept. 18, 2008 Due: Sept. 25, 2008 Problem 1: Y (j) = H(j)F (j) and it is shown
School: Georgia State
Course: MATHEMATICAL STATISTICS II
SOLUTIONS TO 18.01 EXERCISES 2. Applications of Dierentiation 2A. Approximation 2A-1 p d p b b ) f (x) a + p x by formula. a + bx = p dx 2 a 2 a + bx By algebra: 2A-2 D( 1 (1 a p p a + bx = a r 1+ bx p bx a(1 + ), same as above. a 2a 1 b 1 )= ) f (x) a
School: Georgia State
Course: ANALYSIS II
1. Compute the following integral: Z 4 p t ln t dt 1 We apply integration by parts: v = 2p t3/2 3 dv = t dt u = ln t du = 1 dt t Then: Z 4 p Z 4 4 2 3/2 2 3/2 t ln t t t 1 dt 3 3 | cfw_z 1 1 t1/2 4 2 3/2 4 3/2 t ln t t 3 9 1 16 4 3/2 ln 4 (4 1) 3 9 16 28
School: Georgia State
Course: ANALYSIS II
Implicit Dierentiation and the Second Derivative Calculate y 00 using implicit dierentiation; simplify as much as possible. x2 + 4y 2 = 1 Solution As with the direct method, we calculate the second derivative by dierentiating twice. With implicit dierenti
School: Georgia State
Course: ANALYSIS II
18.01 EXERCISES Unit 1. Dierentiation 1A. Graphing 1A-1 By completing the square, use translation and change of scale to sketch b) y = 3x2 + 6x + 2 a) y = x2 2x 1 1A-2 Sketch, using translation and change of scale 2 a) y = 1 + |x + 2| b) y = (x 1)2 1A-3 I
School: Georgia State
Course: ANALYSIS II
Implicit Dierentiation and the Chain Rule The chain rule tells us that: d (f dx g) = df dg . dg dx While implicitly dierentiating an expression like x + y 2 we use the chain rule as follows: d 2 d(y 2 ) dy (y ) = = 2yy 0 . dx dy dx Why can we treat y as a
School: Georgia State
Course: ANALYSIS II
1. Compute the following derivatives. (Simplify your answers when possible.) (a) f 0 (x) where f (x) = f 0 (x) = x 1 1(1 x2 x2 ) (x)( 2x) 1 x2 + 2x2 1 + x2 = = (1 x2 )2 (1 x2 )2 (1 x2 )2 (b) f 0 (x) where f (x) = ln(cos x) 1 2 sin (x) 2 1 1 ( sin x) 2 si
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Solution of Problem Set 7 Assigned: October 30, 2008 Due: November 6, 2008 Problem 1: There are a number of ways to
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Solution of Problem Set 9 Assigned: November 20, 2008 Due: December 4, 2008 Problem 1: + x = + 1 x(ex )dx = ex (x )
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set : FIR Linear Filters Assigned: October 30, 2008 Due: November 6, 2008 Problem 1: Prove the linear phase
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 9 Assigned: November 20, 2008 Problem 1: Due: December 4, 2008 Given a waveform x(t) with a pdf of the
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set : FIR Linear Filters Assigned: November 6, 2008 Due: November 18, 2008 Problem 1: A Mini-project: An Au
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Solution of Problem Set 8: FIR Linear Filters Assigned: November 6, 2008 Due: November 18, 2008 Problem 1: The stan
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
6 856 Randomized Algorithms David Karger Handout #8, September 30, 2002 Homework 3 Solutions Problem We may think of asking a resident as ipping a coin with bias p=f. Flip the coin N times. If you get k heads, set p = k/N . Note k has a binomial distribut
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
6 856 Randomized Algorithms David Karger Handout #5, September 18, 2002 Homework 3, Due 9/25 M. R. refers to this text: Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995. 1. Based on MR 4.1. Suppos
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 6: The Transform and Linear Filters Assigned: October 23, 2008 Due: October 30, 2008 Problem 1: A linea
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
2.094 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS SPRING 2008 Homework 8 - Solution Instructor: Assigned: Due: Prof. K. J. Bathe 04/10/2008 04/17/2008 Problem 1 (20 points): Since H , h b , we only consider the displacement u in the x1 -direction with th
School: Georgia State
Course: EPISTEMOLOGY ADV MATH CONCEPTS
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 6 Solution Assigned: October 23, 2008 Due: October 30, 2008 Problem 1: Given the dierence equation, yn
School: Georgia State
Course: RESEARCH
6 856 Randomized Algorithms David Karger Handout #4, September 21, 2002 Homework 1 Solutions M. R. refers to this text: Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995. Problem MR 1.8. (a) The mi
School: Georgia State
Course: RESEARCH
2.094 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS SPRING 2008 Homework 7 - Solution Instructor: Assigned: Due: Prof. K. J. Bathe 04/03/2008 04/10/2008 Problem 1 (20 points): (a) 1 cos 45 sin 45 2 0 0 0 t X = t R tU = sin 45 cos 45 0 t 0 X= ( X) 0 t 1
School: Georgia State
Course: RESEARCH
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 3: Analog Filter design Assigned: Sept. 25, 2008 Due: Oct. 2, 2008 Problem 1: Consider the following tw
School: Georgia State
Course: RESEARCH
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 3 Solution: Analog Filter design Problem 1: Use the nomenclature in the class handout. For both lters:
School: Georgia State
Course: RESEARCH
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Solution of Problem Set 4 Assigned: Oct. 2, 2008 Due: Oct. 9, 2008 Problem 1: We have shown in class (see the Fouri
School: Georgia State
Course: RESEARCH
6.856 - Randomized Algorithms David Karger Handout #3, September 11, 2000 - Homework 2, Due 9/18 M.R. refers to this text: Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995. 1. MR 1.8. 2. MR 2.3. C
School: Georgia State
Course: RESEARCH
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 4 Assigned: Oct. 2, 2008 Problem 1: Due: Oct. 9, 2008 An AM (amplitude-modulated) radio signal f f M (t
School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
6 856 Randomized Algorithms David Karger Handout #2, September 5, 2002 Homework 1, Due 9/11 M. R. refers to this text: Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995. 1. MR 1.1. (a) Suppose you
School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
j j j Y k j k j kA j I9IIG G A61h%R Q @ C G B i G I q G S 9 I 9 Q q i S E @i uHw w B VC a @ C B i G I qj G E I 9 1Vs1A1PhHE A6ikpi G C %VDkh6tHlATS Ik16Pu1lu1`Y%DB Ys6W%D1%1m%VgkvW5AV%tsA% 6W%1h6%1AAV1thcfw_DuV1kVtmg 9IIG G RQ Qi RQ B X9 R Q i B
School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
6 856 Randomized Algorithms David Karger Handout #4, September 17, 2002 Homework 1 Solutions M.R. refers to this text: Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995. Problem 1 MR 1.1. (a) We re
School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing Continuous and Discrete Fall Term 2008 Problem Set 1 Solution: Convolution and Fourier Transforms Problem 1: Use the convolution definition y (t ) = f $ h =
School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
2.094 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS SPRING 2008 Homework 6 - Solution Instructor: Assigned: Due: Prof. K. J. Bathe 03/13/2008 03/20/2008 Problem 1 (20 points): t Lets define R = t t R t F t , F= and U = . 2kL 2kL L t Since t F = t R at equ
School: Georgia State
Course: NUMERICAL LINEAR ALGEBRA
M SS CHUSETTS INSTITUTE OF TECHNOLOGY DEP RTMENT OF MECH NIC L ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 1: Convolution and Fourier Transforms Assigned: Sept. 9, 2008 Due: Sept. 18, 2008 Problem 1: a) Plot th
School: Georgia State
Course: MATHEMATICAL STATISTICS II
Evaluating an Interesting Limit Using lim n!1 1+ 1 n n = e, calculate: 3n 1 1. lim 1 + n!1 n 5n 2 2. lim 1 + n!1 n 5n 1 3. lim 1 + n!1 2n Solution 3n 1 1. lim 1 + n!1 n n 1 . n!1 n In this problem we do this by using rules of exponents to remove the 3 fro
School: Georgia State
Course: MATHEMATICAL STATISTICS II
Comparing Linear Approximations to Calculator Computations In lecture, we explored linear approximations to common functions at the point x = 0. In this worked example, we use the approximations to calculate values of the sine function near x = 0 and comp
School: Georgia State
Course: MATHEMATICAL STATISTICS II
Product of Linear Approximations Suppose we have two complicated functions and we need an estimate of the value of their product. We could multiply the functions out and then approximate the result, or we could approximate each function separately and the
School: Georgia State
Course: MATHEMATICAL STATISTICS II
Compound Interest If you invest P dollars at the annual interest rate r, then after one year the interest is I = rP dollars, and the total amount is A = P + I = P (1 + r). This is simple interest. For compound interest, the year is divided into k equal ti
School: Georgia State
Course: MATHEMATICAL STATISTICS II
Hyperbolic Angle Sum Formula Find sinh(x + y) and cosh(x + y) in terms of sinh x, cosh x, sinh y and cosh y. Solution sinh(x + y) Recall that: eu + e u . 2 2 The easiest way to approach this problem might be to guess that the hyperbolic trig. angle sum fo
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
Lab Report 5- KH 3650 ° What are the physiological factors that limit V02 max? Would these factors be different for a trained person from a sedentary person? The highest V02 recorded in absolute terms was 3.97[L/ min), in relative terms it was 53.3 [ml/kg
School: Georgia State
Course: COMPLEX ANALYSIS
Chapter 7 Notes - Inference for Single Samples You know already for a large sample, you can invoke the CLT so: X N (, 2 ). Also for a large sample, you can replace an unknown by s. You know how to do a hypothesis test for the mean, either: calculate z-
School: Georgia State
Course: COMPLEX ANALYSIS
Chapter 9 Notes, Part 1 - Inference for Proportion and Count Data We want to estimate the proportion p of a population that have a specic attribute, like what percent of houses in Cambridge have a mouse in the house? We are given X1 , . . . , Xp where Xi
School: Georgia State
Course: COMPLEX ANALYSIS
$ " !$ ( ' " & / + ', 0 " $ !' # - . 0 " ' 1 " ' / ! !' 02 1' 0 ! !' 03 1' & / ' $ ) $& 0 /' & / * # ' $& ! $ /& $ 0& $ /) $% $' % * ! % ! '
School: Georgia State
Course: COMPLEX ANALYSIS
Chapter 14 Nonparametric Statistics A.K.A. distribution-free statistics! Does not depend on the population tting any particular type of distribution (e.g, normal). Since these methods make fewer assumptions, they apply more broadly. at the expense of a le
School: Georgia State
Course: COMPLEX ANALYSIS
Chapter 11 : Multiple Linear Regression We have: height weight . . . age person 1: person 2: : x12 x22 x11 x21 . . x1k x2k amount of lemonade purchased y1 y2 where we assume Yi = 0 + for i = 1, . . . , n and i N (0, 1 xi1 2 + 2 xi2 + + k xik + i ). The xi
School: Georgia State
Course: ADVANCED NUMERICAL ANALYSIS
«WWMWWWWWM.WFMWN~_W.M.,._MW Ordim/xo 999 Equqons Unknown 'wain A) n- 113 d > ODE? , 2( n; -)'f7lt j<> i 0 3! 171%; nlocdzro ODQ (m) 0 - , / 31¢ F 33 mm 3A - an {s «1 Khamawovg ed/M g WNW, w my oDE ' Czcx) 53 + C, or) g 35,00? > _ 5 (A )élénwhw; a! J 3
School: Georgia State
Course: ADVANCED NUMERICAL ANALYSIS
' 6%Mqni xiv" (if M1963 : 0 H: wkfwjulaf 17" 'F i 9 ( x: 9:10 1 Rod :1 RmeO I J Club/(23% (90711,fo a: R viz/56:60: Gamma Qkaq, Nr' I - 2 (53:) 73° Em Tm: 0mg 6, 22) 1 Wfsfi"'jirm mm we. mm aw M if). mng W Qiinxkeaa, éolvrhan 093115591 0' (4)1405?)wa
School: Georgia State
Course: ADVANCED NUMERICAL ANALYSIS
a) I I; If S} Shfmruouvfue 2m um , . _ A, ., wove 01)? xtj +1.11 (xHZrbcb 0} anal» + 509903.:qu mm 4119, #4)qu a; x _ 2" 9W ODE o?- purm Q(x)149\{)34@z(wwi013(ng " ' W Le PM in anmtcwi y , u- I? 91. is,va : gausm, b a: mm by 9:» A PM 3 (, ' V Chi z 0
School: Georgia State
Course: TOPICS IN APPLIED MATH
Problems: Vector Fields 1. Sketch the following vector elds. Pay attention to their names because we will be encountering these elds frequently. (a) Force, constant gravitational eld F(x, y) = gj. x y i+ 2 j = hx, yi/r2 . (This is a shrinking radial eld 2
School: Georgia State
Course: METH OF REGRESSION/ANAL OF VAR
fl 0 h mm, . Kn méi. m. "+ = (i. R Ah, =>, 4h, H V Mu)?" (tins;- - géWFCI£fL I h _-_Ca|:\n;-I' r out Effigg4'5! Kin.- , . . {m ' ._ ,.i_x.ijwag4" ' dag; ' H _. . . _ . wry 5 _{.?"i-"Y'°?°_»_ "3'_'="7) ,. . ivdecw; R=£Vj°twa2 _ _. .A
School: Georgia State
Course: FOUND OF NUMBERS & OPERATIONS
The Tangent Approximation 1. The tangent plane. w For a function of one variable, w = f (x), the tangent line to its graph at a point (x0 , w0 ) is the line passing through (x0 , w0 ) and having slope dw dx w=f(x,y) . w=f(x,y 0) 0 For a function of two va
School: Georgia State
Course: FOUND OF NUMBERS & OPERATIONS
StokesI Theorem Our text states and proves Stokes' Theorem in 12.11, but ituses the scalar form for writing both the line integral and the surface integral involved. In the applications, it is the vector form of the theorem that is most likely to be quote
School: Georgia State
Course: DIRECTED READINGS
GREEN'S THEOREN AND I T S APPLICATIONS The d i s c u s s i o n i n 1 1 . 1 9 - 11.27 o f , Apostol i s n o t complete n o r e n t i r e l y r i g o r o u s , a s t h e a u t h o r himself p o i n t s o u t . We give here a rigorous treatment. nr e e n ' s
School: Georgia State
Course: NUMERICAL ANALYSIS I
Problems: Non-independent Variables 1. Find the total dierential for w = zxey + xez + yez . Answer: dw = zey dx + zxey dy + xey dz + ez dx + xez dz + ez dy + yez dz = (zey + ez )dx + (zxey + ez )dy + (xey + xez + yez )dz. 2. With w as above, suppose we ha
School: Georgia State
Course: NUMERICAL ANALYSIS I
Problems: Chain Rule Practice One application of the chain rule is to problems in which you are given a function of x and y with inputs in polar coordinates. For example, let w = (x2 + y 2 )xy, x = r cos and y = r sin . @w 1. Use the chain rule to nd . @r
School: Georgia State
Course: NUMERICAL ANALYSIS I
Problems: Lagrange Multipliers 1. Find the maximum and minimum values of f (x, y) = x2 + x + 2y 2 on the unit circle. Answer: The objective function is f (x, y). The constraint is g(x, y) = x2 + y 2 = 1. Lagrange equations: fx = gx , 2x + 1 = 2x fy = gy ,
School: Georgia State
Course: NUMERICAL ANALYSIS I
(page 350) 9.1 Polar Coordinates CHAPTER 9 9.1 POLAR COORDINATES AND COMPLEX NUMBERS Polar Coordinates (page 350) Circles around the origin are so important that they have their own coordinate system - polar coordinates. The center at the origin is someti
School: Georgia State
Course: INTRO TO STATISTICAL METHODS
M.1 The exponential and logarithm functions In this section, we study the exponential and logarithm functions and derive their pr0perties. We also dene ab for a > 0 and b arbitrary, and we verify the laws of expo- nents. As we did for the trig functions,
School: Georgia State
Course: INTRO TO STATISTICAL METHODS
Proof of Lagrange Multipliers Here we will give two arguments, one geometric and one analytic for why Lagrange multipliers work. Critical points For the function w = f (x, y, z) constrained by g(x, y, z) = c (c a constant) the critical points are dened as
School: Georgia State
Course: INTRO TO STATISTICAL METHODS
Least Squares Interpolation 1. Use the method of least squares to t a line to the four data points (0, 0), (1, 2), (2, 1), (3, 4). Answer: We are looking for the line y = ax + b that best models the data. The deviation of a data point (xi , yi ) from the
School: Georgia State
Course: BIOSTATISTICS
Speed and arc length 1. A rocket follows a trajectory r(t) = x(t) i + y(t) j = 10t i + ( 5t2 + 10t)j. Find its speed and the arc length from t = 0 to t = 1. Answer: p dr ds p 2 = 10i+( 10t+10)j ) = 10 + ( 10t + 10)2 = 10 1 + (1 dt dt Z 1 Z 1p ds Arc lengt
School: Georgia State
Course: BIOSTATISTICS
Partial derivatives Partial derivatives Let w = f (x, y) be a function of two variables. Its graph is a surface in xyz-space, as w pictured. w=f(x,y) Fix a value y = y0 and just let x vary. You get a function of one variable, (1) w = f (x, y0 ), w=f(x,y 0
School: Georgia State
Course: BIOSTATISTICS
Intersection of a line and a plane 1. Consider the plane P = 2x + y 4z = 4. a) Find all points of intersection of P with the line x = t, y = 2 + 3t, z = t. b) Find all points of intersection of P with the line x = 1 + t, y = 4 + 2t, z = t. c) Find all poi
School: Georgia State
Course: MATH MODELS FOR COMPUTER SCI
SPRING 2015 MATH 3030 MW 3:00 - 4:15 PM, Langdale Hall 601 Instructor: Xiaojing Ye, xye@gsu.edu, COE 704, Phone: 413-6444. Oce Hours: MW 2:00-2:50 PM. Textbook: (Required) Advanced Engineering Mathematics, 10th edition by E. Kreyszig, Wiley 2011. (We cove
School: Georgia State
Course: Discrete Math
COURSE SYLLABUS MATH 2420DISCRETE MATHEMATICS SUMMER, 2015 (Math 2420 Section 005, CRN 50333) Day and Time: MW 4:45-7:15pm. Room: Langdale Hall 403 Instructor: Dr. Mariana Montiel Office: COE 708 Direct phone: (404) 413-6414 e-mail: mmontiel@gsu.edu Offic
School: Georgia State
Course: Calculus Of One Variable I
MATH-2211 Syllabus Course Syllabus MATH-2211 - Calculus of One Variable I Spring semester, 2015 Course: MATH-2211 Calculus of One Variable I (CRN: 10657) Text: Calculus: One and Several Variables, 10th Edition by Salas, Hille & Etgen; Wiley, 2007, ISBN 97
School: Georgia State
Course: Calculus Of One Variable II
MATH-2212 Syllabus Course Syllabus MATH-2212 - Calculus of One Variable II Summer semester, 2015 Course: MATH-2212 Calculus of One Variable II (CRN: 54003) Text: (Required) Calculus: One and Several Variables, 10th Edition by Salas, Hille & Etgen; Wiley,
School: Georgia State
Course: Mathematical Modeling
Georgia State University Department of Computer Information Systems Course Syllabus CIS8630 (CRN xxxxx) Business Computer Forensics and Incident Response Spring 2010 Instructors : Name Office Office Hours Office Phone Office Fax Email Richard Baskerville
School: Georgia State
Course: Mathematical Modeling
CIS 4140E Spring 2010 Implementing IT-Facilitated Business Processes Richard Welke, Ph.D. Director, Center for Process Innovation Professor, Computer Information Systems Robinson College of Business Georgia State University Proposed Catalog Description Im