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School: UCSB
Course: A Concise Introduction To Pure Mathematics
Homework 1 Solutions Kyle Chapman October 26, 2012 9.1 True, True, False, True, False, False, True, False, True 9.2 a D and E b You can only deduce that it is not D. 9.3 a Not valid, would be D C then D C . b Valid, this is contraposition. C D then D C c
School: UCSB
Course: Transitions To Higher Mathematics
Math 8 - Solutions to Home Work 2 Due: October 11, 2007 1. Every/Only. Sometimes sentences with the words only and every can be conditional statements in disguise. For example, Every even number is a multiple of two. can be rephrased as If a number is eve
School: UCSB
Homework 1 Solutions 1. (#1.1.2 in Strauss) Which of the following operators are linear? (a) Lu = ux + xuy (b) Lu = ux + uuy (c) Lu = ux + u2 y (d) Lu = ux + uy + 1 (e) Lu = 1 + x2 (cos y )ux + uyxy [arctan(x/y )]u Solution: (a) Linear. (b) Nonlinear the
School: UCSB
Math 108A Winter Quarter 2014 Practice Problems for Midterm No notes or calculators are permitted on this exam. To obtain full credit you must show all work, provide complete proofs, and provide short but complete explanations for all questions in the Tru
School: UCSB
Course: Numerical Analysis
University of California, Santa Barbara Department of Statistics & Applied Probability PSTAT 120B, Probability & Statistics, Spring 2010 Instructor: Jarad Niemi Email: niemi@pstat.ucsb.edu Course hours: MWF 10:00-10:50am in HFH 1104 TAs: Varvara Kulikova
School: UCSB
Math 108A Winter Quarter 2014 Practice Problems for Final No notes or calculators are permitted on this exam. You must show all work, provide complete proofs, and provide short by complete explanations for all questions in the True/False section in your B
School: UCSB
Course: Probability Theory And Stochastic Processes
PStat 213A: Probability Theory and Stochastic Processes Simon RubinsteinSalzedo Fall 2005 0.1 Introduction These notes are based on a graduate course on probability theory and stochastic processes I took from Professor Raya Feldman in the Fall of 2005. Th
School: UCSB
Course: Vector Calculus
3.2 07/08/15 Chain Rule 3.2 CONTENTS 07/08/15 Chain Rule We now begin to pursue the Fundamental Theorem of Calculus (FTC). Recall that the FTC states that derivatives and integrals are in some sense inverse operations. We rst explore the FTC and its relat
School: UCSB
Course: Vector Calculus
2.3 07/01/15 Critical Points & Extreme Values 2 VECTOR DIFFERENTIATION 2.3 2.3.1 07/01/15 Critical Points & Extreme Values Directional Derivatives and the Gradient Announcements Homework 02 is posted on Gauchospace and due next Wednesday July 8th at 4:20
School: UCSB
Course: Vector Calculus
3.1 07/07/15 Constrained Optimization: Lagrange Multipliers ONTENTS C 3.1 3.1.1 07/07/15 Constrained Optimization: Lagrange Multipliers The Self-Driving Car Let t = time and 0 t T = length of trip p : [0, T ] R2 is target route c : [0, T ] R2 is actual ro
School: UCSB
Course: Vector Calculus
1.2 06/23/15 Dot & Cross Product 1.2 CONTENTS 06/23/15 Dot & Cross Product Announcements: Homework 01 is due as soon as WeBWork is enabled. Jay Roberts oce hours are TR 2:00 PM-3:00 PM. The change is reected on the syllabus. Recall that Rn is the collec
School: UCSB
Course: Vector Calculus
2 VECTOR DIFFERENTIATION 2 Vector Dierentiation 2.1 2.1.1 06/29/15 Curves & Surfaces Review of Paths & Curves Announcements: The number of homework problems have been reduced to 50. The homework is due next Friday at 11:42AM You must take the midterm n
School: UCSB
Math 34A Lecture 17 Copyright Daryl Cooper D.A.R.Y.L. Please do NOT come on stage November 9, 2012 Homework 7.13.43 Some biologists at UCSB have carefully recorded the number of elephant seal births in the Channel Islands from aerial photographs since the
School: UCSB
School: UCSB
M1 (0 {:3 Sngw Er; am; Emilia gAĆ©w k" . I 3 C? i Q RE} .WMW:.;~; ER R if}; PE} WW3? NJ W}? Le; g 53 6ijcv 1}: a mm 2} 3 KQOKQEWW 9% mĆ©gk An :3 \m dim C '1 ML Ev l W4? Wu E .36: -7 {wwmmggim . A 2:; 2ng Egg} V %& x if m \ , ' g fgmwwgmphgwmgkfkk fmail.
School: UCSB
5; NA. 9 a {H 2% Ā«1 v: R Cd) "*9 (wxk o- a; (E M. \I}. < sax L \.x. NVĀ»?! NEW?Ā» g _ .va . y M h a rem. we imamdufu W .1. , . E: .5 w 3. 1.)Ā» g m ,1Ā». . nff _ . . 4. PK MW : k x a; p {L v .uL Mm 3. uni m 7, av km xxw/ n L {L WV. fax aka
School: UCSB
School: UCSB
School: UCSB
Math 108A Winter Quarter 2014 Practice Problems for Midterm No notes or calculators are permitted on this exam. To obtain full credit you must show all work, provide complete proofs, and provide short but complete explanations for all questions in the Tru
School: UCSB
Math 108A Winter Quarter 2014 Practice Problems for Final No notes or calculators are permitted on this exam. You must show all work, provide complete proofs, and provide short by complete explanations for all questions in the True/False section in your B
School: UCSB
Course: Calc With Appli 2
MATH 3B EXAM I PRACTICE January 13, 2011 JEFFREY STOPPLE In these notes you will come up with your own practice exam questions. This will better help internalize the material. You should solve your own exam, or if you have a study partner you should switc
School: UCSB
Course: Vector Calculus 2
Math 5C: Exam #2 Solutions Date: July 16th , 2010 Score: out of 60 1. (10) Match each Maclaurin series to the function from the following list it represents by lling in the blank space below the series. (Note: All listed function are C at x = 0 under the
School: UCSB
Course: Calculus
Being the final examination for Math 3B NO notes or calculators. READ all questions carefully. Make sure your answers are clearly marked and it is clear what work is relevant and should be graded. Each problem is worth 20 points. Note there is a blank pag
School: UCSB
Introduction to Numerical Analysis Math 104A, Winter 2009 Instructor: Carlos J. Garc a-Cervera March 17th, 2009 Answer the following 8 questions. Show all your work for full credit. You must include your computer programs. Follow the guidelines for presen
School: UCSB
Course: A Concise Introduction To Pure Mathematics
Homework 1 Solutions Kyle Chapman October 26, 2012 9.1 True, True, False, True, False, False, True, False, True 9.2 a D and E b You can only deduce that it is not D. 9.3 a Not valid, would be D C then D C . b Valid, this is contraposition. C D then D C c
School: UCSB
Course: Transitions To Higher Mathematics
Math 8 - Solutions to Home Work 2 Due: October 11, 2007 1. Every/Only. Sometimes sentences with the words only and every can be conditional statements in disguise. For example, Every even number is a multiple of two. can be rephrased as If a number is eve
School: UCSB
Homework 1 Solutions 1. (#1.1.2 in Strauss) Which of the following operators are linear? (a) Lu = ux + xuy (b) Lu = ux + uuy (c) Lu = ux + u2 y (d) Lu = ux + uy + 1 (e) Lu = 1 + x2 (cos y )ux + uyxy [arctan(x/y )]u Solution: (a) Linear. (b) Nonlinear the
School: UCSB
Homework 5 Math 104A, Fall 2010 Due on Tuesday, November 9th, 2010 1. Given xi , i = 0, 1, . . . , n, consider the Lagrange polynomials Ln,j for j = 0, 1, . . . , n. Prove that n Ln,j (x) = 1 for all x R. j =0 2. The following data is taken from a polynom
School: UCSB
Course: 117
Homework 2 Hctor Guillermo Cullar R e e os February 2, 2006 12.12 Let D be a nonempty set and suppose that f : D R and g : D R. Dene the function f + g : D R by (f + g)(x) = f (x) + g(x). (a) If f (D) and g(D) are bounded above, then prove that (f
School: UCSB
Course: Differential Equations
chew cn CTGKGNS am '9' Gmle book a 3903; $Ā¢a17> RTeiew Maa In {Ramada- =eve13w has an assign a I. Go over an Iccker aueson, [new in 5 a 2' 1'? We WW; Chow. queous from and 10PTCTD make a {Lest Jaunuf, wa-h mm: Alwags check 86W answer? (like eignveerm' CM
School: UCSB
School: UCSB
Course: Math 4A
Math 4A Midterm Review Prolbems Note: These problems are provided as review of the key ideas that well be tested on the midterm, but this is not a practice midterm. Because we are testing your understanding of concepts and not simply computational uency,
School: UCSB
Course: Differential Equations
Mathematics 4B Winter 2015: Review for Final March 12, 2015 Professor J. Douglas Moore YOU ARE ALLOWED ONE 3 x 5 CARD FOR THE FINAL EXAM. Recall that there is assigned seating for the nal exam. Please write your seat number on your card. You will need to
School: UCSB
School: UCSB
School: UCSB
Course: Numerical Analysis
University of California, Santa Barbara Department of Statistics & Applied Probability PSTAT 120B, Probability & Statistics, Spring 2010 Instructor: Jarad Niemi Email: niemi@pstat.ucsb.edu Course hours: MWF 10:00-10:50am in HFH 1104 TAs: Varvara Kulikova
School: UCSB
Course: Vector Calculus
Math 6A - Vector Calculus with Applications, First Course Instructor: Oce: E-mail: Oce Hours: Lectures: Classroom: Jon Tjun Seng Lo Kim Lin Graduate Tower, Oce 6431H jlokimlin@math.ucsb.edu TR 1:00 PM-2:00 PM, also available by appointment. MTWR 8:00 AM-9
School: UCSB
SPRING 2015, MATH 6 B, VECTOR CALCULUS 2 INSTRUCTOR : Gustavo Ponce (o. SH 6505 #8938365) SCHEDULE : TR 330 445 ROOM : HFH 1104 INSTRUCTOR OFFICE HOURS : T. 5 6, R. 11 12, 5 6. TEACHING ASSISTANT : Kathleen Hake (SH 6431 K), Garo Sarajian (SH 6432 F) TEAC
School: UCSB
Math 6A - Vector Calculus with Applications, First Course Instructor: Oce: E-mail: Oce Hours: Lectures: Amanda R. Curtis Graduate Tower, Oce 6432Q arcurtis@math.ucsb.edu MTWR 1:00 PM-2:00 PM, also available by appointment. MTWR 3:30-4:35PM, 3515 Phelps Ha
School: UCSB
Course: Vector Calculus
Math 6A (Vector Calculus) Syllabus1 TR, 11:00 AM to 12:15 PM, Room 1701 in Theater/Dance West Instructor/E-mail: Jordan Schettler (jcs@math.ucsb.edu) Ofce Hours: Tuesday 2-3 pm, Friday 9-10 am, or by appointment, South Hall, Room 6721 Website: Use the cou
School: UCSB
Course: Homological Algebra
Math 236B, Spring 2015, MWF 9-9:50, HSSB 1223 Homological Algebra Instructor: Birge Huisgen-Zimmermann, SH 6518, Oce hours M, F 11 - 12, W 12:30 1:30. Accompanying texts, as for the winter quarter: The manuscript I will put on the board will again serve
School: UCSB
Course: A Concise Introduction To Pure Mathematics
Homework 1 Solutions Kyle Chapman October 26, 2012 9.1 True, True, False, True, False, False, True, False, True 9.2 a D and E b You can only deduce that it is not D. 9.3 a Not valid, would be D C then D C . b Valid, this is contraposition. C D then D C c
School: UCSB
Course: Transitions To Higher Mathematics
Math 8 - Solutions to Home Work 2 Due: October 11, 2007 1. Every/Only. Sometimes sentences with the words only and every can be conditional statements in disguise. For example, Every even number is a multiple of two. can be rephrased as If a number is eve
School: UCSB
Homework 1 Solutions 1. (#1.1.2 in Strauss) Which of the following operators are linear? (a) Lu = ux + xuy (b) Lu = ux + uuy (c) Lu = ux + u2 y (d) Lu = ux + uy + 1 (e) Lu = 1 + x2 (cos y )ux + uyxy [arctan(x/y )]u Solution: (a) Linear. (b) Nonlinear the
School: UCSB
Math 108A Winter Quarter 2014 Practice Problems for Midterm No notes or calculators are permitted on this exam. To obtain full credit you must show all work, provide complete proofs, and provide short but complete explanations for all questions in the Tru
School: UCSB
Course: Numerical Analysis
University of California, Santa Barbara Department of Statistics & Applied Probability PSTAT 120B, Probability & Statistics, Spring 2010 Instructor: Jarad Niemi Email: niemi@pstat.ucsb.edu Course hours: MWF 10:00-10:50am in HFH 1104 TAs: Varvara Kulikova
School: UCSB
Math 108A Winter Quarter 2014 Practice Problems for Final No notes or calculators are permitted on this exam. You must show all work, provide complete proofs, and provide short by complete explanations for all questions in the True/False section in your B
School: UCSB
Course: Calc With Appli 2
MATH 3B EXAM I PRACTICE January 13, 2011 JEFFREY STOPPLE In these notes you will come up with your own practice exam questions. This will better help internalize the material. You should solve your own exam, or if you have a study partner you should switc
School: UCSB
Homework 5 Math 104A, Fall 2010 Due on Tuesday, November 9th, 2010 1. Given xi , i = 0, 1, . . . , n, consider the Lagrange polynomials Ln,j for j = 0, 1, . . . , n. Prove that n Ln,j (x) = 1 for all x R. j =0 2. The following data is taken from a polynom
School: UCSB
Course: 117
Homework 2 Hctor Guillermo Cullar R e e os February 2, 2006 12.12 Let D be a nonempty set and suppose that f : D R and g : D R. Dene the function f + g : D R by (f + g)(x) = f (x) + g(x). (a) If f (D) and g(D) are bounded above, then prove that (f
School: UCSB
Course: Vector Calculus 2
Math 5C: Exam #2 Solutions Date: July 16th , 2010 Score: out of 60 1. (10) Match each Maclaurin series to the function from the following list it represents by lling in the blank space below the series. (Note: All listed function are C at x = 0 under the
School: UCSB
Course: Calculus
Being the final examination for Math 3B NO notes or calculators. READ all questions carefully. Make sure your answers are clearly marked and it is clear what work is relevant and should be graded. Each problem is worth 20 points. Note there is a blank pag
School: UCSB
Course: Probability Theory And Stochastic Processes
PStat 213A: Probability Theory and Stochastic Processes Simon RubinsteinSalzedo Fall 2005 0.1 Introduction These notes are based on a graduate course on probability theory and stochastic processes I took from Professor Raya Feldman in the Fall of 2005. Th
School: UCSB
Course: Differential Equations
-7 -3 -1 1 -2 26.(1 pt) 0 -2 -1 -2 -28 -12 -6 3 . 32.(1 pt) Let M = -2 3 Compute the rank of the above matrix -2 2 1 Find c1 , c2 , and c3 such that M 3 + c1 M 2 + c2 M + c3 I3 = 0, where 7 4 7 I3 is the identity 3 3 matrix. 27.(1 pt) 7 4 3 , c1 = 21 12
School: UCSB
Introduction to Numerical Analysis Math 104A, Winter 2009 Instructor: Carlos J. Garc a-Cervera March 17th, 2009 Answer the following 8 questions. Show all your work for full credit. You must include your computer programs. Follow the guidelines for presen
School: UCSB
Course: Graph Theory
HOMEWORK 3 SOLUTIONS (1) Show that for each n N the complete graph Kn is a contraction of Kn,n . Solution: We describe the process for several small values of n. In this way, we can discern the inductive step. Clearly, K1 , which is just one vertex, is a
School: UCSB
Introduction to Numerical Analysis Math 104A, Winter 2009 Instructor: Carlos J. Garc a-Cervera December 8th, 2010 Answer the following 7 questions. Show all your work for full credit. You must include your computer programs. Follow the guidelines for pres
School: UCSB
Math 34A Lecture 17 Copyright Daryl Cooper D.A.R.Y.L. Please do NOT come on stage November 9, 2012 Homework 7.13.43 Some biologists at UCSB have carefully recorded the number of elephant seal births in the Channel Islands from aerial photographs since the
School: UCSB
Course: Differential Equations
Sample WeBWorK problems. 1.(1 pt) Which of the following are vectors in R2 ? A. (1,0,0) B. (1,0) C. x2 D. x E. 1 F. (0,1) G. None of the above Which of the following is the zero vector in R2 ? A. 0 B. (0,0,0) C. (0,0) D. None of the above Which pairs belo
School: UCSB
October 15, 2011 13:47 ast Sheet number 3 Page number xx cyan magenta yellow black October 10, 2011 15:10 frs Sheet number 3 Page number iii cyan magenta yellow black 10 th EDITION David Henderson/Getty Images CALCULUS EARLY TRANSCENDENTALS HOWARD ANTON I
School: UCSB
Course: Vector Calculus
3.2 07/08/15 Chain Rule 3.2 CONTENTS 07/08/15 Chain Rule We now begin to pursue the Fundamental Theorem of Calculus (FTC). Recall that the FTC states that derivatives and integrals are in some sense inverse operations. We rst explore the FTC and its relat
School: UCSB
Course: Vector Calculus
2.3 07/01/15 Critical Points & Extreme Values 2 VECTOR DIFFERENTIATION 2.3 2.3.1 07/01/15 Critical Points & Extreme Values Directional Derivatives and the Gradient Announcements Homework 02 is posted on Gauchospace and due next Wednesday July 8th at 4:20
School: UCSB
Course: Vector Calculus
3.1 07/07/15 Constrained Optimization: Lagrange Multipliers ONTENTS C 3.1 3.1.1 07/07/15 Constrained Optimization: Lagrange Multipliers The Self-Driving Car Let t = time and 0 t T = length of trip p : [0, T ] R2 is target route c : [0, T ] R2 is actual ro
School: UCSB
Course: Vector Calculus
1.2 06/23/15 Dot & Cross Product 1.2 CONTENTS 06/23/15 Dot & Cross Product Announcements: Homework 01 is due as soon as WeBWork is enabled. Jay Roberts oce hours are TR 2:00 PM-3:00 PM. The change is reected on the syllabus. Recall that Rn is the collec
School: UCSB
Course: Vector Calculus
2 VECTOR DIFFERENTIATION 2 Vector Dierentiation 2.1 2.1.1 06/29/15 Curves & Surfaces Review of Paths & Curves Announcements: The number of homework problems have been reduced to 50. The homework is due next Friday at 11:42AM You must take the midterm n
School: UCSB
Course: Vector Calculus
1.1 06/22/15 Vector Basics 1.1 CONTENTS 06/22/15 Vector Basics In calculus, we previously studied functions f: RR (1) with domain R (or a subset) which produce real numbers as output. For example f (x) = x2 (2) The study of functions of more than one vari
School: UCSB
Course: Vector Calculus
1.3 06/24/15 Lines & Planes 1.3 1.3.1 CONTENTS 06/24/15 Lines & Planes Lines in R2 through the origin Announcements: There was an typo in yesterdays lecture notes. The cross product is v w = (v2 w3 v3 w2 , v3 w1 v1 w3 , v1 w2 v2 w1 ). (62) Therefore, i j
School: UCSB
Course: Vector Calculus
1.4 06/25/15 Paths in Rn 1.4 1.4.1 CONTENTS 06/25/15 Paths in Rn Lines in R2 The line through x0 = (x0 , y0 ) and perpendicular (orthogonal) to n = (A, B) consists of the set of points x = (x, y) satisfying the expression Ax + By + C (standard form) (99)
School: UCSB
Course: Vector Calculus
3.3 07/09/15 Vector Fields 3.3 CONTENTS 07/09/15 Vector Fields Denition 2. A vector eld is a function F : Rn Rn (dimensions must match!) (40) Denition 3. Suppose the vector eld F : Rn Rn satises the equation F= V (41) for some real-valued function V : Rn
School: UCSB
Course: Vector Calculus
4.2 07/14/15 Double Integrals 4.2 4.2.1 CONTENTS 07/14/15 Double Integrals Volume beneath a Surface Denition 3. The rectangle R = [a, b] [c, d] in R2 consists of all points (x, y) satisfying y d axb c cxd a b x Question 2. Given a function f : R2 R (which
School: UCSB
Course: Probability Theory And Stochastic Processes
PStat 213A: Probability Theory and Stochastic Processes Simon RubinsteinSalzedo Fall 2005 0.1 Introduction These notes are based on a graduate course on probability theory and stochastic processes I took from Professor Raya Feldman in the Fall of 2005. Th
School: UCSB
Course: Vector Calculus
3.2 07/08/15 Chain Rule 3.2 CONTENTS 07/08/15 Chain Rule We now begin to pursue the Fundamental Theorem of Calculus (FTC). Recall that the FTC states that derivatives and integrals are in some sense inverse operations. We rst explore the FTC and its relat
School: UCSB
Course: Vector Calculus
2.3 07/01/15 Critical Points & Extreme Values 2 VECTOR DIFFERENTIATION 2.3 2.3.1 07/01/15 Critical Points & Extreme Values Directional Derivatives and the Gradient Announcements Homework 02 is posted on Gauchospace and due next Wednesday July 8th at 4:20
School: UCSB
Course: Vector Calculus
3.1 07/07/15 Constrained Optimization: Lagrange Multipliers ONTENTS C 3.1 3.1.1 07/07/15 Constrained Optimization: Lagrange Multipliers The Self-Driving Car Let t = time and 0 t T = length of trip p : [0, T ] R2 is target route c : [0, T ] R2 is actual ro
School: UCSB
Course: Vector Calculus
1.2 06/23/15 Dot & Cross Product 1.2 CONTENTS 06/23/15 Dot & Cross Product Announcements: Homework 01 is due as soon as WeBWork is enabled. Jay Roberts oce hours are TR 2:00 PM-3:00 PM. The change is reected on the syllabus. Recall that Rn is the collec
School: UCSB
Course: Vector Calculus
2 VECTOR DIFFERENTIATION 2 Vector Dierentiation 2.1 2.1.1 06/29/15 Curves & Surfaces Review of Paths & Curves Announcements: The number of homework problems have been reduced to 50. The homework is due next Friday at 11:42AM You must take the midterm n
School: UCSB
Course: Vector Calculus
1.1 06/22/15 Vector Basics 1.1 CONTENTS 06/22/15 Vector Basics In calculus, we previously studied functions f: RR (1) with domain R (or a subset) which produce real numbers as output. For example f (x) = x2 (2) The study of functions of more than one vari
School: UCSB
Course: Vector Calculus
1.3 06/24/15 Lines & Planes 1.3 1.3.1 CONTENTS 06/24/15 Lines & Planes Lines in R2 through the origin Announcements: There was an typo in yesterdays lecture notes. The cross product is v w = (v2 w3 v3 w2 , v3 w1 v1 w3 , v1 w2 v2 w1 ). (62) Therefore, i j
School: UCSB
Course: Vector Calculus
1.4 06/25/15 Paths in Rn 1.4 1.4.1 CONTENTS 06/25/15 Paths in Rn Lines in R2 The line through x0 = (x0 , y0 ) and perpendicular (orthogonal) to n = (A, B) consists of the set of points x = (x, y) satisfying the expression Ax + By + C (standard form) (99)
School: UCSB
Course: Vector Calculus
3.3 07/09/15 Vector Fields 3.3 CONTENTS 07/09/15 Vector Fields Denition 2. A vector eld is a function F : Rn Rn (dimensions must match!) (40) Denition 3. Suppose the vector eld F : Rn Rn satises the equation F= V (41) for some real-valued function V : Rn
School: UCSB
Course: Vector Calculus
4.2 07/14/15 Double Integrals 4.2 4.2.1 CONTENTS 07/14/15 Double Integrals Volume beneath a Surface Denition 3. The rectangle R = [a, b] [c, d] in R2 consists of all points (x, y) satisfying y d axb c cxd a b x Question 2. Given a function f : R2 R (which
School: UCSB
Course: Vector Calculus
5.3 07/22/15 Flux Integrals 5.3 CONTENTS 07/22/15 Flux Integrals Since r and r are tangent to the surface (i.e. lie in the tangent plane to at each u v point on ), then their cross product r r is perpendicular to the tangent plane to the u v surface at ea
School: UCSB
Course: Vector Calculus
5.1 07/20/15 Path Integrals and Greens Theorem 5.1 5.1.1 CONTENTS 07/20/15 Path Integrals and Greens Theorem Path Independence f d r is independent of the path between any Theorem 1. In a region R, the line integral C f d r = 0 for every closed curve C wh
School: UCSB
Course: Vector Calculus
4.1 07/13/15 Path (Line) Integrals CONTENTS 4.1 07/13/15 Path (Line) Integrals 4.1.1 Intuitive idea behind Line Integrals In single-variable calculus you learned how to integrate a real-valued function f (x) over an interval [a, b] in R. This integral (us
School: UCSB
Course: Vector Calculus
4.3 07/15/15 Change of Variables CONTENTS 4.3 07/15/15 Change of Variables 4.3.1 Interchanging Order of Integration Example 10. Find the volume V under the plane z = 8x + 6y over the region R = cfw_(x, y) : 0 x 1, 0 y 2x2 . Using vertical slices we get: y
School: UCSB
Course: Vector Calculus
4.4 07/16/15 Triple Integrals 4.4 4.4.1 CONTENTS 07/16/15 Triple Integrals Double Integrals in PSTAT Example 17. A famous distribution function is given by the standard normal distribution, whose probability density function (PDF) f is 1 2 f (x) = ex /2 ,
School: UCSB
Course: Vector Calculus
6.1 07/27/15 6.1 6.1.1 CONTENTS 07/27/15 The parallelogram law Example 1. Find the area of the triangle that is determined by the points (2, 2, 0), (1, 0, 2), and (0, 4, 3). The area of the triangle, say A, is half the area of the parallelogram determined
School: UCSB
Using Mathematica to Solve Dierenital Equations Math 4B: Winter 2015 John Douglas Moore In solving dierential equations, it is sometimes necessary to do calculations which would be prohibitively dicult to do by hand. Fortunately, computers can do the calc
School: UCSB
Course: Linear Algebra
" Sq , l (L ) w W o p e r ms (E ) qn t rp ,U l v(i v , T& t r k y fEr /1/ (th 1y . t cn r r ) ri x L o u # _ /H w " - l ti m . . . " " " l yh . ; 0 1 1 B Y/ /B3 , , ) Scanned by CamS
School: UCSB
Math 34A Lecture 17 Copyright Daryl Cooper D.A.R.Y.L. Please do NOT come on stage November 9, 2012 Homework 7.13.43 Some biologists at UCSB have carefully recorded the number of elephant seal births in the Channel Islands from aerial photographs since the
School: UCSB
School: UCSB
M1 (0 {:3 Sngw Er; am; Emilia gAĆ©w k" . I 3 C? i Q RE} .WMW:.;~; ER R if}; PE} WW3? NJ W}? Le; g 53 6ijcv 1}: a mm 2} 3 KQOKQEWW 9% mĆ©gk An :3 \m dim C '1 ML Ev l W4? Wu E .36: -7 {wwmmggim . A 2:; 2ng Egg} V %& x if m \ , ' g fgmwwgmphgwmgkfkk fmail.
School: UCSB
5; NA. 9 a {H 2% Ā«1 v: R Cd) "*9 (wxk o- a; (E M. \I}. < sax L \.x. NVĀ»?! NEW?Ā» g _ .va . y M h a rem. we imamdufu W .1. , . E: .5 w 3. 1.)Ā» g m ,1Ā». . nff _ . . 4. PK MW : k x a; p {L v .uL Mm 3. uni m 7, av km xxw/ n L {L WV. fax aka
School: UCSB
School: UCSB
School: UCSB
School: UCSB
School: UCSB
,g M '-' - g) Find the Fourier series of x) = g for :c E (~7z, 7r]. Pme 2: x .33 eĀ§L E \ E} "W VJ TL, TL Q 'l \ ~ g 9 MEN wimĆ©jp war smgwĆ©x T'L " Kg m u i} N any GECN(. .j:"ll'*l"i (b) Compute 5320253 using (2) to nd the value of Ā°Ā°1 2152' k: _|
School: UCSB
Math 4B Lecture 9 February 3, 2015 Doug Moore Announcements. 1. Midterm this Thursday. You should know linear DEs (differential equations), exact dierentials, Cauchy-Euler polygon and homogeneous linear second order DEs with constant coefcients. No calcul
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Math 4B Lecture 16 February 26, 2015 Doug Moore Electrical circuits give rise to complicated systems of dierential equations. Circuits which include linear resistors, inductors, and capacitors give rise to linear systems of equations. Other circuit elemen
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Math 4B Lecture 14 February 19, 2015 Doug Moore . Our next goal is to consider the circuit given by a resistor of resistance R, an inductor of inductance L, and a capacitor of capacitance C, connected in series to a source of electromotive force E(t). Let
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Math 4B Lecture 15 February 24, 2015 Doug Moore Announcements. 1. i-Clicker scores are now posted on gauchospace. You get one point for attending when you answer most of the questions in a given lecture. (The number of questions you need to answer depends
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Math 4B Lecture 12 February 12, 2015 Doug Moore The method of variation of parameters, also known as variation of constants, was discovered by Euler and Lagrange, and used to understand perturbations of planetary motion from the exact elliptical motion pr
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Math 4B Lecture 13 February 17, 2015 Doug Moore In the last several lectures, we have studied how to solve certain nonhomogeneous second order linear dierential equations, which are of the form d2 x dx + Q(t)x = R(t), + P (t) dt2 dt where L is the linear
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Math 4B Lecture 17 March 3, 2015 Doug Moore Our rst goal today is to discuss phase portraits for homogeneous systems of dierential equations of the form dx1 /dt = a11 x1 + a12 x2 + . . . + a1n xn , dx2 /dt = a21 x1 + a22 x2 + . . . + a2n xn , dxn /dt = an
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Math 4B Lecture 20 March 12, 2015 Doug Moore A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature. Henri Poincar (1854-1912) e Announcements. 1
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Math 4B Lecture 18 March 5, 2015 Doug Moore Linear systems of dierential equations of the form dx1 /dt = a11 x1 + a12 x2 + . . . + a1n xn + f1 (t), dx2 /dt = a21 x1 + a22 x2 + . . . + a2n xn + f2 (t), dxn /dt = an1 x1 + an2 x2 + . . . + ann xn + fn (t). c
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Math 4B Lecture 19 March 10, 2015 Doug Moore Announcements. 1. If you have not yet registered your i-Clicker, be sure to do so on gauchospace. Once you have registered you will credit for i-Clicker scores from the beginning of the quarter. 2. If you have
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Math 4B Lecture 11 February 10, 2015 Doug Moore Announcement. 1. New deadline for Homework on Wiley Plus. Assignments will be due Saturday at 11:45 pm (not Friday). Let V = cfw_ functions f : R R which have continuous derivatives of all orders . If f and
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Math 4B Lecture 7 January 27, 2015 Doug Moore Einstein is wrong (but not too wrong) because actually log 2 = .693147. not .72. A good approximation, however, is . log 2 = .7 So it should be the law of sevens, not the slightly misstated rule of 72 appearin
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Math 4B Lecture 8 January 29, 2015 Doug Moore Announcements. 1. Midterm next Thursday. You should know linear DEs (dierential equations), exact dierentials, Cauchy-Euler polygon and homogeneous linear second order DEs with constant coecients (treated toda
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Math 4B Lecture 2 January 8, 2015 Doug Moore Announcements. 1. WileyPLUS Homework 1 has been assigned and is due Friday, January 9 at 11:45 pm. (Read Chapter 1 in the text to prepare for the homework.) This assignment will NOT count as part of your grade.
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Math 4B Lecture 4 January 15, 2015 Doug Moore Review of rst-order linear dierential equations. To solve the dierential equation d (t2 + 1)y = cos t dt we simply integrate both sides to obtain (1) (t2 + 1)y = sin t + c. But the dierential equation (1) migh
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Math 4B Lecture 1 January 6, 2015 Doug Moore Announcements. 1. The TAs, Changliang Wang, Xingshan Cui, Lan Liu, Peter Merkx and Laura Veith, will give quizzes in discussion sections almost every week (but not the rst week). 2. My oce hours will be Wednesd
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Math 4B Lecture 5 January 20, 2015 Doug Moore ANNOUNCEMENTS: 1. If you have problems accessing WileyPlus you should try to clearing your browser cache and cookies, and if that doesnt work try using a dierent browser. 2. If there seems to be a mistake in a
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Math 4B Lecture 6 January 22, 2015 Doug Moore Reviewing the method of exact dierentials. Given the dierential equation dy = 0, M (x, y) + N (x, y) dx we rst rewrite it as M (x, y)dx + N (x, y)dy = 0, then try to nd a function (x, y) such that d = M (x, y)
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Math 4B Lecture 3 January 13, 2015 Doug Moore There are several explicit methods for solving the simplest rst order dierential equations: I. If the rst-order dierential equation can be written in the form, M (x)dx + N (y)dy = 0, the equation is separable,
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Course: Calculus For Social And Life Sciences
Math 34B Lecture 23 Copyright Daryl Cooper D.A.R.Y.L. March 9, 2015 The graph of a function f (x) of one variable is the curve y = f (x) in the xy -plane. The tangent line to the graph at the point x = u is the straight line which goes through the point o
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Course: Calculus For Social And Life Sciences
Math 34B Lecture 22 Copyright Daryl Cooper D.A.R.Y.L. March 6, 2015 f (x, y ) = 2x + 3y + xy + x 2 y 3 A = 6x 2 y B = 2y 3 C = 2 + y + 2xy 3 fx = f x = 2 + y + 2xy 3 fy = f y = 3 + x + 3x 2 y 2 fxx = x f x fyy = y f y fyx = y f x fxy = x f y = = 2y 3 6x 2
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Math 108A Winter Quarter 2014 Practice Problems for Midterm No notes or calculators are permitted on this exam. To obtain full credit you must show all work, provide complete proofs, and provide short but complete explanations for all questions in the Tru
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Math 108A Winter Quarter 2014 Practice Problems for Final No notes or calculators are permitted on this exam. You must show all work, provide complete proofs, and provide short by complete explanations for all questions in the True/False section in your B
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Course: Calc With Appli 2
MATH 3B EXAM I PRACTICE January 13, 2011 JEFFREY STOPPLE In these notes you will come up with your own practice exam questions. This will better help internalize the material. You should solve your own exam, or if you have a study partner you should switc
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Course: Vector Calculus 2
Math 5C: Exam #2 Solutions Date: July 16th , 2010 Score: out of 60 1. (10) Match each Maclaurin series to the function from the following list it represents by lling in the blank space below the series. (Note: All listed function are C at x = 0 under the
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Course: Calculus
Being the final examination for Math 3B NO notes or calculators. READ all questions carefully. Make sure your answers are clearly marked and it is clear what work is relevant and should be graded. Each problem is worth 20 points. Note there is a blank pag
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Introduction to Numerical Analysis Math 104A, Winter 2009 Instructor: Carlos J. Garc a-Cervera March 17th, 2009 Answer the following 8 questions. Show all your work for full credit. You must include your computer programs. Follow the guidelines for presen
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Introduction to Numerical Analysis Math 104A, Winter 2009 Instructor: Carlos J. Garc a-Cervera December 8th, 2010 Answer the following 7 questions. Show all your work for full credit. You must include your computer programs. Follow the guidelines for pres
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Course: Vector Calculus
MATH 6A Final Exam, Session A, Summer 2015 Name: Perm #: I have read and understand the directions below, and I pledge that I have neither given nor received any unauthorized assistance on this exam. (signature) Directions: 1. Dont panic. 2. Show all your
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Course: Vector Calculus
MATH 6A Midterm, Session A, Summer 2015 Name: Perm #: I have read and understand the directions below, and I pledge that I have neither given nor received any unauthorized assistance on this exam. (signature) Directions: 1. Dont panic. 2. Show all your wo
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MATH 6-B SPRING 2015 MIDTERM; _PERMIT: SOLVE ALL PROBLEMS. Put your nal answer in BOXES. Write clearly. Show your work. Otherwise no partialcredit. Q 1. (15 points) m Q 2. (10 points) _ Q 3. (15 points) _ Q 4. (10 points) m_ MID-TERM. 2 MATH 6-B SPRIN G
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MATH 6-B SPRING 2015 MID-TERM. SOLVE ALL PROBLEMS. Put your nal answer in BOXES. Write clearly. Show your work. Otherwise no partial credit. Q l. (15 points) _m Q 2. (10 points) _m _ Q 3. (15 points) _ Q 4. (10 points) _ 2 MATH 6-B - SPRING 2015 MID-TE
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version PRINT NAME A Math 34A Fall 2009 Prof Cooper Tardis Midterm #1 no calculators Quality Bonus SCORE 2 16 Put final answers in boxes on this page. When a question says SHOW WORK put high quality work in the blue book. Points might be awarded for this.
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version Tardis Midterm 2 Red PRINT name no calculators Math 34A Winter 2010 Prof D.A.R.Y.L. Quality Bonus Signature 2 22 SCORE Put final answers in boxes on this page. SHOW WORK for all questions in the blue book. If your work does not match your answer w
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version PRINT NAME Red Math 34A Winter 2011 Prof D.A.R.Y.L. Tardis Midterm #1 no calculators Quality Bonus SCORE 2 16 Put final answers in boxes on this page. SHOW WORK in the blue book. If the work in the blue book does not match the answer you give on t
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version PRINT NAME A Math 34A Fall 2012 Prof D.A.R.Y.L. Tardis Midterm #1 no calculators Quality Bonus SCORE 2 16 Put final answers in boxes on this page. SHOW WORK in the blue book. If the work in the blue book does not match the answer you give on this
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version Red Math 34A Fall 2010 Prof D.A.R.Y.L. PRINT NAME Tardis Quality Bonus Midterm #2 no calculators SCORE 2 24 Put final answers in boxes on this page. SHOW WORK in the blue book. If the work in the blue book does not match the answer you give on thi
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version Math 34A Winter 2011 Midterm #1 Prof D.A.R.Y.L. n0 calculators Tard is SCORE 16 Put nal answers in boxes on this page. SHOW WORK in the blue book. If the work in the blue book does not match the answer you give on this test we may investigate. Num
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Course: A Concise Introduction To Pure Mathematics
Homework 1 Solutions Kyle Chapman October 26, 2012 9.1 True, True, False, True, False, False, True, False, True 9.2 a D and E b You can only deduce that it is not D. 9.3 a Not valid, would be D C then D C . b Valid, this is contraposition. C D then D C c
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Course: Transitions To Higher Mathematics
Math 8 - Solutions to Home Work 2 Due: October 11, 2007 1. Every/Only. Sometimes sentences with the words only and every can be conditional statements in disguise. For example, Every even number is a multiple of two. can be rephrased as If a number is eve
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Homework 1 Solutions 1. (#1.1.2 in Strauss) Which of the following operators are linear? (a) Lu = ux + xuy (b) Lu = ux + uuy (c) Lu = ux + u2 y (d) Lu = ux + uy + 1 (e) Lu = 1 + x2 (cos y )ux + uyxy [arctan(x/y )]u Solution: (a) Linear. (b) Nonlinear the
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Homework 5 Math 104A, Fall 2010 Due on Tuesday, November 9th, 2010 1. Given xi , i = 0, 1, . . . , n, consider the Lagrange polynomials Ln,j for j = 0, 1, . . . , n. Prove that n Ln,j (x) = 1 for all x R. j =0 2. The following data is taken from a polynom
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Course: 117
Homework 2 Hctor Guillermo Cullar R e e os February 2, 2006 12.12 Let D be a nonempty set and suppose that f : D R and g : D R. Dene the function f + g : D R by (f + g)(x) = f (x) + g(x). (a) If f (D) and g(D) are bounded above, then prove that (f
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Course: Graph Theory
HOMEWORK 3 SOLUTIONS (1) Show that for each n N the complete graph Kn is a contraction of Kn,n . Solution: We describe the process for several small values of n. In this way, we can discern the inductive step. Clearly, K1 , which is just one vertex, is a
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October 15, 2011 13:47 ast Sheet number 3 Page number xx cyan magenta yellow black October 10, 2011 15:10 frs Sheet number 3 Page number iii cyan magenta yellow black 10 th EDITION David Henderson/Getty Images CALCULUS EARLY TRANSCENDENTALS HOWARD ANTON I
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2.1 FIRST-ORDER LINEAR EQUATIONS MATH 124A HW 02 You are encouraged to collaborate with your classmates and utilize internet resources provided you adhere to the following rules: (i) You read the problem carefully and make a serious effort to solve it bef
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Course: Introduction To Partial Differential Equations
7.3 GREENS FUNCTIONS MATH 124B Solution Key HW 07 PRELIMINARIES: All of our arguments rely on the fact that the function 1 for n = 1, 2 |x x 0 | 1 log | x x0 | for n = 2, v(x) = v(x; x0 ) = 2 1 | x x0 |2n for n 3 (2 n) An where x and x0 represent disti
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Course: Introduction To Partial Differential Equations
5.3 ORTHOGONALITY AND GENERAL FOURIER SERIES MATH 124B Solution Key HW 02 5.3 ORTHOGONALITY AND GENERAL FOURIER SERIES 1. (a) Find the real vectors that are orthogonal to the given vectors (1, 1, 1) and (1, 1, 0). (b) Choosing an answer to (a), expand the
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Course: MATH 3A
ESTRATIFICAO Na falta de mudas de certas espcies no mercado, tanto pela raridade quanto pelo alto preo cobrado, compensa em muito comear com sementes. Algumas dessas espcies podem precisar de estratificao. O que estratificao? A estratificao um tipo de que
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Course: MATH 3A
DETALHES ESTRATIFICAO Na falta de mudas de certas espcies no mercado, tanto pela raridade quanto pelo alto preo cobrado, compensa em muito comear com sementes. Algumas dessas espcies podem precisar de estratificao. O que estratificao? A estratificao um ti
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Course: MATH 3A
THE METRIC SYSTEM The metric system or SI (International System) is the most common system of measurements in the world, and the easiest to use. The base units for the metric system are the units of: length, measured in meters (m); time, measured in secon
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Course: MATH 3A
January 2001 Mathbits Minnesota Council of Teachers of Mathematics www.mctm.org NCTMS Principles and Standards for School Mathematics The Principles Equity This article continues a series on the NCTM Principles and Standards for School Mathematics for the
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Course: MATH 3A
PENGENALAN Matematik didefinisikan sebagai pembelajaran atau kajian mengenai kuantiti, corak struktur, perubahan dan ruang, atau dalam erti kata lain, kajian mengenai nombor dan gambar rajah. Matematik juga ialah penyiasatan aksiomatik yang menerangkan st
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Course: MATH 3A
Zavod za primjenjenu geodeziju Geodetskog fakulteta ZAGREB Datum i sat Stajalite Girus Vizurna toka 1 2 3 I II Poloaj durbina Poloaj durbina ' 4 ' 5 Sredina iz I i II ' 6 Dvostruka kolimaciona pogreka 2c = II I Trigonometrijski obrazac br. 1 Reducirana sr
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Course: MATH 3A
Cairo Governorate Nozha Directorate of Education Nozha Language Schools Ismailia Road Branch Department : Math Form : 4th primary 1st term Revision Sheet Lesson (1) Hundred Thousands 1- Write following numbers in digits as in the example :Example :One hun
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Course: MATH 3A
SUR LES SEMIGROUPES DYNAMIQUES QUANTIQUES ROLANDO REBOLLEDO A la mmoire dAlbert Badrikian. e Resume. Les semigroupes dynamiques quantiques sont apparus dans la littrature physique au cours des annes 70, de la plume de plusieurs aue e teurs, notamment Krau
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Course: MATH 3A
Le Chatelier's Principle Le Chatelier's principle states that when a system in chemical equilibrium is disturbed by a change of temperature, pressure, or a concentration, the system shifts in equilibrium composition in a way that tends to counteract this
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Course: Differential Equations
chew cn CTGKGNS am '9' Gmle book a 3903; $Ā¢a17> RTeiew Maa In {Ramada- =eve13w has an assign a I. Go over an Iccker aueson, [new in 5 a 2' 1'? We WW; Chow. queous from and 10PTCTD make a {Lest Jaunuf, wa-h mm: Alwags check 86W answer? (like eignveerm' CM
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School: UCSB
Course: Math 4A
Math 4A Midterm Review Prolbems Note: These problems are provided as review of the key ideas that well be tested on the midterm, but this is not a practice midterm. Because we are testing your understanding of concepts and not simply computational uency,
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Course: Differential Equations
Mathematics 4B Winter 2015: Review for Final March 12, 2015 Professor J. Douglas Moore YOU ARE ALLOWED ONE 3 x 5 CARD FOR THE FINAL EXAM. Recall that there is assigned seating for the nal exam. Please write your seat number on your card. You will need to
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Math 3C Practice Word Problems Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB 1) A dangerous substance known as Chemical X is lethal if its concentration in the air is 100 parts per million by volume (ppmv). The half-life of che
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Math 6B Midterm Review #1 1 Greens Theorem (y + e 1. Compute the line integral x ) dx + (2x + cos(y 2 ) dy where C is the positively oriented boundary C of the region D enclosed by the parabolas y = x2 and x = y 2 . Solution: Here we use (curl form) Q P x
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Course: Calc With Appli 2
This is a study guide for the second Math 3B midterm. It indicates which types of problems you may be expected to answer on the midterm, with instructions on where to nd these topics in the Stewart calculus book. Plenty of examples can be found in the e
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Course: Numerical Analysis
University of California, Santa Barbara Department of Statistics & Applied Probability PSTAT 120B, Probability & Statistics, Spring 2010 Instructor: Jarad Niemi Email: niemi@pstat.ucsb.edu Course hours: MWF 10:00-10:50am in HFH 1104 TAs: Varvara Kulikova
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Course: Vector Calculus
Math 6A - Vector Calculus with Applications, First Course Instructor: Oce: E-mail: Oce Hours: Lectures: Classroom: Jon Tjun Seng Lo Kim Lin Graduate Tower, Oce 6431H jlokimlin@math.ucsb.edu TR 1:00 PM-2:00 PM, also available by appointment. MTWR 8:00 AM-9
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SPRING 2015, MATH 6 B, VECTOR CALCULUS 2 INSTRUCTOR : Gustavo Ponce (o. SH 6505 #8938365) SCHEDULE : TR 330 445 ROOM : HFH 1104 INSTRUCTOR OFFICE HOURS : T. 5 6, R. 11 12, 5 6. TEACHING ASSISTANT : Kathleen Hake (SH 6431 K), Garo Sarajian (SH 6432 F) TEAC
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Math 6A - Vector Calculus with Applications, First Course Instructor: Oce: E-mail: Oce Hours: Lectures: Amanda R. Curtis Graduate Tower, Oce 6432Q arcurtis@math.ucsb.edu MTWR 1:00 PM-2:00 PM, also available by appointment. MTWR 3:30-4:35PM, 3515 Phelps Ha
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Course: Vector Calculus
Math 6A (Vector Calculus) Syllabus1 TR, 11:00 AM to 12:15 PM, Room 1701 in Theater/Dance West Instructor/E-mail: Jordan Schettler (jcs@math.ucsb.edu) Ofce Hours: Tuesday 2-3 pm, Friday 9-10 am, or by appointment, South Hall, Room 6721 Website: Use the cou
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Course: Homological Algebra
Math 236B, Spring 2015, MWF 9-9:50, HSSB 1223 Homological Algebra Instructor: Birge Huisgen-Zimmermann, SH 6518, Oce hours M, F 11 - 12, W 12:30 1:30. Accompanying texts, as for the winter quarter: The manuscript I will put on the board will again serve
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Course: Abstact Algebra
Math 111C, Spring 2015, MWF 10 10:50, Building 387, Room 103 Introduction to Abstract Algebra Instructor: Birge Huisgen-Zimmermann, SH 6518 Oce Hours: Mon, Fri 11-12, Wed 12:30 - 1:30 Teaching Assistant: Nathan Schley, SH 6431P, Oce hours Tue, Thur 4-5. E
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Math 8: Transition to higher mathematics Syllabus Text: How to prove it (A structured approach) by D. J. Velleman, Second Edition Lectures: TR 12:30-1:45 ARTS 1353 Discussions : MW 5:00-5:50 HSSB 1223 MW 6:00-6:50 HSSB 1207 Instructor: Eleni Panagiotou Of
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Course: Math 4A
Math 4A - Jacob Course Information and Syllabus Spring Quarter 2015 Monday, Wednesday, Friday 1:00 - 1:50 Instructor: Bill Jacob Oce Hours: Monday and Wednesday 2:15 - 3:15, Friday 9:45 -10:45, and by appointment. Oce: South Hall 6719 Email: jacob@math.uc
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Course: Differential Equations
SYLLABUS FOR MATHEMATICS 4B CALCULUS WINTER 2015 Professor John Douglas Moore Office: South Hall 6714 Office hours: TuTh 3:30, W 1 Telephone: 893-3688 email: moore@math.ucsb.edu Lectures: Lotte Lehman Concert Hall TuTh 9:30-10:45 Text: Boyce, Diprima, Ele
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Course: Differential Equations
Math 4B UCSB, Spring 2015 Lecture: MWF 11:00-11:50, MUSICLLCH Textbook: The textbook for this course is optional. For those who would like a reference and extra practice problems the book Elementary Dierential Equations by Boyce and DiPrima will work. Ins
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Course: Math 4A
Math 4A Syllabus Winter 2014 Lecture: MWF 10:00 10:50am, MUSIC LLCH Text: Linear Algebra with applications by David C. Lay, Addison-Wesley, 4th Edition. Material to be covered: Chapters 1-6 in the text book. iClicker: You should purchase an iClicker and b
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Math 108a Professor: Padraic Bartlett Syllabus for Math 108a Weeks 1-10 UCSB 2013 Basic Course Information Professor: Padraic Bartlett. Class time/location: MWF 9-9:50, Phelps 3505. Oce hours/location: TTh 2-3pm, South Hall 6516. Additionally, I am tea
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Analysis with an introduction to proof - Math 117 Spring2009 Monday, Wednesday, & Friday, 12:00-12:50pm, South Hall 6635 Instructor: Carlos J. Garc a-Cervera. Oce: South Hall, 6707. Phone: 893-3681. E-mail: cgarcia@math.ucsb.edu URL: http:/www.math.ucsb.e
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Analysis with an introduction to proof - Math 117 Spring2009 Monday, Wednesday, & Friday, 12:00-12:50pm, South Hall 6635 Instructor: Carlos J. Garc a-Cervera. Oce: South Hall, 6707. Phone: 893-3681. E-mail: cgarcia@math.ucsb.edu URL: http:/www.math.ucsb.e
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Intro. to Numerical Analysis - Math 104B Winter 2011 Tuesday & Thursday, 8:00-9:15am, South Hall 6635 Instructor: Carlos J. Garc a-Cervera. Oce: South Hall, 6707. Phone: 893-3681. E-mail: cgarcia@math.ucsb.edu URL: http:/www.math.ucsb.edu/~cgarcia/Courses
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Math 104A, Fall 2010 Intro. to Numerical Analysis Tuesday & Thursday, 9:30-10:45am, 387 101 Instructor: Carlos J. Garc a-Cervera. Oce: South Hall, 6707. Phone: (805) 893-3681. E-mail: cgarcia@math.ucsb.edu URL: http:/www.math.ucsb.edu/~cgarcia/Courses/Mat
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Math 104A, Winter 2009 Intro. to Numerical Analysis Monday, Wednesday, & Friday, 9:00-9:50am, Arts 1426 Instructor: Carlos J. Garc a-Cervera. Oce: South Hall, 6707. Phone: (805) 893-3681. E-mail: cgarcia@math.ucsb.edu URL: http:/www.math.ucsb.edu/~cgarcia
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Math 108B Intro to Linear Algebra Winter 2010 Professor: Kenneth C. Millett Office: 6512 South Hall Office Hours: R 8:30 11:00 Email: millet@math.ucsb.edu Graduate Assistant: Tomas Kabbabe Office: 6432K South Hall Office Hour: W 10:00 11:00 Email: tomas@m