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##### MA 261 - MULTIVARIATE CALCULUS - Purdue Study Resources
• 10 Pages
###### 261E2-F2011

School: Purdue

Course: Calculus III

• 1 Page
###### Ans-261E2-S2009

School: Purdue

Course: Calculus III

• 1 Page
###### Sol-261E2-F1998

School: Purdue

Course: Calculus III

FALL 1998 ANSWERS FOR EXAM II: 1. B 2. C 3. E 4. A 5. D 6. B 7. E 8. 2 2 9. 0 1 r 4r 2 + 1 dr d= (173/2 - 53/2 ) 6 3/2 3-2x2 5-x2 10. - 3/2 - 3-2x2 dz dy dx 2+x2 +y 2 1

• 11 Pages
###### Sol-261E2-F2006

School: Purdue

Course: Calculus III

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###### Sol-261E2-S1999

School: Purdue

Course: Calculus III

SPRING 1999 ANSWERS FOR EXAM II: 1. E 2. B 3. B 4. B 5. B 6. E 7. D 2 1/2 1-r2 8. 0 0 - 1-r2 r dz dr d 9. 3/2 6 (13 - 1) 10. (1) (3, 3/2) minimum (2) (-2, -1) saddle 1

• 1 Page
###### Sol-261E2-S2000

School: Purdue

Course: Calculus III

SPRING 2000 ANSWERS FOR EXAM II: 1. C 2. D 3. B 4. E 5. A 6. (0, 0) saddle, (1, -1) min. /2 1 7. (a) (1/2, 0) (b) r = cos 0 25-x2 0 25-r2 (c) 0 cos r 3 dr d 25-x2 -y 2 8. (a) -1 5 0 z dz dy dx (b) /2 0 3 6-2x 0 0 zrdz dr d. 6-2x-y 9. 0 0 dz dy dx 1

• 6 Pages
###### Sol-261E2-S2001

School: Purdue

Course: Calculus III

• 14 Pages
###### 261FE-F2007

School: Purdue

Course: Calculus III

• 12 Pages
###### 261FE-F2008

School: Purdue

Course: Calculus III

• 14 Pages
###### 261FE-S1999

School: Purdue

Course: Calculus III

MA 261 NAME STUDENT ID # INSTRUCTOR INSTRUCTIONS FINAL EXAM Spring 1999 Page 1/14 1. There are 14 different test pages (including this cover page). Make sure you have a complete test. 2. Fill in the above items in print. I.D.# is your 9 digit ID (probably

• 3 Pages
###### Ans-261E2-S2008

School: Purdue

Course: Calculus III

Exam 2 Answer Key MA 262 Spring 2008 1. C 2. E 3. D 4. B 5. B 6. A 7. D 8. B 9. C 10. E

• 1 Page
###### Ans-261E2-S2006

School: Purdue

Course: Calculus III

• 7 Pages
###### 261E2-S1999

School: Purdue

Course: Calculus III

MA 261 NAME STUDENT ID # INSTRUCTOR INSTRUCTIONS EXAM II Spring 1999 Page 1/7 1. There are 7 different test pages (including this cover page). Make sure you have a complete test. 2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your

• 8 Pages
###### 261E2-S2000

School: Purdue

Course: Calculus III

MA 261 NAME STUDENT ID # Exam 2 Spring 2000 Page 1/8 RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1) Fill in the above information. Also write your name at the top of each page of the exam. 2) The test has 8 pages, including this one. 3) Problems 1 th

• 6 Pages
###### 261E2-S2001

School: Purdue

Course: Calculus III

MA 261 NAME STUDENT ID # Exam 2 Spring 2001 Page 1/6 RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1) Fill in the above information. Also write your name at the top of each page of the exam. 2) The exam has 6 pages, including this one. 3) Problems 1 th

• 6 Pages
###### 261E2-S2002

School: Purdue

Course: Calculus III

• 7 Pages
###### 261E2-S2003

School: Purdue

Course: Calculus III

• 7 Pages
###### 261E2-S2009

School: Purdue

Course: Calculus III

• 1 Page
###### Ans-261E2-F2005

School: Purdue

Course: Calculus III

• 1 Page
###### Ans-261E2-F2007

School: Purdue

Course: Calculus III

• 1 Page
###### Ans-261E2-F2011

School: Purdue

Course: Calculus III

• 9 Pages
###### 261FE-S2000

School: Purdue

Course: Calculus III

MATH 261 - SPRING 2000 Name Signature Div. Sect. No. Instructor (Test 01) Recitation Instructor FINAL EXAM INSTRUCTIONS 1. You must use a #2 pencil on the mark-sense sheet (answer sheet). 2. If you have test 01, mark 01 and blacken the corresponding circl

• 11 Pages
###### 261FE-S2001

School: Purdue

Course: Calculus III

MATH 261 - SPRING 2001 FINAL EXAM Name Signature Div. Sect. No. Instructor Recitation Instructor FINAL EXAM INSTRUCTIONS 1. You must use a #2 pencil on the mark-sense sheet (answer sheet). 2. On the mark-sense sheet, fill in the instructor's name and the

• 1 Page
###### Ans-153E3-F01

School: Purdue

MA 153 Exam 3 Answers Fall 2001 1. (a) 6 9 (b) 2 (c) 10 x 3 - 3 2. (a) [- 4,2] (b) [- 3,4] 1 (c) (- 4,-2 ) ( ,2] 3. (4,3)and (- 1,-7 ) 4. g -1 (x ) = 2 x+5 5. 14 7 or or 1.75 8 4 y = f (x - 2 )+ 5 6. -13 7. (2,5) (6,5) (4,2) 8. 2a + h - 1 9. y = - 10 (x -

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###### Assignment3

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• 2 Pages
###### Basic

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###### Ci2

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###### Df

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Direction Fields -deld6 The routine deld6 is already loaded on all PUCC machines as standard software. To access it from any PUCC machine: StartAll ProgramsStandard SoftwareComputational PackagesMATLAB6.1MATLAB6.1 If you are using your own copy of Matlab

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###### FEx

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###### Groundbase

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• 9 Pages
###### Lsqgame

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%LSQGAME Least Squares Line Game last updated 2/10/96 % % An interactive 'game' to select the least squares line % to a set of data. Two guesses for the lsq line can be made % using the mouse to select two points that are then connected. % The 'true' leas

• 1 Page
###### Num

School: Purdue

Numerical Methods & .m Files In order to use Matlab routines for the Euler, Improved Euler and Runge-Kutta Methods, you will need the les eul.m, rk2.m and rk4.m, respectively. These les are already present on all PUCC machines as standard software. If you

• 1 Page
###### Ans-153E1-S03-O

School: Purdue

Question # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Orange Form D C D A B C A A B D C Answer y-x x x4y6 3z 4 7 4x 9 5 x 3 - 6 x 2 + 5 x - 14 9 x 3 - 24 x 2 + 16 x ( x + 4) x + 2 ( ) 4x3 + 5 b2 + a2 a ( x + 5)( x 2 + 4) x+2 9t - t 2 (t + 4 )( t - 4) x is betwee

• 1 Page
###### Ans-153E1-F01

School: Purdue

MA 153 Exam 1 Answers Fall 2001 1. 6 x 3 + 19 x2 26 x + 5 2. x + 8 x + 15 x 25 3. y = 4. mW gm x 2 x +2 5 (a) 2(3 x + 4)(2 x 1) (b) (4 x + y )(4 x y)(a + 3c) 6. (a) x= -5, 7 (b) x = 6 7. (a) 20 ab11 (b) 3a3b 4 8. 3:00 p.m. 9. 16.4 cm

• 9 Pages
###### 261FE-S2003

School: Purdue

Course: Calculus III

• 11 Pages
###### 261FE-S2008

School: Purdue

Course: Calculus III

MA 261 FINAL EXAM Form A Spring 2008 1. Find an equation of the plane that contains the point (2, 1, 1) and the line x = 1 + 3t, y = 2 + t, z = 4 + t. A. 3x + y + z = 8 B. 2x + y + z = 6 C. x + 2y + 4z = 8 D. x - 5y + 2z = -1 E. x - 2y + z = 1 2. Compute

• 1 Page
###### Ans-261FE-F2005

School: Purdue

Course: Calculus III

• 1 Page
###### Ans-261FE-F2007

School: Purdue

Course: Calculus III

• 3 Pages
###### Ans-261FE-F2008

School: Purdue

Course: Calculus III

MA26100 FinalExamKey 1. E 2. C 3. A 4. D 5. E 6. B 7. E 8. C 9. A 10. E 11. C 12. B 13. C 14. D 15. D 16. B 17. D 18. D 19. E 20. A 21. B 22. A Fall08

• 3 Pages
###### Ans-261FE-S2002

School: Purdue

Course: Calculus III

MA261 Final Exam Spring 2002 1. D 2. A 3. B 4. C 5. E 6. D 7. B 8. A 9. D 10. E 11. C 12. A 13. A 14. C 15. A 16. B 17. A 18. B 19. E 20. D

• 5 Pages
###### 153E1-F00

School: Purdue

MA 153 Exam 1 Fall 2000 Name: _ Student ID: _ Instructor: _ Class Hour: _ INSTRUCTIONS: (1) There is no credit for guessing. You must show your work to receive credit! (2) Please fill in all the above information and write your name on the top of each of

• 5 Pages
###### 153E2-F00

School: Purdue

MA 153 Exam 2 Fall 2000 Name: _ Student ID: _ Instructor: _ Class Hour: _ INSTRUCTIONS: (1) There is no credit for guessing. You must show your work to receive credit! (2) Please fill in all the above information and write your name on the top of each of

• 6 Pages
###### 153E3-S02-O

School: Purdue

MA 153 Exam 3 Spring 2002 1. Find the slope, m , and the y -intercept, b , of the line given by the equation 3 x - 4 y = 8 . 3 A. m = - ; b = -2 4 3 B. m = ; b = 8 4 3 C. m = - ; b = 8 4 3 D . m = ; b = -2 4 E . None of the above Use the graph of a functi

• 1 Page
###### Pp

School: Purdue

Phase Portraits - pplane6 The routine pplane6 is already loaded on all PUCC machines as standard software. If you are using your own copy of Matlab you may need to download pplane6. Here is a link : http:/math.rice.edu/dfield/ (Note: pplane5 is an older

• 0 Pages
• ###### Screen shot 2012-03-16 at 5.09.38 PM
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###### Screen Shot 2012-03-16 At 5.09.38 PM

School: Purdue

Course: CALCULUS 3

• 2 Pages
###### Quiz8

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Course: MULTIVARIATE CALCULUS

• 2 Pages
###### Quiz9

School: Purdue

Course: MULTIVARIATE CALCULUS

• 2 Pages
###### Quiz10

School: Purdue

Course: MULTIVARIATE CALCULUS

• 5 Pages
###### StudyGuide1

School: Purdue

Course: MULTIVARIATE CALCULUS

MA 261 - Fall 2009 Study Guide # 1 1. Vectors in R2 and R3 (a) v = a, b, c = a i + b j + c k; vector addition and subtraction geometrically using paral lelograms spanned by u and v; length or magnitude of v = a, b, c , |v| = a2 + b2 + c2 ; directed vector

• 8 Pages
###### StudyGuide2Updated

School: Purdue

Course: MULTIVARIATE CALCULUS

MA 261 - Fall 2009 Study Guide # 2 (updated) 1. Relative/local extrema; critical points ( f = 0 or f does not exist); 2nd Derivatives Test; absolute extrema; Max-Min Problems; Lagrange Multipliers: Extremize f (x) subject to a constraint g (x) = C , solve

• 26 Pages
###### Curvatureslides

School: Purdue

Some Examples of Arclength parametrization and Curvature Turkay Yolcu tyolcu@math.purdue.edu

• 3 Pages
###### Examples13.2

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• 12 Pages
###### Examples13.3

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Problem Solution

• 3 Pages
###### Ans-261FE-S2003

School: Purdue

Course: Calculus III

MA261 Final Exam Spring 2003 1. D 2. A 3. D 4. B 5. E 6. A 7. C 8. D 9. D 10. E 11. E 12. A 13. C 14. C 15. D 16. C 17. D 18. E 19. B 20. C 21. D 22. C 23. E 24. A

• 2 Pages
###### Quiz7

School: Purdue

Course: MULTIVARIATE CALCULUS

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###### Quiz6

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Course: MULTIVARIATE CALCULUS

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Course: CALCULUS 3

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Course: CALCULUS 3

• 4 Pages
###### Quiz1

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Course: MULTIVARIATE CALCULUS

• 3 Pages
###### Quiz2

School: Purdue

Course: MULTIVARIATE CALCULUS

• 2 Pages
###### Quiz3

School: Purdue

Course: MULTIVARIATE CALCULUS

• 3 Pages
###### Quiz4

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Course: MULTIVARIATE CALCULUS

• 3 Pages
###### Quiz5

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Course: MULTIVARIATE CALCULUS

• 1 Page
###### Ans-261FE-S2006

School: Purdue

Course: Calculus III

• 11 Pages
###### Ans-261FE-S2008

School: Purdue

Course: Calculus III

MA 261 FINAL EXAM Form A Spring 2008 Answer Key: 1D 2A 3D 4B 5C 6D 7B 8D 9B 10A 11A 12E 13A 14A 15E 16B 17B 18B 19A 20E 21B 22B 1. Find an equation of the plane that contains the point (2, 1, 1) and the line x = 1 + 3t, y = 2 + t, z = 4 + t. A. 3x + y + z

• 1 Page
###### Ans-261E1-F2007

School: Purdue

Course: Calculus III

• 1 Page
###### Ans-261E1-F2008

School: Purdue

Course: Calculus III

• 1 Page
###### Ans-261E1-S2006

School: Purdue

Course: Calculus III

• 1 Page
###### Ans-261E1-S2009

School: Purdue

Course: Calculus III

• 6 Pages
###### Sol-261E1-F1998

School: Purdue

Course: Calculus III

• 11 Pages
###### Sol-261E1-F2006

School: Purdue

Course: Calculus III

• 28 Pages
###### Sol-261E1-S1998

School: Purdue

Course: Calculus III

• 10 Pages
###### Sol-261E1-S2000

School: Purdue

Course: Calculus III

• 6 Pages
###### Sol-261E1-S2001

School: Purdue

Course: Calculus III

• 1 Page
###### Ans-261E1-F2005

School: Purdue

Course: Calculus III

• 7 Pages
###### 261E1-S2009

School: Purdue

Course: Calculus III

• 1 Page
###### Sol-261FE-S2000

School: Purdue

Course: Calculus III

Answers to MA261 Final (Spring 2000) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. D E C C B A D A D D B C C C C E D E A E

• 11 Pages
###### Sol-261FE-S2001

School: Purdue

Course: Calculus III

• 5 Pages
###### 261E1-F2000

School: Purdue

Course: Calculus III

MATH 261 FALL 2000 FIRST EXAM September 26, 2000 STUDENT NAME -STUDENT ID -RECITATION HOUR -RECITATION INSTRUCTOR - INSTRUCTIONS: 1. This test booklet has 5 pages including this one. 2. Fill in your name, your student ID number, your recitation hour and y

• 8 Pages
###### 261E1-F2008

School: Purdue

Course: Calculus III

• 8 Pages
###### 261E1-F2011

School: Purdue

Course: Calculus III

• 6 Pages
###### 261E1-S1998

School: Purdue

Course: Calculus III

MA 261 NAME STUDENT ID # INSTRUCTOR INSTRUCTIONS EXAM I Spring 1998 Page 1/6 1. There are 6 different test pages (including this cover page). Make sure you have a complete test. 2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your

• 9 Pages
###### 261E1-S2000

School: Purdue

Course: Calculus III

MA 261 NAME STUDENT ID # Exam 1 Spring 2000 Page 1/9 RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1) Fill in the above information. Also write your name at the top of each page of the exam. 2) The test has 9 pages, including this one. 3) Problems 1 th

• 6 Pages
###### 261E1-S2001

School: Purdue

Course: Calculus III

MA 261 NAME STUDENT ID EXAM 1 Spring 2001 Page 1/6 Page 1 Page 2 Page 3 Page 4 /12 /7 /18 /18 /27 /18 /100 RECITATION INSTRUCTOR RECITATION TIME Page 5 Page 6 TOTAL DIRECTIONS 1. Write your name, student ID number, recitation instructor's name and recitat

• 6 Pages
###### 261E1-S2002

School: Purdue

Course: Calculus III

• 9 Pages
###### 261E2-F2008

School: Purdue

Course: Calculus III

• 4 Pages
###### Practicefinal

School: Purdue

• 2 Pages
###### Quiz10

School: Purdue

Course: Calculus

Quiz 10 David Imberti November 27, 2012 (1) Give a parametrization of the shell of a sphere in the rst octant with radius 1. (2) Find F dS with S the surface as in 1 and F = xi + y j + z k (i.e., nd the linear heat ow across S the octalsphere) 1

• 2 Pages
###### Quiz3

School: Purdue

Course: Calculus

DavidImberti September 10, 2012 Quiz 3-show work You are helping design a railroad for good ol Union Pacic, you approximate a model parametric equation for the track as: r(t) = tikm + tjkm for 0 t 1 r(t) = (cos( 34 (t 1) + 1)ikm + (sin( 34 ) (t 1) + 1)jkm

• 2 Pages
###### Quiz2Solutions

School: Purdue

Course: Calculus

Quiz 2 Solutions David Imberti November 28, 2012 (1) I.e., does < cos(t), sin(t) >=< t, 1 > for 0 t 2: 2 cos(t) = t 2 sin(t) = 1 The second equation is satised for t = , 32 . 2 At 2 , cos( 2 ) = 0 = 2 2 . Thus they collide at t = (and note that is in [0,

• 2 Pages
###### Quiz2

School: Purdue

Course: Calculus

David Imberti November 28, 2012 1-Let r1 , r2 describe two particle paths, do they collide for 0 t 2? r1 =< cos(t), sin(t) > r2 =< t, 1 > 2 2-Find the parametric equations for the tangent line of < 1, cos(t), sin(t) > at t = 2 3-Let r(t) =< cos(t), sin(t)

• 2 Pages
###### Final Exam Fall 2011

School: Purdue

Course: Calculus

• 3 Pages
###### MA261quiz_12

School: Purdue

Course: Multivariate Calculus

MA261 0021&0022 Quiz 12 Spring 2011 Problem 1. (a) Given a function f (x, y, z ) = xyz , nd its gradient f (x, y, z ) and then the curl of the gradient, namely curl( f (x, y, z ). Solution. Given f (x, y, z ) = xyz , we know f (x, y, z ) = fx , fy , fz =

• 3 Pages
###### MA261quiz_11

School: Purdue

Course: Multivariate Calculus

MA261 0021&0022 Quiz 11 Spring 2011 Problem 1. (a) Given F(x, y ) = y exy , xexy , nd a function f (x, y ) such that f (x, y ) = F(x, y ). Solution. Since we are told f (x, y ) = F(x, y ), we have fx = yexy and fy = xexy . After integrating the rst equali

• 2 Pages
###### MA261quiz_10

School: Purdue

Course: Multivariate Calculus

MA261 0021&0022 Quiz 10 Spring 2011 Problem 1. Find the length of a wire C in the shape of a helix described by the parametric equation C : x = cos t, y = sin t, z = t, 0 t 4 Solution. To get the length of the wire, let us integrate the constant function

• 3 Pages
###### MA261quiz_9

School: Purdue

Course: Multivariate Calculus

MA261 0021&0022 Quiz 9 Spring 2011 Problem 1 (Test II.8, Spring 2008). [Warning: No use of cell phone browsing the internet during the quiz!] Let D be the part of disk centered at 0 with radius 2 that lies to the right of the line x = 1. Then which of the

• 3 Pages
###### MA261quiz_8

School: Purdue

Course: Multivariate Calculus

MA261 0021&0022 Quiz 8 Spring 2011 Problem 1 (modied from Problem 2 in the second midterm of Spring 2 2009). We will nd the maximum of f (x, y ) = xy on the ellipse x + y 2 = 1 using the 4 Lagrange multiplier method. 2 (a) Let g (x, y ) = x + y 2 . Write

• 2 Pages
###### Quiz3Solutions

School: Purdue

Course: Calculus

Quiz 3 Solutions David Imberti November 28, 2012 (1) One way to do this is to recognize that the rst part of the track is a straight line from (0, 0) to (1, 1) which is thus of length 2, and the other piece is an eighth part of a circle of radius 1 which

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