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MA 261  MULTIVARIATE CALCULUS  Purdue Study Resources
 Purdue University (Purdue)
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261S12sg2
School: Purdue
Course: Multivariate Calculus
MA 261  Spring 2011 Study Guide # 2 f f 0. Gradient vector for f (x, y ): f (x, y ) = , , properties of gradients; gradient points in x y direction of maximum rate of increase of f ; The maximum value of the directional derivative is equal to f ; f (x0 ,

261FES2000
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 marksense sheet (answer sheet). 2. If you have test 01, mark 01 and blacken the corresponding circl

261FES2001
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 marksense sheet (answer sheet). 2. On the marksense sheet, fill in the instructor's name and the

261FES2008
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

Ans261FEF2008
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

Ans261FES2002
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

261FES1999
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

Ans261E2S2008
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

Sol261E2F1998
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 32x2 5x2 10.  3/2  32x2 dz dy dx 2+x2 +y 2 1

Sol261E2S1999
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 1r2 8. 0 0  1r2 r dz dr d 9. 3/2 6 (13  1) 10. (1) (3, 3/2) minimum (2) (2, 1) saddle 1

Sol261E2S2000
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 25x2 0 25r2 (c) 0 cos r 3 dr d 25x2 y 2 8. (a) 1 5 0 z dz dy dx (b) /2 0 3 62x 0 0 zrdz dr d. 62xy 9. 0 0 dz dy dx 1

153E1F00
School: Purdue
Course: Multivariate Calculus
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

153E2F00
School: Purdue
Course: Multivariate Calculus
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

lsqgame
School: Purdue
Course: Multivariate Calculus
%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

num
School: Purdue
Course: Multivariate Calculus
Numerical Methods & .m Files In order to use Matlab routines for the Euler, Improved Euler and RungeKutta 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

pp
School: Purdue
Course: Multivariate Calculus
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

practicefinal7
School: Purdue
Course: Multivariate Calculus
MA 261 PRACTICE PROBLEMS 1. If the line x1 2 has symmetric equations y 3 = = z+2 7 , find a vector equation for the line A. r = (1 + 2t)i  3tj + (2 + 7t)k that contains the point (2, 1, 3) and is parallel to . B. r = (2 + t)i  3j + (7  2t)k D. r =

project
School: Purdue
Course: Multivariate Calculus
function project(u,w) %last updated 5/9/94 %PROJECT Projecting vector U onto vector W orthogonally. Vectors % U and W can be either a pair of 2D or 3D vectors. A sketch % showing U being projected onto W is displayed sequentially. % % Use in the form => p

reduce
School: Purdue
Course: Multivariate Calculus
function AEQ = reduce(A) %last updated 5/7/94%REDUCE Perform row reduction on matrix A by explicitly choosing% row operations to use. A row operation can be "undone", but% this feature cannot be used in succession.% Use in the form => reduce(A) <=% By: Da

rowop
School: Purdue
Course: Multivariate Calculus
%last updated 2/10/96 %ROWOP Perform row reduction on real matrix A by explicitly choosing % row operations to use. A row operation can be "undone", but % this feature cannot be used in succession. Matrices can be % at most 6 by 6. % % Use in the form =>