# Multivariate calculus final exam with solutions pdf Due DatePractice Problems
(Do not hand in.)Homework Problems
(These must be handed in.) 1 January 3112.1/ 9, 13, 17, 29, 31
12.2/ 1, 3, 5, 9, 13
12.3/ 1, 3, 5, 7, 13, 23, 25
12.1/ 16, 27, 28, 32
12.2/ 4, 14, 16, 20
12.3/ 6, 10, 16, 31, 32
2 February 712.4/ 1, 3, 5, 7-10, 11, 13, 17, 25
12.5/ 1, 5, 9, 13, 17, 21, 25
12.4/ 6, 16, 18, 26, 28, 30
12.5/ 2, 8, 10, 12, 14, 16, 24, 26, 30
3 February 1412.6 (p. 598-599)/ 1, 2, 3, 7, 13, 17
Ch. 12 Review (p. 600-601)/ 1, 5, 9, 13, 25
Ch. 12 C.Y.U. (p. 602-603)/ 3, 9, 19, 29, 35, 37, 43
12.6 (p. 598-599)/ 4, 12, 18
Ch. 12 Review (p. 600-601)/ 14, 20, 21
Ch. 12 C.Y.U. (p. 602-603)/ 8, 28, 30, 38, 48, 52, 53
4 February 2113.1/ 1, 4, 5, 9, 11, 15, 19, 27
13.2/ 7, 9, 11, 13, 15, 21
13.3/ 1, 5, 7, 9, 17, 27
13.1/ 16, 20, 28
13.2/ 14, 22
13.3/ 16, 18, 20, 22, 32, 33, 36
5 March 713.4/ 1, 5, 9, 11, 13, 15, 17, 21
17.1/ 1, 7, 9, 17, 25, 29, 33, 41, 49
17.2/ 1, 5, 13, 21, 25
13.4/ 4, 8, 16, 18, 31
17.1/ 2, 8, 12, 26, 32, 50
17.2/ 2, 8, 28, 36, 37
6 March 1414.1/ 3, 9, 11
14.2/ 1-33 odds, 39
14.3/ 1, 3, 5, 9, 15
14.1/ 4, 7, 12, 14
14.2/ 4, 8, 24, 38, 44
14.3/ 4, 8, 13, 14, 22
7 March 2814.4/ 1, 5, 9, 13, 17, 21, 25, 29, 39
14.5/ 1, 3, 9, 11, 13, 17, 23, 29
14.4/ 2, 12, 18, 50, 56, 60, 66
14.5/ 12, 22, 24, 26, 30, 36
8 April 414.6/ 1, 3, 5, 9, 15, 21
14.7/ 1, 5, 9, 13, 19-25 odds, 31, 33
14.6/ 16, 18, 20, 23, 33
14.7/ 18, 20, 26, 27, 30, 35, 36
9 April 1815.1/ 1, 3, 5, 7, 13, 17, 21
15.2/ 3, 5, 9, 13, 17, 23
15.1/ 12, 18, 20, 24, 25, 26
15.2/ 6, 8, 14, 16, 24, 27
Note: Use Maple for 15.1/25.
A Maple plot or contour diagram is also recommended for 15.2/27. 10 April 2515.3/ 1, 5, 9, 13, 17, 23, 25
15.3/ 2, 6, 8, 12, 14, 16, 18, 19, 20, 28
Ch. 15 Review Problems (p. 730)/ 27, 32
11 May 216.1/ 3, 13, 31
16.2/ 1-17 odds, 23, 27, 33
16.3/ 1-13 odds, 17, 37
16.1/ 6
16.2/ 4, 8, 12, 16, 34, 36, 47
16.3/ 2, 10, 12, 14, 38
* * 16.4/ 1-17 odds, 21, 23
16.5/ 1, 5, 7, 11, 19, 21(a), 25(a,b), 27(a,b)

Sours: http://math.colgate.edu/~wweckesser/math113Spring03/

## Math 251, Fall 2010

### Course Materials

Schedule and Homework (Updated Daily)

### Aug 31st (Day One Material)

Syllabus (pdf)
Course Objectives and Learning Goals
Diagnostic Quiz (pdf)
Diagnostic Quiz: Solutions to Questions 1-7 (pdf)
Diagnostic Quiz: Solutions to Question 8 (pdf)
Study Plan Essay (html)

### Brushing Up on Single Variable Calculus

If you need to brush up on your single variable calculus, here are the sections Stewart's "Calculus (Early Transcendentals)" that we rely on in Math 251. Starred sections are especially important.

2.1, 2.7, 2.8, 3.1, 3.2, 3.3, 3.4**, 3.6, 3.11, 4.1, 4.3, 4.5, 4.7, 4.9, 5.1-5.4, 5.5**, 6.1, 6.2, 7.1

The material from Chapter 5,6,7 is used in Math 251 Chapters 15, 16.

The material from Chapter 4,5,6 is used in Math 251 Chapters 14, 15.

Matlab for Multivariable Calculus

### Past Exams

Here are the exams I gave in Math 251H, Fall 2003.

Midterm One (pdf)
Midterm Two (pdf)
Midterm Three (pdf)
Final (pdf)

Here are the midterm exams I gave in Math 251, Fall 2004.

Midterm One (pdf)
Midterm Two (pdf)
Midterm Three (pdf)

Here are the exams I gave in Math 251, Spring 2004.

Midterm One (pdf)
Midterm Two (pdf)
Midterm Three (pdf)
Final (pdf)

Here are the solutions to the exams I gave in Math 251, Spring 2004.

Exam One Solutions (pdf)
Exam Two Solutions (pdf)
Exam Three Solutions (pdf)

Here are the midterm exams I gave in Math 251H, Fall 2006

Exam One (pdf)
Exam Two (pdf)
Exam Three (pdf)

Here are the solutions to the exams I gave in Math 251H, Fall 2006

Solutions to Exam One (pdf)
Solutions to Exam Two (pdf)
Solutions to Exam Three (pdf)

Here are the exams I gave in Math 251, Fall 2008

Exam One (pdf)
Exam Two (pdf)
Exam Three (pdf)
Final (pdf)

Here are the solutions to the midterm exams I gave in Math 251, Fall 2008

Solutions to Exam One (pdf)
Solutions to Exam Two (pdf)
Solutions to Exam Three (pdf)

Here are the exams I gave in Math 251, Fall 2009

Exam One
Exam Two
Exam Three
Final Exam

Here are the solutions to the midterm exams I gave in Math 251, Fall 2009

Solutions to Exam One
Solutions to Exam Two
Solutions to Exam Three

### Exam I

Exam I will cover Chapter 12, and the parts of 15.7 and 15.8 on cylindrical and spherical coordinate systems (i.e., no integration).

Exam One [pdf]
Exam One Solutions [pdf]

### Exam II

Exam II will cover 13.1, 13.2, 13.3 (arclength only), 14.1-14.7, and 16.6.

Exam Two [pdf]
Exam Two Solutions [pdf]

### Exam III

Exam III will cover 14.7, 14.8, 15.1-15.4, 16.1-16.5

Exam Three [pdf]
Exam Three Solutions [pdf]

### Final Exam

Final Exam Solutions [pdf]

Sours: https://personal.utdallas.edu/~jwz120030/Teaching/PastCoursesUMBC/M251F10/index.html

## Meeting Time

Lecture 1: Introduction, Coordinates, & VectorsPDFLecture 2: Dot and Cross ProductsPDFLecture 3: Lines and PlanesPDFLecture 4: Quadric SurfacesPDFLecture 5: Vector Valued FunctionsPDFLecture 6: Arc LengthPDFLecture 7: Functions of 2 VariablesPDFLecture 8: Partial DerivativesPDFLecture 9: Tangent PlanesPDFLecture 10: Chain RulePDFLecture 11: Directional DerivativesPDFLecture 12: Maxima & MinimaPDFLecture 13: Langrage MultipliesPDFLecture 14: Multiple IntegralsPDFLecture 15: General Regions & Polar CoordinatesPDFLecture 16: Polar Coordinates & Change of VariablesPDFLecture 17: Change of Variables & Triple Integrals IPDFLecture 18: Triple Integrals II & Spherical CoordinatesPDFLecture 19: Spherical Coordinates & Vector FieldsPDFLecture 20: Line IntegralsPDFLecture 21: Fundamental Theorem of Line IntegalsPDFLecture 22: Green's TheoremPDFLecture 23: Curl and DivergencePDFLecture 24: Surface IntegralsPDFLecture 25: Stokes' TheoremPDFLecture 26: ExamplesLecture 27: Divergence TheoremPDFLecture 28: Review
Sours: https://www.math.ucla.edu/~mikehill/Teaching/Math231.html
Multivariable Calculus: Exam 2 Review A Solutions

## Math 251, Fall 2011

### Course Materials

Schedule and Homework (Updated Daily)
Lecture Notes (Updated Daily)

### Sept 1st (Day One Material)

Syllabus (pdf)
Course Objectives and Learning Goals
Diagnostic Quiz (pdf)
Diagnostic Quiz: Solutions to Questions 1-7 (pdf)
Diagnostic Quiz: Solutions to Question 8 (pdf)
Study Plan Essay (html)
Surface Sketching Primer (pdf)
Surface Sketching Homework (html)
Alexander Calder's wire-frame sculptures (See them at the National Gallery of Art in Washington DC!)
The Cornell Note taking System [pdf]
Tips for Success in Math 251 by ex-student Esther Gross (pdf)

### Brushing Up on Single Variable Calculus

If you need to brush up on your single variable calculus, here are the sections Stewart's "Calculus (Early Transcendentals)" that we rely on in Math 251. Starred sections are especially important.

2.1, 2.7, 2.8, 3.1, 3.2, 3.3, 3.4**, 3.6, 3.11, 4.1, 4.3, 4.5, 4.7, 4.9, 5.1-5.4, 5.5**, 6.1, 6.2, 7.1

The material from Chapter 5,6,7 is used in Math 251 Chapters 15, 16.

The material from Chapter 4,5,6 is used in Math 251 Chapters 14, 15.

Matlab for Multivariable Calculus

### EXAM I

Exam I will be held THURSDAY SEPT 29 in first 65 mins of class. (Note the change of date). It will cover 12.1, 12.2, 12.3, 12.4, 12.5, 12.6
I will hold a review session for the exam from 1:30-2'ish on Tuesday Sept 27 in BIOL 120. Bring your questions!

### EXAM II

Exam II will be held THURSDAY OCT 27 in first 65 mins of class. It will cover 15.7, 15.8 (cyl+sph coordinates material only), 13.1-13.3, 14.1-14.5, and 16.6.
I will hold review sessions for the exam from 1:30-2'ish on Thursday Oct 20 and Tuesday Oct 25th in BIOL 120. Bring your questions!

### EXAM III

Exam III will be held TUESDAY NOV 22 in first 65 mins of class. It will cover 14.5-14.8, 15.1-15.4, 16.1, 16.2.
I will hold review sessions for the exam from 1:30-2'ish on Tuesday Nov 15 and Thursday Nov 17 in BIOL 120. Bring your questions!

### FINAL EXAM

The final will cover all material on exmas 1,2,3 together with 16.3,16.4, 16.5, 16.6, 16.7, 16.8, 15.7, 15.8.

Exam I [pdf]
Exam I Solutions [pdf]
Exam II Solutions [pdf]
Exam III [pdf]
Exam III Solutions [pdf]

### Past Exams

Here are the exams I gave in Math 251H, Fall 2003.

Midterm One (pdf)
Midterm Two (pdf)
Midterm Three (pdf)
Final (pdf)

Here are the midterm exams I gave in Math 251, Fall 2004.

Midterm One (pdf)
Midterm Two (pdf)
Midterm Three (pdf)

Here are the exams I gave in Math 251, Spring 2004.

Midterm One (pdf)
Midterm Two (pdf)
Midterm Three (pdf)
Final (pdf)

Here are the solutions to the exams I gave in Math 251, Spring 2004.

Exam One Solutions (pdf)
Exam Two Solutions (pdf)
Exam Three Solutions (pdf)

Here are the midterm exams I gave in Math 251H, Fall 2006

Exam One (pdf)
Exam Two (pdf)
Exam Three (pdf)

Here are the solutions to the exams I gave in Math 251H, Fall 2006

Solutions to Exam One (pdf)
Solutions to Exam Two (pdf)
Solutions to Exam Three (pdf)

Here are the exams I gave in Math 251, Fall 2008

Exam One (pdf)
Exam Two (pdf)
Exam Three (pdf)
Final (pdf)

Here are the solutions to the midterm exams I gave in Math 251, Fall 2008

Solutions to Exam One (pdf)
Solutions to Exam Two (pdf)
Solutions to Exam Three (pdf)

Here are the exams I gave in Math 251, Fall 2009

Exam One
Exam Two
Exam Three
Final Exam

Here are the solutions to the midterm exams I gave in Math 251, Fall 2009

Solutions to Exam One
Solutions to Exam Two
Solutions to Exam Three

Here are the exams I gave in Math 251, Fall 2010

Exam One [pdf]
Exam Two [pdf]
Exam Three [pdf]
Final Exam[pdf]

Here are the solutions to the midterm exams I gave in Math 251, Fall 2010

Exam One Solutions [pdf]
Exam Two Solutions [pdf]
Exam Three Solutions [pdf]
Final Exam Solutions [pdf]

Sours: https://personal.utdallas.edu/~jwz120030/Teaching/PastCoursesUMBC/M251F11/index.html

## Calculus pdf multivariate solutions final with exam

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What are the big ideas of Multivariable Calculus?? Full Course Intro

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