Math 213 Calculus III

Monday, Wednesday, and Friday

11:10am-12:00pm

Peirce L09

 

Textbook

Calculus: Multivariable, Fifth Edition, by McCallum, Hughes-Hallett, Gleason, et al.

         

Syllabus

 

Office Hours (Hayes 309-A)

Monday 2:10-3:00pm

Tuesday 11:10am-1:00pm

Wednesday 2:10-3:00pm

Thursday 10:10-11:00am

 

Drop-in Tutoring with Emily at the MSSC

Tuesday 7:00-9:00pm

Thursday 8:00-10:00pm

 

Math and Science Skills Center Tutoring (Tomsich 101)

Sunday, Tuesday, Thursday 7:00-10:00

 

Homework

Lesson

Date

Section(s)

Topic

Homework

Due

1

1/14/2013

12.1

Functions of Two Variables

Section 12.1: #2, 5, 7-9, 12

Read Section 12.1 and 12.2.

1/16/2013

2

1/16/2013

12.2

Graphs of Functions of Two Variables

Section 12.1: #26, 28

Section 12.2: #6, 7, 10, 11-13, 15

Worksheet: #1 (all examples on the worksheet are in the book, but it’s a good idea to think through them on your own since these types of functions will show up a lot).

Read Section 12.3.

1/18/2013

3

1/18/2013

12.3

Contour Diagrams

Section 12.3: #6, 10, 11, 16-18, 21, 22ab, 30, 32, 33

Contours Worksheet: #1, 2, 5

Read Section 12.4.

1/16/2013

4

1/21/2013

12.4

Linear Functions

Section 12.4: #9, 11-16, 19, 22, 24, 26, 27

Read Section 12.6.

1/23/2013

5

1/23/2013, 1/25/2013

12.6

Limits and Continuity

Maple Intro Worksheet (optional)

Section 12.6: #2, 3, 9, 11, 14, 15, 17, 18

Work on Project 1 (due Wednesday).

1/28/2013

6

1/28/2013

13.1, 13.2

Displacement Vectors,

Vectors in General

Project 1 (due Wednesday!)

Required:

Vector Primer

Section 13.1: #6, 19, 23, 24

Section 13.2: 1-6, 12

Recommended:

Section 13.1: #2, 13, 14, 18, 30

Section 13.2: 7, 11, 15, 17, 19, 22

Read Sections 13.1-13.3.

2/1/2013

7

1/30/2013,

2/1/2013

13.3, 13.4

Dot Product,

Cross Product

Section 13.3 # 8, 15, 16, 18, 28, 34, 36, 38, 47, 50

Section 13.4 # 4, 8, 11, 16, 17, 25, 28, 34

2/4/2013

8

2/4/2013

13.1-13.4

Vector Review

Chapter 13 Review Worksheet

Read Sections 14.1 and 14.2.

2/6/2013

9

2/6/2013

14.1-14.2

Partial Derivatives

Section 14.1: #2, 3, 11-13, 16, 20, 22

Section 14.2: #8, 34, 35, 37, 40, 45

Banking Problem from worksheet

Read Section 14.3.

2/8/2013

10

2/8/2013

14.3

Local Linearity and the Differential

Section 14.3: # 1, 5, 12, 13, 17, 18

2/11/2013

11

2/13/2013

Review

 

Review Homework: (Please note that these problems are a tool to help you study – they are not intended to represent a sample exam).

Turn in two (or more) problems from each section.

Chapter 12 Review Exercises: #7, 8, 11, 17, 24, 28, 30, 31, 32
Chapter 13 Review Exercises: #1, 2, 5-7, 19, 21, 23, 35, 41, 42, 47, 48

Chapter 14 Review Exercises: #5, 6, 9, 57, 58, 59ab, 64-67

2/15/2013

12

2/11/2013, 2/18/2013

14.4

Gradients and Directional Derivatives

Section 14.4: #5, 18, 30, 32, 36, 40, 45, 62, 65, 73, 74

Gradient worksheet: #7,8

Directional Derivative worksheet

Read Sections 14.4 and 17.1.

2/20/2013

13

2/20/2013

17.1

Parametrized Curves

Parametric exercises in Maple file on P drive:

Class/Math/Smith/Math213Sp13/ParametricPlots.

Work through ParametricPlotsExercises.mw,

Then submit answers using ParametricExercisesAnswers.mw.

Project description is in ParametricPlotsProject.mw.

Phase 1: 3/1/2013,

Phase 2: 3/22/2013

14

2/22/2013

14.6

The Chain Rule

Section 14.6: #2, 8, 14, 15, 18, 29

Implicit Differentiation Problems 1 and 2

Read Sections 14.6 and 14.7.

2/25/2013

15

2/25/2013

14.7

Second-Order Partial Derivatives

Section 14.7: #7, 8, 22, 23, 26, 27, 37, 40, 44

Read Section 14.8.

2/27/2013

16

2/27/2013

14.8

Differentiability

Section 14.8: #4, 12, 14, 16, 20

Parametric plots project exercises and start of masterpiece.

Read Section 15.1.

 

17

3/1/2013

15.1

Local Extrema

Worksheet questions: 6, 7(b) and (c)

Section 15.1: 1, 2, 10, 27, 28, 34

Read Section 15.2.

3/20/2013

(now 3/22/2013)

18

3/18/2013, 3/20/2013, 3/22/2013

15.1, 15.2

Optimization

Project 2

Worksheet questions 1-5

Read Section 15.3

3/22/2013

 

3/25/2013

19

3/25/2013, 3/27/2013

15.3

Lagrange Multipliers

Worksheet questions (book problems 22, 24, 28),

Section 15.3: #32 and 32+

3/29/2013

20

3/29/2013

16.1

The Definite Integral of a Function of Two Variables

Worksheet questions 2-4

Section 16.1: #6, 8, 26, 28

4/1/2013

21

4/1/2013

16.2

Iterated Integrals

Section 16.2: # 8, 14, 17, 23, 29, 30, 35, 39, 44, 48, 49

4/3/2013

 

 

 

 

Review Homework: (Please note that these problems are a tool to help you study – they are not intended to represent a sample exam).

These problems will not be collected.

Chapter 14 Review Exercises: #1, 2, 24, 41, 59, 68, 73, 75, 76, 78

Section 14.6: #2, 10, 16, 27

Section 14.8 : #13, 16

Chapter 15 Review Exercises: #1, 6-8, 11, 26, 35

Section 15.2: #4

Optimize  on (a) the closed disk centered at (0,0) with radius 2, (b) the triangle

(c) the region

 

22

4/8/2013

16.3

Triple Integrals

Section 16.3: #5, 6, 10, 23, 35, 37, 40, 45, 49,

Handout: #22

4/10/2013

23

4/10/2013

16.2, 16.3

Double and Triple Integrals

Worksheet

4/12/2013

24

4/12/2013

16.4

Double Integrals in Polar Coordinates

Section 16.4: #5, 6, 9, 14, 21, 22, 23, 26, 28, in-class problem

4/15/2013

 

 

 

 

Review Homework: (Please note that these problems are a tool to help you study – they are not intended to represent a sample exam).

These problems will not be collected.

Section 16.1 # 3, 28
Chapter 16 Review Exercises: 1, 3, 8, 9, 10, 12, 16, 21, 28, 30, 31

 ,

35-37, 46, 48, 52, 57, 59, 69 (challenging)
Chapter 16 Check Your Understanding: 1-3, 8, 19

 

25

4/15/2013, 4/17, 2013

16.5

Integrals in Cylindrical and Spherical Coordinates

Section 16.5: #2-6, 8, 15-19, 27-29, 33, 42

4/19/2013

26

4/22/2013

17.1, 17.2

Parametrized Curves

Motion, Velocity, and Acceleration

Sec 17.1: # 1, 4, 23, 45, 57, 62, 70

Sec 17.2: #6, 10, 21 (plotting the points would be a good start…)

We’ll do more with Sec 17.2 next time.

4/24/2013

27

4/24/2013

17.2

Motion, Velocity, and Acceleration

Sec 17.2: #14, 17, 18, 20, 23, 27, 35, 42, 44

(See length of curve formula on page 891 for #14 – if you want a good exercise, you can do #47 to justify the formula).

Fun challenge problem (optional): #37

4/26/2013

28

4/26/2013

17.3, 17.4

Vector Fields and Flow Lines

Section 17.3 # 5 - 10, 26, 29 - 31, 33, 34

Example Maple commands for drawing

 a vector field:
with(plots);
fieldplot([x+2, y^2+x], x = -1 .. 1, y = -1 .. 1, arrows = medium, grid = [10, 10]);

Section 17.4 # 6, 7, 8, 10, 18

4/29/2013

29

4/29/2013

18.1

The Idea of a Line Integral

Section 18.1: #1, 2, 5, 15, 17, 20, 22, 34, 40

Think about: #41, 42

5/1/2013

30

5/1/2013

18.2

Computing Line Integrals

Section 18.2 # 1, 4, 12, 16, 20, 29, 30, 35

5/3/2013

31

5/3/2013

18.3, 18.4

Gradient Fields and Path-Independent Fields

Section 18.3 # 4, 8, 13, 22, 23, 25, 35

5/9/2013