Syllabus and Homework

Week

Dates

Sections, topics

Required problems

Suggested problems

Problem sets

0

Aug 28-30

5.1-5.3, 5.4

Review of 112, Fundamental Theorem of Calculus

5.3 2, 8, 22, 58, 68

5.4 2, 32, 50, 64

5.3 3, 9, 13, 21, 25, 57, 67

5.4 1, 21, 37, 49, 63

1

Sept

2-6

5.4 (cont.), 5.5, 6.1
Indefinite integrals, net change theorem and the substitution rule. Areas between curves.

5.5 14, 32, 38, 60, 86

6.1 2, 18, 22, 46

5.5 3, 7, 23, 25, 31, 55, 85

6.1 1, 7, 21, 23, 47

2

Sept

9-13

6.2, 6.3, 7.1
Volumes by discs/washers, volumes by cylinders. Integration by parts.

6.2 4, 16, 22, 58;

6.3 8, 18, 30

7.1  4, 10, 22, 40,62

6.2 3, 9, 15, 25, 27, 55

6.3 1, 9, 11, 17, 29

7.1 3, 15, 17, 23, 27, 39, 63

Problem Set #1 (Sections 5.3, 5.4, 5.5)

3

Sept

16-20

7.1 (cont.), 7.5, 7.6
Strategies for integration, using a table of integrals (pdf). Integration using tables and computer algebra systems.

7.5 10, 22, 48, 64, 66

7.6 6, 22

7.5: 9, 13, 17, 33, 51, 63

7.6  7, 11, 23, 39, 41

Problem Set #2 (Sections 6.1, 6.2, 6.3)

4

Sept

23-26

7.6 (cont.), 7.7, 7.8
Approximate integration, improper integrals.

7.7 2, 4, 8, 46

7.8 2, 24, 34, 52, 78

7.7 1, 3,7, 45

7.8 1, 7, 15, 19, 31, 35, 51, 77

Problem Set #3 (Sections 7.1, 7.5)

5

Sept

30-Oct 4

8.1, 8.2, 10.1
Arc length, areas of surfaces of revolution, and parametric functions.

8.1 10, 18
8.2 6, 14, 26, 28
10.1 14, 26, 34, 38

8.1 1, 7, 13, 17
8.2  5, 7, 11, 15, 25
10.1 13, 25, 33, 37

Problem Set #4 (Sections 7.6, 7.7)

Oct 3

Mid term #1, 7-8:30p.

Content: Sections 5.3 through 7.8.

Locations:

·    Sections 1, 5,6,7, and 8 (instructed by A. Auel, P. Zhao and J. Rolf) be held in Davies Auditorium.

·    Sections 2 and 3 (instructed by W Leeb and Z. Wang) will be in 119 WLH.

6

Oct

7-11

10.2, 10.3, 10.4

Calculus on parametric functions, polar coordinates. calculus on polar functions.

10.2 12, 18, 34, 42, 58, 74 (hard problem, will be extra credit).
10.3 16, 24, 48, 56
10.4 2, 12, 30, 48

10.2 13, 17, 33, 41
10.3 : 9, 13, 17, 23, 47, 55 
10.4 1, 11, 23, 29, 47

Problem Set #5 (Sections 7.8, 8.1, 8.2)

7

Oct

14-18

11.1, 11.2, 11.3

Sequences, series, integral test.

11.1 14, 34, 36, 38
11.2 18, 30, 34, 40, 68
11.3: 6, 24, 30

11.1 5, 13, 17, 25, 33, 45, 47
11.2 15, 17, 29, 39, 61, 67
11.3 9, 21, 25

Problem Set #6 (Sections 10.1, 10.2)

8

Oct

21-25

11.4

Comparison tests, Fall Break!

11.4 10, 24, 28, 30, 38, 44

11.4 11, 15, 17, 23, 25, 29, 39, 43,45

9

Oct

28-Nov 1

11.4 (cont.), 11.5, 11.6

Comparison test, alternating series, ratio and root tests.

11.5 4, 10, 32
11.6 4, 10, 12 20, 22, 24, 26

11.5 3, 1, 17
11.6 5, 7, 9, 15, 21, 23, 25

Problem Set #7 (Sections 10.3, 10.4, 11.1)

10

Nov

4-8

11.7, 11.8

Strategies for testing convergence, power series.

11.7 14, 26, 38  

11.8  6, 16, 20, 30, 32, 42

11.7 9, 11, 13, 21, 27, 35, 37

11.8 5, 7, 11, 19, 29, 31, 33, 37, 41

Problem Set #8 (Sections 11.2, 11.3, 11.4)

11

Nov

11-15

11.9-11.10

Representing functions by power series, Taylor and Maclaurin series.

11.9 8, 18, 26, 40

11.10 8, 18, 34

11.9 5, 7, 11, 15, 17, 25

11.10 5, 13, 15, 33

Problem Set #9 (Sections 11.5, 11.6)

Nov

13

Mid-term #2 7-8:30p.

12

Nov

18-22

11.10 (cont.), 11.11

Taylor and Maclaurin series and error.

11.10 48, 56, 64 
11.11 14, 26, 28, 30

11.10 47, 55, 57, 59, 69
11.11 13, 25, 27, 31

Problem Set #10 (Sections 11.7, 11.8)

Nov

25-29

Thanksgiving Break!

Prove the Riemann Hypothesis

Get some rest!

13

Dec

2-6

11.11 (cont.) and applications.
Applications to probability and differential equations; a theorem about prime numbers, and another theorem about prime numbers, the mathematics of sound.

Problem Set #11 (Sections 11.9, 11.10)

Final Exam