MATH 151: PROBLEMS AND SYLLABUS

FALL, 2004 


 


Lecture

Text

Topics

Suggested Problems

1

Appendices A,B,D; 1.1--1.5

Review of real numbers, absolute value, inequalities, lines, functions, exponential and trig functions}

App. A: 6, 7, 23, 28, 49, 52, 61, 62

 

 

 

App. B: 1, 7, 23, 25, 29, 35

 

 

 

App. D: 15, 19, 27, 31, 67, 74

 

 

 

1.1: 2, 7, 8, 19, 21, 22, 25, 38, 50, 51

 

 

 

1.2: 4, 11, 15, 16

 

 

 

1.3: 4, 5, 9, 16, 20, 23, 27, 36, 53

 

 

 

1.4: 1, 14, 15, 19, 25, 27

 

 

 

1.5: 11, 13, 17, 18, 22

2

Appendix D, 1.6

Inverse functions; logs and inverse trig functions

1.6: 6, 12, 14, 26, 27, 35, 38, 48, 49, 50, 52

3

2.1, 2.2

Tangents and velocity; limits

2.1: 1, 3, 6, 8

 

 

 

2.2: 5, 6, 8, 9, 14, 19, 23, 27, 28, 30, 31

4

2.3, 2.4

Limit laws and definition of limit

2.3: 1, 3, 6, 7, 10, 13, 20, 26, 29, 37, 35, 38, 40, 47, 58

 

 

 

2.4: 1, 3, 4, 6, 7, 20, 41, 42

5

2.5

Continuity; Intermediate Value Theorem

2.5: 3, 4, 15, 16, 19, 20, 25, 26, 37, 40, 47, 50, 51

6

2.6

Infinity; asymptotes

2.6: 4, 11, 16, 18, 19, 23, 26, 39, 40, 55, 58

7

2.7, 2.8, 2.9

Rates of change; derivatives

2.7: 5, 8, 11, 12, 15

 

 

 

2.8: 3, 7, 11, 15, 16

 

 

 

2.9: 2, 4, 11, 22, 29, 30, 34, 37, 41

8

3.1, 3.2

Differentiation formulas; derivatives of exponential functions

3.1: 5, 7, 13, 16, 20, 33, 39, 46, 51, 54, 57

 

 

 

3.2: 3, 4, 5, 8, 9, 20, 27, 41, 42

9

3.3, 3.4

Rates of change; derivatives of trig functions

3.3: 3, 8, 13, 18, 25, 31

 

 

 

3.4: 3, 5, 8, 10, 13, 16, 18, 23, 29, 35, 36, 39

10

3.5, 3.6

The chain rule, implicit differentiation

3.5: 1, 2, 9, 14, 15, 16, 21, 22, 25, 33, 35, 44, 47

 

 

 

3.6: 3, 9, 16, 29, 41--44, 47, 48

11

First exam (usual class time and place)

12

3.6, 3.7, 3.8

Derivatives of logs and inverse trig functions, higher derivatives

3.7: 1, 5, 8, 11, 19, 20, 39, 48, 51, 57

 

 

 

3.8: 3, 4, 7, 8, 13, 15, 24, 25, 26, 32, 35, 38, 41

13

3.10

Related rates

3.10: 1, 6, 14, 23, 24, 31

14

3.11, 4.9

Linear approximation, Newton's Method

3.11: 5, 7, 10, 13, 31, 36, 42

 

 

 

4.9: 1, 5, 14, 36

15

4.4

L'H\^opital's Rule

4.4: 1, 2, 3, 7, 10, 15, 21, 22, 29, 36, 37, 38, 47, 53, 54, 68

16

4.1, 4.2

Max and min; the Mean Value Theorem

4.1: 3, 22, 34, 39, 46, 55, 61, 62, 65, 68, 77

 

 

 

4.2: 5, 11, 14, 17, 23, 24, 29

17

4.3

f'(x), f''(x) and the graph of f

4.3: 1, 5, 7, 11, 21, 22, 31, 32, 33, 36, 37, 42, 45, 47

18

4.5, 4.6

Sketching graphs

4.5: 3, 18, 30, 35, 45, 48

 

 

 

4.6: 7, 14, 15, 26, 27

19

4.7

Applied max/min

4.7: 2, 9, 17, 22, 27, 33, 40, 56

20

4.10

Antiderivatives

4.10: 3, 10, 12, 15, 25, 28, 35, 40, 48, 53, 55, 60, 63

21

5.1, Appendix E

Area, distance, sigma notation

5.1: 4, 11, 18, 21

22

Second exam (usual class time and place)

 

 

 

App. E: 1, 6, 12, 14, 25, 30, 44

23

5.2

The definite integral

5.2: 3, 5, 12, 23, 33, 34, 37, 38, 48, 49, 53, 54

24

5.3, 5.4

The Fundamental Theorem of Calculus

5.3: 2, 8, 11, 17, 18, 25, 30, 31, 35, 37, 68

 

 

 

5.4: 1, 2, 5, 7, 8, 10, 11, 18, 19, 22, 29, 30, 38, 47, 54, 55

25

5.5

Substitution rule

5.5: 1, 3, 4, 5, 10, 12, 19, 20, 21, 25, 32, 44, 51, 53, 58, 63, 66, 68

26

6.1

Computation of areas

6.1: 1, 2, 3, 4, 9, 14, 17, 18, 43, 44, 45

27

5.6

Logarithm defined as an integral

5.6: 1, 3

28

Catch up or review for final exam