Math 151 - Syllabus and General Information, Fall 2005

Lecturer : Dr. Vladimir Shtelen
Office & Office Hours: Hill Center 613, Mondays 2 - 3pm
e-mail address: shtelen@math.rutgers.edu
web site: http://www.math.rutgers.edu/~shtelen
TEXTBOOK: James Stewart, Calculus (Early Transcendentals) 5e., Brooks/Cole Publishing Co.
CALCULATOR: A graphing calculator is required for this course. We have traditionally used the TI-82 or 83 and recommend either of them, but any calculator with equivalent capacities can be used, such as the popular TI-85 or 86. Calculators will not be permitted on final exams
Grading: Final exam - 40%, Midterm exams - 40%, , Quizzes - 10%, Homework - 5%, Workshops - 5%

Lecture Date Sections 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, 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, 26, 33, 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 10/07
First exam

12 10/11 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 10/14 3.10 Related rates 3.10: 1, 6, 14, 23, 24, 31

14 10/18 3.11, 4.9 Linear approximation, Newton's Method 3.11: 5, 7, 10, 13, 32, 36, 42
4.9: 1, 5, 14, 36

15 10/21 4.4 L'Hôpital's Rule 4.4: 1, 2, 3, 7, 10, 15, 21, 22, 29, 36, 37, 38, 47, 53, 54, 68

16 10/25 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 10/28 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 11/01 4.5, 4.6 Sketching graphs 4.5: 3, 18, 30, 35, 45, 48
4.6:7, 14, 15, 26, 27

19 11/04 4.7 Applied max/min 4.7: 2, 9, 17, 22, 27, 33, 40, 56

20 11/08 4.10 Antiderivatives 4.10: 3, 10, 12, 15, 25, 28, 35, 40, 48, 53, 55, 60, 63

21 11/11 5.1, Appendix E Area, distance, sigma notation 5.1: 4, 11, 18, 21
App. E: 1, 6, 12, 14, 25, 30, 44

22 11/15
Second exam

23 11/18 5.2 The definite integral 5.2:3, 5, 12, 23, 33, 34, 37, 38, 48, 49, 53, 54

24 11/29 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 12/02 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 12/06 6.1 Computation of areas 6.1: 1, 2, 3, 4, 9, 14, 17, 18, 43, 44, 45

27 12/09 5.6 Logarithm defined as an integral 5.6: 1, 3

28 12/13
Catch up and review for final exam

Lecture	Date	Sections	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, 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, 26, 33, 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	10/07		First exam
12	10/11	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	10/14	3.10	Related rates	3.10: 1, 6, 14, 23, 24, 31
14	10/18	3.11, 4.9	Linear approximation, Newton's Method	3.11: 5, 7, 10, 13, 32, 36, 42 4.9: 1, 5, 14, 36
15	10/21	4.4	L'Hôpital's Rule	4.4: 1, 2, 3, 7, 10, 15, 21, 22, 29, 36, 37, 38, 47, 53, 54, 68
16	10/25	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	10/28	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	11/01	4.5, 4.6	Sketching graphs	4.5: 3, 18, 30, 35, 45, 48 4.6:7, 14, 15, 26, 27
19	11/04	4.7	Applied max/min	4.7: 2, 9, 17, 22, 27, 33, 40, 56
20	11/08	4.10	Antiderivatives	4.10: 3, 10, 12, 15, 25, 28, 35, 40, 48, 53, 55, 60, 63
21	11/11	5.1, Appendix E	Area, distance, sigma notation	5.1: 4, 11, 18, 21 App. E: 1, 6, 12, 14, 25, 30, 44
22	11/15		Second exam
23	11/18	5.2	The definite integral	5.2:3, 5, 12, 23, 33, 34, 37, 38, 48, 49, 53, 54
24	11/29	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	12/02	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	12/06	6.1	Computation of areas	6.1: 1, 2, 3, 4, 9, 14, 17, 18, 43, 44, 45
27	12/09	5.6	Logarithm defined as an integral	5.6: 1, 3
28	12/13		Catch up and review for final exam