Trigonometric, Inverse Trigonometric, Logarithmic and Exponential Functions.
Derivatives, Antiderivatives and Integrals of functions of one real variable.
Applications including graphing, maximizing and minimizing functions.
Areas and Volumes.
You are expected to read the textbook before the classroom discussion of each topic.
| Week 1 | 1.1
1.2 |
Functions and their representations A catalog of essential functions |
19, 21, 23, 25, 37, 57
18, 28, 49, 62 |
| 1.3
1.4 |
The limit of a function
Calculating limits |
11, 13, 16, 33
10, 11, 13, 20, 23, 31 |
|
| Week 2 | 1.5
1.6 |
Continuity Limits involving infinity |
13, 20, 24, 29
14, 18, 21, 29, 47, 49 |
| 2.1
2.2 |
Derivatives and rates of change
The derivative as a function |
23, 24, 25, 28
1, 16, 17, 18, 19, 20 |
|
| Week 3 | 2.2
2.3 |
The derivative as a function Basic differentiation formulas |
3, 9, 14, 18, 22, 28, 33, 35
11, 16, 26, 32, 39, 48, 52, 62 |
| 2.4
2.5 |
The product and quotient rules
The chain rule |
2, 11, 23, 29, 38, 43, 46, 52
3, 11, 21, 34, 37, 45, 54, 64 |
|
| Week 4 | 2.6
2.7 |
Implicit differentiation
Related rules (optional) |
5, 13, 14, 17, 23, 32, 36, 38
3, 7, 11, 14, 20, 25, 31, 36 |
| 2.8 | Linear approximations and differentials | 3, 10, 13, 18, 20, 21, 23, 28 | |
| Week 5 | 3.1
3.2 |
Exponential functions Inverse functions and logarithms |
16, 18, 19, 25, 30, 31, 11, 32
4, 17, 22, 36, 48, 53, 63, 66, 73 |
| 3.3
3.4 |
Derivatives of logarithms and exponential functions
Exponential growth and decay |
7, 23, 24, 30, 38, 51, 57, 63
1, 4, 5, 9, 18, 12, 20 | |
| Week 6 | 3.5
3.6 3.7 |
Inverse trignometric functions
Hyperbolic functions (optional) Indeterminate forms and L'Hospital's rule |
4, 7, 8, 13, 17, 20, 28, 32
7, 10, 11, 32, 19, 44, 48, 34 6, 12, 30, 31, 35, 40, 41, 49 |
| 4.1
4.2 |
Maximum and minimum values
The mean value theorem |
8, 14, 28, 29, 36, 43, 55, 61
4, 13, 15, 18, 27, 32, 36, 30 |
|
| Week 7 | 4.3
4.4 4.5 |
Derivatives and shapes of graphs Curve sketching (optional) Optimization problems |
4, 24, 30, 34, 35, 37, 48, 53
2, 14, 22, 31, 38 |
| 4.5
4.6 |
Optimization problems
Newton's method |
6, 9, 12, 24, 28, 32, 38, 43
| |
| Week 8 | 4.6
4.7 |
Newton's method Antiderivatives |
6, 8, 10, 12, 18, 22, 25, 29
1, 2, 3, 4, 11, 23, 26 |
| 5.1
5.2 |
Areas and distances
The definite integral |
2, 8, 14, 16
| |
| Week 9 | 5.2
5.3 |
The definite integral Evaluating definite integrals |
2, 8, 14, 18, 29, 32, 39, 50
|
| 5.3
5.4 |
Evaluating definite integrals
The fundamental theorem of calculus |
3, 12, 15, 20, 32, 37, 43, 62
| |
| Week 10 | 5.4
5.5 |
The fundamental theorem of calculus The substitution rule |
2, 4, 8, 22, 24, 27, 28, 33
|
| 5.5
6.1 |
The substitution rule
Integration by parts |
6, 15, 21, 31, 39, 47, 55, 62
2, 8, 14, 19, 26, 31, 40, 43 | |
| Week 11 | 6.1
6.2 |
Integration by parts Trignometric integrals and substitutions |
2, 8, 14, 19, 26, 31, 40, 43
8, 12, 20, 28, 34, 51, 58 |
| 6.3 | Partial Fractions | 19, 22, 28, 38, 41 | |
| Week 12 | 6.5 | Approximate integration | 7, 8, 10, 15, 16 |
| 6.6 | Improper integrals | 7, 10, 14, 22, 28, 32, 41, 46 | |
| Week 13 | 7.1 | Areas between curves | 5, 6, 7, 8, 14, 15, 18, 20, 33 |
| Review |
The course grade is based on the total number of points from hour exams, homework, quizzes, computer labs, and the final exam.
| Homework and quizzes | 20% |
| Midterm | 30%
|
| Final Exam | 50% |
| V63.0121.001 | Jain, Sonal | jain@cims.nyu.edu | 998-3210 | WWH 820 |
| V63.0121.002 | Hu, David | dhu@cims.nyu.edu | 998-3203 | WWH 103 |
| V63.0121.003 | Goldberg, Daniel | dgoldberg@cims.nyu.edu | 998-3198 | WWH 808 |
| V63.0121.004 | Zhang, Jun | jun@cims.nyu.edu | 998-3239 | WWH 104 |
| V63.0121.005 | Albers, Peter | albers@cims.nyu.edu | 998-3185 | WWH 1025 |
| V63.0121.006 | Bae, Hantaek | hantaek@cims.nyu.edu | 998-3196 | WWH 806 |
| V63.0121.007 | Lim, Sukbin | sukbin@cims.nyu.edu | 998-3125 | WWH 528 |
| V63.0121.008 | Gunturk, Sinan | gunturk@cims.nyu.edu | 998-3246 | WWH 622 |
| V63.0121.009 | Weare, Jonathan | weare@cims.nyu.edu | 998-3148 | WWH 621 |
| V63.0121.011 | Sheffield, Scott | sheff@cims.nyu.edu | 998-3262 | WWH 1107 |
| V63.0121.015 | Holmes, Miranda | holmes@cims.nyu.edu | 998-3207 | WWH 809 |