| SES # | TOPICS | LECTURE NOTES | |
|---|---|---|---|
| Derivatives | |||
| 1 | Derivatives, slope, velocity, rate of change | (PDF - 1.1 MB) | Ses #1-7 complete (PDF - 5.2 MB) |
| 2 |
Limits, continuity Trigonometric limits | (PDF - 2.6 MB) | |
| 3 | Derivatives of products, quotients, sine, cosine | (PDF) | |
| 4 |
Chain rule Higher derivatives | (PDF) | |
| 5 | Implicit differentiation, inverses | (PDF) | |
| 6 |
Exponential and log Logarithmic differentiation; hyperbolic functions | (PDF) | |
| 7 | Exam 1 review | (PDF) | |
| 8 | Exam 1 covering Ses #1-7 | (No Lecture Notes) | |
| Applications of Differentiation | |||
| 9 | Linear and quadratic approximations | (PDF) | Ses #9-16 complete (PDF - 6.9 MB) |
| 10 | Curve sketching | (PDF - 1.8 MB) | |
| 11 | Max-min problems | (PDF - 1.1 MB) | |
| 12 | Related rates | (PDF - 1.0 MB) | |
| 13 | Newton's method and other applications | (PDF - 1.2 MB) | |
| 14 |
Mean value theorem Inequalities | (PDF) | |
| 15 | Differentials, antiderivatives | (PDF) | |
| 16 | Differential equations, separation of variables | (PDF) | |
| 17 | Exam 2 covering Ses #8-16 | (No Lecture Notes) | |
| Integration | |||
| 18 | Definite integrals | (PDF) | Ses #18-25 complete (PDF - 8.6 MB) |
| 19 | First fundamental theorem of calculus | (PDF) | |
| 20 | Second fundamental theorem | (PDF) | |
| 21 | Applications to logarithms and geometry | (PDF - 1.4 MB) | |
| 22 | Volumes by disks and shells | (PDF - 1.7 MB) | |
| 23 | Work, average value, probability | (PDF - 2.2 MB) | |
| 24 | Numerical integration | (PDF - 1.1 MB) | |
| 25 | Exam 3 review | (PDF) | |
| Techniques of Integration | |||
| 26 | Trigonometric integrals and substitution | (PDF) | Ses #26-38 complete (PDF - 8.6 MB) |
| 27 | Exam 3 covering Ses #18-24 | (No Lecture Notes) | |
| 28 | Integration by inverse substitution; completing the square | (PDF) | |
| 29 | Partial fractions | (PDF) | |
| 30 | Integration by parts, reduction formulae | (PDF - 1.4 MB) | |
| 31 | Parametric equations, arclength, surface area | (PDF) | |
| 32 |
Polar coordinates; area in polar coordinates Exam 4 review |
(PDF) | |
| 33 | Exam 4 covering Ses #26-32 | (No Lecture Notes) | |
| 34 | Indeterminate forms - L'Hôspital's rule | (PDF) | |
| 35 | Improper integrals | (PDF) | |
| 36 | Infinite series and convergence tests | (PDF - 1.4 MB) | |
| 37 | Taylor's series | (PDF) | |
| 38 | Final review | (PDF) | |
