These video lectures of Professor David Jerison teaching 18.01 were recorded live in the Fall of 2007 and do not correspond precisely to the lectures taught in the Fall of 2006 (e.g., the lecture notes).
Video lectures table.
| SES # |
TOPICS |
| Differentiation |
| 1 |
Derivatives, slope, velocity, rate of change |
| 2 |
Limits, continuity - Trigonometric limits |
| 3 |
Derivatives of products, quotients, sine, cosine |
| 4 |
Chain rule - Higher derivatives |
| 5 |
Implicit differentiation, inverses |
| 6 |
Exponential and log - Logarithmic differentiation; hyperbolic functions |
| 7 |
Hyperbolic functions (cont.) and exam 1 review |
| 8 |
Exam 1 covering Ses #1-7 (No video) |
| Applications of Differentiation |
| 9 |
Linear and quadratic approximations |
| 10 |
Curve sketching |
| 11 |
Max-min problems |
| 12 |
Related rates |
| 13 |
Newton's method and other applications |
| 14 |
Mean value theorem
Inequalities |
| 15 |
Differentials, antiderivatives |
| 16 |
Differential equations, separation of variables |
| 17 |
Exam 2 covering Ses #8-16 (No video) |
| Integration |
| 18 |
Definite integrals |
| 19 |
First fundamental theorem of calculus |
| 20 |
Second fundamental theorem |
| 21 |
Applications to logarithms and geometry |
| 22 |
Volumes by disks and shells |
| 23 |
Work, average value, probability |
| 24 |
Numerical integration |
| 25 |
Exam 3 review |
| 26 |
Exam 3 covering Ses #18-24 (No video) |
| Techniques of Integration |
| 27 |
Trigonometric integrals and substitution |
| 28 |
Integration by inverse substitution; completing the square |
| 29 |
Partial fractions |
| 30 |
Integration by parts, reduction formulae |
| 31 |
Parametric equations, arclength, surface area |
| 32 |
Polar coordinates; area in polar coordinates |
| 33 |
Exam 4 review |
| 34 |
Exam 4 covering Ses #27-33 (No video) |
| 35 |
Indeterminate forms - L'Hôspital's rule |
| 36 |
Improper integrals |
| 37 |
Infinite series and convergence tests |
| 38 |
Taylor's series |
| 39 |
Final review |