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).¡@
| 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 |