MIT Single Variable Calculus

This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

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