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# Single Variable Calculus (video)

 16

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
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

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Tags: Single Variable Calculus, Calculus, video, Variable, functions, variable, Differentiation, Integration, Applications, Techniques