| Differentiation |
| 0 |
Recitation: graphing |
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| 1 |
Derivatives, slope, velocity, rate of change |
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| 2 |
Limits, continuity
Trigonometric limits
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| 3 |
Derivatives of products, quotients, sine, cosine |
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| 4 |
Chain rule
Higher derivatives
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| 5 |
Implicit differentiation, inverses |
Problem set 1 due |
| 6 |
Exponential and log
Logarithmic differentiation; hyperbolic functions
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| 7 |
Continuation and review |
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| 8 |
Exam 1 covering Ses #1-7 |
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| Applications of differentiation |
| 9 |
Linear and quadratic approximations |
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| 10 |
Curve sketching |
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| 11 |
Max-min problems |
Problem set 2 due |
| 12 |
Related rates |
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| 13 |
Newton's method and other applications |
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| 14 |
Mean value theorem
Inequalities
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Problem set 3 due |
| 15 |
Differentials, antiderivatives |
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| 16 |
Differential equations, separation of variables |
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| 17 |
Exam 2 covering Ses #8-16 |
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| Integration |
| 18 |
Definite integrals |
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| 19 |
First fundamental theorem of calculus |
Problem set 4 due |
| 20 |
Second fundamental theorem
Definition of log
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| 21 |
Areas between curves, volumes by slicing |
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| 22 |
Volumes by disks, shells |
Problem set 5 due |
| 23 |
Work, average value, probability |
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| 24 |
Numerical integration |
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| Techniques of integration |
| 25 |
Trigonometric integrals |
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| 26 |
Exam 3 covering Ses #18-24 |
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| 27 |
Integration by inverse substitution; completing the square |
Problem set 6 due |
| 28 |
Partial fractions |
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| 29 |
Integration by parts; reduction formulas |
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| 30 |
Parametric equations, arclength, surface area |
Problem set 7 due |
| 31 |
Polar coordinates; area in polar coordinates |
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| 32 |
Continuation and review |
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| 33 |
Exam 4 covering Ses #25-32 |
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| 34 |
Indeterminate forms; L'Hospital's rule |
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| 35 |
Improper integrals |
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| 36 |
Infinite series
Convergence tests
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| 37 |
Taylor series |
Problem set 8 due |
| 38 |
Final review |
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Final exam |
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