| Week |
Topic |
| 1 |
The Riemann Integral |
| 2 |
Fundamental Theorem of Calculus, Mean Value Theorem for Integrals |
| 3 |
Integration by Substitutions, Integration by Parts |
| 4 |
Integrals of Rational Functions, Inverse Substitutions |
| 5 |
Other Integration Techniques |
| 6 |
Improper Integrals, Volumes by Slicing, Solids of Revolution |
| 7 |
Arc length, Surface Area, Polar Coordinates and Polar Curves, Arc Lengths for Polar Curves |
| 8 |
Sequences and Convergence, Cauchy Sequence, Infinite series, Convergence Tests for Positive series |
| 9 |
Absolute and Conditional Convergence, Power Series, Taylor and Maclaurin Series The Binomial Theorem, Infinite Products, Convergence of Infinite Product |
| 10 |
Analytic Geometry in Three Dimensions, Vectors, The Cross Product, Planes and Lines, Vector Functions of One Variable, Curves and Parametrization |
| 11 |
Functions of Several Variables, Limits and Continuity |
| 12 |
Partial Derivatives, Higher order Derivatives, The Chain Rule, Differentiability and Differentials |
| 13 |
Gradients and Directional Derivatives, Implicit Functions, Taylor Series |
| 14 |
Extreme Values, Extreme Values of Functions Defined on Restricted Domains, Lagrange Multipliers |
| |