Below is a (tentative) schedule of the course topics.
| Week # | Monday | Wednesday | Thursday | Friday |
|---|---|---|---|---|
| 1 | No classes. | Areas under curves, approximating areas. | Sigma notation, Riemann sums, numerical integration. | Numerical integration (cont’d), integrability. |
| 2 | The Fundamental Theorem of Calculus. | Methods of integration: substitution, trigonometric integrals. | Methods of integration: trigonometric substitution, integration by parts. | Methods of integration: partial fractions. Basic applications of integration. |
| 3 | Improper integrals, applications of integration: probability. | In-class midterm (July 19). | Applications of integration: probability. | Sequences, convergence of sequences, series, partial sums, geometric series. |
| 4 | Tests for convergence of series: divergence test, comparison and limit comparison tests, ratio test. | Tests for convergence of series: integral test, p-series. | Alternating series, absolute and conditional convergence, alternating series test. | Power series, interval and radius of convergence, power series representations of functions. |
| 5 | Manipulations of power series, Taylor series. Taylor’s Theorem. | Applications of Taylor series. | Introduction to multivariable calculus: vectors, functions of two variables. | Partial derivatives, directional derivatives, the gradient, tangent planes. |
| 6 | Holiday — no class. | Critical points and the second derivatives test. | General multivariable optimization problems, constrained optimization problems: Lagrange multipliers. | Constrained optimization problems with Lagrange multipliers (cont’d). |
The university has scheduled our final exam to be on August 16th at 12pm in ANGU 098.