The following is a tentative syllabus for the course. The textbook section listed for each day is the one that we intend to cover that day, and it should be read before coming to class.
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Appendices A-C | Review of some topics in precalculus | |
9/16 | 1.1 | Functions, operations on functions, sequences |
9/18 | 1.1 | Graphs of functions, even and odd functions, types of sequences |
9/21 | 1.2, 1.4 | Catalogue of functions, average rate of change of a function |
9/22 (x-hour) | Quiz 1 | |
9/23 | 1.2 | Modeling with functions, Lagrange interpolation |
9/25 | 1.3 | Geometric interpretation of function composition |
9/28 | 6.1, 6.2*-6.4* | Inverse functions, exponential functions, and logarithmic functions |
9/29 (x-hour) | Quiz 2 | |
9/30 | Appendix D | Trigonometric functions |
10/2 | 6.6 | Inverse trigonometric functions, solving trigonometric expressions |
10/5 | 11.1 | (Informal) limits and convergence of sequences |
10/6 (x-hour) | Review | |
10/7 | 11.1 | (Formal) limits of sequences |
10/8 | Exam 1 | |
10/9 | 11.1 | More on convergent sequences |
10/12 | 1.5 | (Informal) limits of functions, limits at infinity, asymptotes |
10/13 (x-hour) | Quiz 3 | |
10/14 | 1.6, 1.7 | (Formal) limits of functions, properties of limits |
10/16 | 1.8 | Continuous functions |
10/19 | 1.6, 1.8 | Squeeze Theorem, limits and continuity of trigonometric, exponential, and logarithmic functions |
10/20 (x-hour) | Quiz 4 | |
10/21 | 1.4, 2.1 | Rates of change and the derivative, tangent lines |
10/23 | 2.2 | The derivative as a function |
10/24 (Saturday class) | 2.3, 6.2 | Derivative rules |
10/26 | 2.3 | Product and Quotient Rules, higher order derivatives |
10/27 (x-hour) | Review | |
10/28 | 2.4 | Derivatives of trigonometric functions |
10/29 | Exam 2 | |
10/30 | 6.4 | Derivatives of exponential and logarithmic functions |
11/2 | 2.5 | Chain Rule |
11/3 (x-hour) | Quiz 5 | |
11/4 | 2.6, 6.6 | Implicit differentiation, derivatives of inverse trigonometric functions |
11/6 | 6.8 | L'Hospital's Rule |
11/9 | 3.8 | Newton's Method |
11/10 (x-hour) | Quiz 6 | |
11/11 | 2.9 | Linear approximation |
11/13 | 2.9, 11.10 | Taylor polynomials |
11/16 | 11.11 | Approximation using Taylor polynomials |
11/17 (x-hour) | Review/wrap-up | |
11/20 | Final exam |