Calendar
References are to the textbook: Apostol, Calculus, Vol. I, Second Edition (1967); Readings are from the course notes by Prof. J. Munkres.
| SES # | TOPICS | REFERENCES | READINGS |
|---|---|---|---|
| 1 | Real Numbers | I 3.1 - 3.4, 3.7 | Chapter A (PDF) |
| 2 | Integers, Rationals; Mathematical Induction | I 3.6, 4.1 - 4.6 | |
| 3 | Completeness Axiom; Triangle Inequality | I 3.8 - 3.13, 4.8 | Chapter B (PDF) |
| 4 | Functions; Step Functions | 1.2 - 1.10 | |
| 5 | Definition of the Integral | 1.12 - 1.17 | Chapter C.1 - C.2 (PDF) |
| 6 | Piecewise-Monotonic Functions | 1.20 - 1.22 | Chapter E (PDF) |
| 7 | Integral of a Power of X, Properties of the Integral | 1.23 - 1.25 | Chapter C.3 - C.11 (PDF) |
| 8 | Proof of the Properties; Some Applications | 1.27, pp. 88-90 | Chapter D (PDF) |
| 9 | Limits | 3.1 - 3.4 | |
| 10 | Basic Limit Theorems | 3.5 - 3.7 | Chapter F (PDF) |
| 11 | Intermediate Value Theorem | 3.9 - 3.12 | |
| 12 | Inverse Functions | 3.12 - 3.14 | Chapter G (PDF) |
| 13 | Quiz | ||
| 14 | Extreme-value Theorem; Uniform Continuity | 3.16 - 3.17 | Chapter H (PDF) |
| 15 | Derivatives | 4.3 - 4.8 | |
| 16 | Composite and Inverse Functions | 4.10, 6.20 | Chapter I (PDF) |
| 17 | Mean Value Theorem | 4.13 - 4.18 | Chapter I (PDF) |
| 18 | The Fundamental Theorem of Calculus | 5.1 - 5.3, 5.6 | Chapter K (PDF) Chapter L (PDF) |
| 19 | Integration by Substitution; Primitives of Elementary Functions | 5.7 - 5.8 | Chapter N (PDF) |
| 20 | Integration by Parts | 5.9 | |
| 21 | Logarithms and Exponentials | 6.3 - 6.7, 6.12 - 6.16 | Chapter M (PDF) |
| 22 | Inverse Trigonometric Functions, Trig Substitutions | 6.21 | |
| 23 | Integration by Partial Fractions | 6.23 | |
| 24 | Taylor's Formula | 7.1 - 7.2, 7.5 | Chapter O (PDF) |
| 25 | Applications of Taylor's Formula | 7.2, 7.4 | |
| 26 | L'Hopital's Rule, Infinite Limits | 7.12 - 7.15 | Chapter P (PDF) |
| 27 | Behaviour of Log and Exp | 7.16 | |
| 28 | Sequences and Series, Geometric Series | 10.2 - 10.6, 10.8 | |
| 29 | Tests for Convergence I | 10.11 - 10.16 | |
| 30 | Quiz | ||
| 31 | Alternating Series, Absolute Convergence | 10.17 - 10.18 | |
| 32 | Tests for Convergence II | 10.19 | Chapter Q (PDF) |
| 33 | Improper Integrals | 10.23 | |
| 34 | Series of Functions | 11.1 | |
| 35 | Power Series | 11.6 - 11.7 | Chapter R (PDF) |
| 36 | Taylor's Series | 11.9 | |
| 37 | Convergence of Taylor Series | 11.10 - 11.11 | Chapter S (PDF) |
| 38 | Fourier Series | P. 575 | |
| 39 | Review | Chapter T (PDF - 1.2 MB) |
