# Calendar

References are to the textbook: Apostol, Calculus, Vol. I, Second Edition (1967); Readings are from the course notes by Prof. J. Munkres.

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)