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) |
|
|
|
|
|
|
|
|
|