Readings

All textbook readings are from:

Buy at Amazon Apostol, Tom M. Calculus, Volume 1: One-Variable Calculus, with An Introduction to Linear Algebra. Waltham, Mass: Blaisdell, 1967. ISBN: 9780471000051.

 Additional course notes by James Raymond Munkres, Professor of Mathematics, Emeritus, are also provided. 

SES # TOPICS TEXTBOOK READINGS COURSE NOTES READINGS
Real numbers
0 Proof writing and set theory I 2.1-2.4  
1 Axioms for the real numbers I 3.1-3.7  
2 Integers, induction, sigma notation I 4.1-4.6 Course Notes A
3 Least upper bound, triangle inequality I 3.8-3.10, I 4.8 Course Notes B
4 Functions, area axioms 1.2-1.10  
The integral
5 Definition of the integral 1.12-1.17  
6 Properties of the integral, Riemann condition   Course Notes C
7 Proofs of integral properties 88-90, 113-114 Course Notes D
8 Piecewise, monotonic functions 1.20-1.21 Course Notes E
Limits and continuity
9 Limits and continuity defined 3.1-3.4 Course Notes F
10 Proofs of limit theorems, continuity 3.5-3.7  
11 Hour exam I    
12 Intermediate value theorem 3.9-3.11  
13 Inverse functions 3.12-3.14 Course Notes G
14 Extreme value theorem and uniform continuity 3.16-3.18 Course Notes H
Derivatives
15 Definition of the derivative 4.3-4.4, 4.7-4.8  
16 Composite and inverse functions 4.10, 6.20 Course Notes I
17 Mean value theorem, curve sketching 4.13-4.18  
18 Fundamental theorem of calculus 5.1-5.3 Course Notes K
19 Trigonometric functions   Course Notes L
Elementary functions; integration techniques
20 Logs and exponentials 6.3-6.7, 6.12-6.16 Course Notes M
21 IBP and substitution 5.7, 5.9 Course Notes N
22 Inverse trig; trig substitution 6.21  
23 Hour exam II    
24 Partial fractions 6.23 Course Notes N
Taylor's formula and limits
25 Taylor's formula 7.1-7.2  
26 Proof of Taylor's formula   Course Notes O
27 L'Hopital's rule and infinite limits 7.12-7.16 Course Notes P
Infinite series
28 Sequences and series; geometric series 10.1-10.6, 10.8 (first page only)  
29 Absolute convergence, integral test 10.11, 10.13, 10.18  
30 Tests: comparison, root, ratio 10.12, 10.15 Course Notes Q
31 Hour exam III    
32 Alternating series; improper integrals 10.17, 10.23  
Series of functions
33 Sequences of functions, convergence 11.1-11.2  
34 Power series 11.3-11.4 Course Notes R
35 Properties of power series   Course Notes R
36 Taylor series 11.9 Course Notes S
37 Fourier series   Course Notes T