MAIN SECTIONS and PROBLEMS

NOTE: problems marked (E) will usually be treated in class, or should be considered
review problems. Problems marked (H) are to be turned in as homework; due dates
are included below.

I. Introduction

I.3 Axioms for the real numbers
I.3.12 (E) 1,3,6

I.4 Mathematical induction
I.4.4 (E) 1(a),4 (H)1(c),5 9/3
I.4.7 (E) 4,5 (H)6,9 9/3

I.4.8 Absolute values; inequalities
I.4.9 (E) 2(1),(2); 3(a)(b) (H)2(7)(8); 3(c)(d)(e) 9/3

Ch. 1 Theory of integration

1.6 Area as a set function; measurable sets
1.7 (E)1,3 (H)2 9/7

1.12 Integral of step functions
1.15 (E)5 (H)2,4 9/7

1.16 Integrable functions
1.18 Area and integral
1.21 Integrability of bounded monotone functions
1.26 (E)25,26 (H)28 9/7

Ch. 2 Applications of integration

2.2 Area of planar regions
2.4 (E) 17(a), 19 (H)14, 17(b) 9/13

2.6 Integration of trigonometric functions
2.8 (E) 23, 29(a) (H)21, 29(b) 9/13

2.10 Area in polar coordinates
2.11 (E)1,3,7,11 (H)2,4 9/13
(H)12,13 9/20

2.12 Volume of Cavalieri solids
2.13 (E)16, (H)14,15 9/20
2.16 Average values
2.17 (E)9,18,21(a)8 (H)12(b),22 9/20

2.18 indefinite integrals
2.19 (E)19 (H)16,20 9/20

Ch. 3 Limits and continuity

3.1-3.5 limits and continuity
3.7 compositions
3.6 (E) 4,6,11,12,16,21,27 (H)13,18,25,30 9/22
3.8 (E) 3,4,13,18 (H)16,14,19 9/22

EXAM 1: Ch.1,2, and 3 (up to and including 3.8)

3.10 Intermediate value theorem
3.11 (E)1,3,5 (H) 4,6 10/1

3.16 Extreme value theorem
3.18 Integrability of continuous functions
3.20 (E)1,5,7 (H)2,6 10/1

Ch.4: Differential Calculus

4.14,4.15 Mean-value theorem and applications
4.15 (E) 1,5,8(a) (H)2,8(b) 10/1