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Reading, Assignments, and Exams

All readings and daily problem assignments are from the textbook:

Amazon logo Mattuck, Arthur. Introduction to Analysis. Upper Saddle River, NJ: Prentice Hall, 1999. ISBN: 9780130811325.

Table of Contents (PDF)

Key to the Readings

Chapter 1.1-1.3, Appendix A means:

Read: Chapter 1, sections 1, 2, 3, and Appendix A (in the back of the book)

Key to the Assignments

1.4/3,5 Q1.4/2 P1-3,4* means:

Work:

Exercises 3, 5 in Exercise Section 1.4 (at the end of Chapter 1)
Question 1.4/2 (at end of Chapter1, Section 4, answered at very end of Chapter 1)
Problems 3 and 4 at end of Chapter 1
* means Problem 4 is corrected in one or more printings.

Textbook Corrections

Note on the Table below: The daily reading assignments depended on what the class had been able to cover that day, so they differed a little in order and content from the overall plan laid out in the "topics" column.

SES # TOPICS READINGS ASSIGNMENTS
1 Monotone sequences; completeness property Chapter 1; Appendix A, 2.1 (as needed) 1.4/2 (consider an+1= an); 1.5/2; prob 1-1b, c
2 Estimations and approximations Chapter 2 2.1/2; 2.4/2; 2.5/3; 2.6/2; prob2-1a
3 Limit of a sequence Chapter 3.1-.6 3.1/1a; 3.2/4; 3.3/3; 3.4/5; 3.6/1b
4 Error term; algebraic limit theorems Chapter 4 (omit 4.3), 5.1 4.2/1ab; 4.4/2 (assume A > B); Q5.1/1a,3; 5.1/4
5 Limit theorems for sequences Chapter 5.2-3, .5 5.2/3; 5.3/1; 5.3/4 (a: omit hint; b: counterexample?); prob 5-1*
6 Nested intervals; cluster points

Chapter 5.4, 6.2

5.4/1(take k = 2); P5-3; 5.4/3 (below); Q6.2/1(for {cos(n + 1/n)π}; Q6.2/2ab

5.4/3: Do 5.4/2, using p(n)/n; p(n) = highest prime factor of n (e.g., p(12) = 3; p(15) = 5)
7 Bolzano-Weierstrass theorem; Cauchy sequences Chapter 6.1-4 6.1/1b; 6.3/1; 6.4/2; P6-4
8 Completeness property for sets Chapter 6.5 6.4/3(cf.sec. 3.1); 6.5/1ac, 3ag; P6-2ab
9 Infinite series Chapter 7.1-4 7.2/2,5; 7.1/2, P 7-5 (go together); 7.4/1bdeh
10 Infinite series (cont.) Chapter 7.5-7 7.4/1acfg; 7.4/3a; P7-6; P7-1
11 Power series Chapter 8.1-.3, (8.4 lightly) 8.2-3; 8.4 (skip proofs); 8.1/1adh; 8.2/1adh; 8.1/3; 8.3/1, 2; 8.4/1a(i), b
12 Functions; local and global properties Chapters 9, 10: 9.2/2; 9.3/3, 5; 9.4/1c; 10.1/5, 6b, 7b; 10.3/2, 4*(= 5 in early ptgs.) Chapters 9, 10: 9.2/2; 9.3/3, 5; 9.4/1c; 10.1/5, 6b, 7b; 10.3/2, 4*(= 5 in early ptgs.)
  Exam 1 covering Ses #1-12    
13 Continuity Chapter 11.1-3 11.1/1, 4, 5 (exp.law:ea+b = eaeb); 11.3/1, 3a
14 Continuity (cont.) Chapter 11.4-5 11.4/1, 2; 11.5/1ab; P11-2
15 Intermediate-value theorem Chapter 12.1-.2 12.1/3, 5; 12.2/2, 3, 4; (P12-5 opt'l, for + or gold star)
16 Continuity theorems Chapter 13.1-3 13.1/Q1 (give ctrexs.); 1, 2; 13.2/1; 13.3/3, 1b*
17 Uniform continuity Chapter 13.5 (13.4 lightly) 13.5/5, 6; P13-2; P13-6
18 Differentiation: local properties Chapter 14 14.1/1, 4; 14.3/1, 2a; P14-2; P14-6ab
19 Differentiation: global properties Chapter 15 15 15.2/1ab; 15.4/1; P15-2; P15-3ab
20 Convexity; Taylor's theorem (skip proofs) Chapter 16 to p.225, (17.1-.3 lightly) 17.4. 16.1/1a; 17.2/4ab (use x2(x - 1)2 ; P16-3, 5
21 Integrability Chapter 18.1-.3, (18.4 lightly) 18.2/2; Q18.3/3ab; 18.3/1, 3
22 Riemann integral Chapter 19.1-.4; (.5, .6 lightly) 19.2/1; 19.3/1, 3; 19.4/2
23 Fundamental theorems of calculus Chapter 20.1-4 20.1/1; 20.2/4; 20.3/2, 3; P20-2a
24 Stirling's formula; improper integrals Chapter 21.1-2 21.1/2(set x = 1/u); 21.2/1c, e, h(x = 1/ u), 2, 4
25 Gamma function, convergence Chapter 20.5, 21.3 20.5/1a, 2; Q21.3/1, 2; 21.3/1
  Exam 2 covering Ses #13-25    
26 Uniform convergence of series Chapter 22.1-2 22.1/1ac, 2; 22.2/2bd, 3
27 Integration term-by-term Chapter 22.3-4 22.3/1, 3 (cf. warning in 22.3/2); 22.4/1, 3; P22-3b
28 Differentiation term-by-term; analyticity Chapter 22.5-6 22.5/1; Q22.5/1; 22.6/2; 22.6/5; P22-2 (just show J0 solves the ODE)
29 Quantifiers and negation Appendix B Negation Not required, no assignment, but recommend trying QB.1, QB.2, QB.3
30 Continuous functions on the plane Chapter 24.1-.5 24.1/3; 24.2/2, 3; 24.4/1; 24.5/2, 5
31 Continuous functions on the plane (cont.); plane point-set topology Chapter 24.6-.7 25.1-.2 24.7/1, 2; P24-1; 25.1/1; 25.2/2
32 Compact sets and open sets Chapter 25.2-.3 25.3/1; P25-1; 25.3/3; 25.2/5; P25-3a
33 Differentiating finite integrals Chapter 26.1-.2 26.1/1b; 26.2/1ab; (but use: 0∫π cos (xt) dt ; P26-1 (use 20.1 or 20.3A)
34 Differentiating finite integrals (cont.); Fubini's theorem in rectangular regions Chapter 26.2-.3 Q26.2/1; 26.2/5; 26.3/1, 2
35 Uniform convergence of improper integrals Chapter 23.1-.2 Q27.2/1,2; Q27.3/1,2 (not to hand in)
36 Differentiation and integration of improper integrals; applications Chapter 23.3-.4 Q27.4/1,2 (not to hand in)
37 Comments; review   Practice final given out (PDF)
  Three-hour final exam during finals week