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Reading, Assignments, and Exams



Reading, Assignments, and Exams

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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 #TOPICSREADINGSASSIGNMENTS
1Monotone sequences; completeness propertyChapter 1; Appendix A, 2.1 (as needed)1.4/2 (consider an+1= an); 1.5/2; prob 1-1b, c
2Estimations and approximationsChapter 22.1/2; 2.4/2; 2.5/3; 2.6/2; prob2-1a
3Limit of a sequenceChapter 3.1-.63.1/1a; 3.2/4; 3.3/3; 3.4/5; 3.6/1b
4Error term; algebraic limit theoremsChapter 4 (omit 4.3), 5.14.2/1ab; 4.4/2 (assume A > B); Q5.1/1a,3; 5.1/4
5Limit theorems for sequencesChapter 5.2-3, .55.2/3; 5.3/1; 5.3/4 (a: omit hint; b: counterexample?); prob 5-1*
6Nested 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)

7Bolzano-Weierstrass theorem; Cauchy sequencesChapter 6.1-46.1/1b; 6.3/1; 6.4/2; P6-4
8Completeness property for setsChapter 6.56.4/3(cf.sec. 3.1); 6.5/1ac, 3ag; P6-2ab
9Infinite seriesChapter 7.1-47.2/2,5; 7.1/2, P 7-5 (go together); 7.4/1bdeh
10Infinite series (cont.)Chapter 7.5-77.4/1acfg; 7.4/3a; P7-6; P7-1
11Power seriesChapter 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
12Functions; local and global propertiesChapters 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
13ContinuityChapter 11.1-311.1/1, 4, 5 (exp.law:ea+b = eaeb); 11.3/1, 3a
14Continuity (cont.)Chapter 11.4-511.4/1, 2; 11.5/1ab; P11-2
15Intermediate-value theoremChapter 12.1-.212.1/3, 5; 12.2/2, 3, 4; (P12-5 opt'l, for + or gold star)
16Continuity theoremsChapter 13.1-313.1/Q1 (give ctrexs.); 1, 2; 13.2/1; 13.3/3, 1b*
17Uniform continuityChapter 13.5 (13.4 lightly)13.5/5, 6; P13-2; P13-6
18Differentiation: local propertiesChapter 1414.1/1, 4; 14.3/1, 2a; P14-2; P14-6ab
19Differentiation: global propertiesChapter 15 1515.2/1ab; 15.4/1; P15-2; P15-3ab
20Convexity; 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
21IntegrabilityChapter 18.1-.3, (18.4 lightly)18.2/2; Q18.3/3ab; 18.3/1, 3
22Riemann integralChapter 19.1-.4; (.5, .6 lightly)19.2/1; 19.3/1, 3; 19.4/2
23Fundamental theorems of calculusChapter 20.1-420.1/1; 20.2/4; 20.3/2, 3; P20-2a
24Stirling's formula; improper integralsChapter 21.1-221.1/2(set x = 1/u); 21.2/1c, e, h(x = 1/ u), 2, 4
25Gamma function, convergenceChapter 20.5, 21.320.5/1a, 2; Q21.3/1, 2; 21.3/1
Exam 2 covering Ses #13-25
26Uniform convergence of seriesChapter 22.1-222.1/1ac, 2; 22.2/2bd, 3
27Integration term-by-termChapter 22.3-422.3/1, 3 (cf. warning in 22.3/2); 22.4/1, 3; P22-3b
28Differentiation term-by-term; analyticityChapter 22.5-622.5/1; Q22.5/1; 22.6/2; 22.6/5; P22-2 (just show J0 solves the ODE)
29Quantifiers and negationAppendix B NegationNot required, no assignment, but recommend trying QB.1, QB.2, QB.3
30Continuous functions on the planeChapter 24.1-.524.1/3; 24.2/2, 3; 24.4/1; 24.5/2, 5
31Continuous functions on the plane (cont.); plane point-set topologyChapter 24.6-.725.1-.2 24.7/1, 2; P24-1; 25.1/1; 25.2/2
32Compact sets and open setsChapter 25.2-.325.3/1; P25-1; 25.3/3; 25.2/5; P25-3a
33Differentiating finite integralsChapter 26.1-.226.1/1b; 26.2/1ab; (but use: 0π cos (xt) dt ; P26-1 (use 20.1 or 20.3A)
34Differentiating finite integrals (cont.); Fubini's theorem in rectangular regionsChapter 26.2-.3Q26.2/1; 26.2/5; 26.3/1, 2
35Uniform convergence of improper integralsChapter 23.1-.2Q27.2/1,2; Q27.3/1,2 (not to hand in)
36Differentiation and integration of improper integrals; applicationsChapter 23.3-.4Q27.4/1,2 (not to hand in)
37Comments; reviewPractice final given out (PDF)
Three-hour final exam during finals week

 








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