Math 171. Intermediate Mathematical Analysis I. Spring 2005.
Tentative class schedule with homework assignments
This schedule is subject to change.
Assignments shown in gray may change. The ones shown in black will not (except I may occasionally decide to give more points for a problem).
Each part (a, b, etc.) of each problem (for which a, b, etc. are shown) is worth 1 point, except problems marked by * (which are either longer or more difficult or more important than other problems) are worth 2 points, problems marked by ** are worth 3 points, etc. If no parts are shown and the problem is not marked by *, then the whole problem is worth 1 point.
| Feb 1: | Last day to ADD classes without special permission, DROP classes without a serious and compelling reason | |||||
| Apr 19: | Last day to WITHDRAW from a course for serious and compelling reasons | |||||
| Date | Read before class | Chapter | Topic | Problems recommended but will not graded |
HW due | Optional problems for extra credit |
| Jan 19 | Introduction - First class | |||||
| 1 | The real number system 1.1 Ordered field axioms (Read App. A on your own) |
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| Jan 21 | 1.1: 1-11 App. A: 570-573 |
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| Jan 24 | 1.2: 13-16 | 1.2 Well-ordering principle | ||||
| Jan 26 | 1.3: 18-23 | 1.3 Completeness axiom | ||||
| Jan 28 | 1.4: 24-33 | |||||
| Jan 31 | 1.1: 1(ab), 2(abd), 3(ab), 4(89) 1.2: 1(ab) |
1.1: 2(c), 4(7)*, 7(a)*, 8(a) 1.2: 1(c), 2(a), 6(ab*) Solutions |
1.2: 7, 8(ab), 9 | |||
| 1.4 Functions, countability, and the algebra of sets | ||||||
| Feb 2 | ||||||
| Feb 4 | 2.1: 35-38 | 2 | Sequences in R 2.1 Limits of sequences |
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| Feb 7 | 2.2: 39-43 | 2.2 Limit theorems | 1.3: 1(abcdeg) 1.4: 1(abd), 2, 4(ab), 5 |
1.3: 1(f), 2*, 3**, 5(ab) 1.4: 3*, 4(c), 7* Solutions |
1.3: 4 1.4: 1(e), 6**, 11(ab*c*), write an explicit formula for a bijection from Z to N (prove that your function is a bijection) |
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| Feb 9 | 2.3: 45-48 | |||||
| 2.3 Bolzano-Weierstrass theorem | ||||||
| Feb 11 | 2.4: 49-51 | |||||
| 2.4 Cauchy sequences |
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| Feb 14 | 2.1: 1(acd), 4(a) 2.2: 1, 2 |
2.1: 1(b), 6(abc), 7 2.2: 3*, 5*, 9* Solutions |
2.2: 10(a*b*c*) | |||
| 3 | Continuity on R 3.1 Two-sided limits |
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| Feb 16 | 3.1: 58-63 | |||||
| Feb 18 | 3.2: 66-69 | 3.2 One-sided limits and limits at infinity | ||||
| Feb 21 | Presidents' day - all offices closed - no classes, no office hours | |||||
| Feb 22 | office hours: 11- 1. No office hours on Feb 23. | |||||
| Feb 23 | 3.3: 71-78 | 3 | 3.3 Continuity | 3.1: 1(bc), 2(a), 3(abc) | 2.3: 1*, 2* 2.4: 1*, 2*, 3* 3.1: 1(a), 3(d), 5* Solutions |
2.3: 5* 2.4: 6*, 9(a*b*) |
| Feb 25 | Review (review sheet for test 1) | |||||
| Feb 28 | Test 1 (covers 1.1 - 3.1), Solutions | |||||
| Mar 2 | 3 | 3.3 Continuity | ||||
| Mar 4 | ||||||
| Mar 7 | 3.4: 79-83 | 3.2: 1(bc), 2, 3(abcdf) 3.3: 2 |
3.2: 1(ad), 3(e), 4(abc**) 3.3: 5* Solutions |
3.2: 7(ab), 10* 3.3: 8***, 9*** |
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| 3.4 Uniform continuity | ||||||
| Mar 9 | ||||||
| Mar 11 | 4.1: 85-90 | 4 | Differentiability on R 4.1 The derivative |
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| Mar 14 | 4.2: 92-93 | 3.3: 1(ac) 3.4: 1(ab) |
3.3: 1(b), 4*, 10* 3.4: 2(c)**, 5(a*b*) Solutions |
3.4: 3*, 9* | ||
| 4.2 Differentiability theorems | ||||||
| Mar 16 | 4.3: 94-100 | 4.3 Mean Value Theorem | ||||
| Mar 18 | ||||||
| Mar 21 | Spring recess - no classes, no office hours | |||||
| Mar 23 | ||||||
| Mar 25 | ||||||
| Mar 28 | 4.4: 102-105 | 4 | 4.4 Monotone functions and inverse function theorem | 4.1: 1(ac), 3, 6 4.2: 1(ab), 2, 8 |
4.1: 1(b), 3(ab*c*d) 4.2: 1(d)*, 5(ab*), 6 Solutions |
4.1: 4(abcde) 4.2: 1(c)* |
| Mar 30 | 5.1: 107-114 | 5 | Integrability on R 5.1 Riemann integral |
Talk "How vs. Why" by Paul Zeitz, Friday 4/1 from 3:30-4:30 in IT 101. You will get 10 extra points for attending (or doing this extra assignment) | ||
| Apr 1 | ||||||
| 5.2 Riemann sums | ||||||
| Apr 4 | 5.2: 117-125 | 4.3: 1(acdef), 7 4.4: 1(a) |
4.3: 1(b), 4(a), 6*, 8* 4.4: 1(b), 2(abc), 4** Solutions |
4.3: 4(bc), 9* 4.41(c), 1(b - find a solution that does not require calculus but only uses high school algebra) |
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| Apr 6 | Review (review sheet for test 2) | |||||
| Apr 8 | Test 2 (covers 3.2 - 4.4), Solutions | |||||
| Apr 11 | 5 | 5.2 Riemann sums | 5.1: 1(a), 2(ab) | 5.1: 1(c)*, 2(c(beta))*, 4(a*bc), 7(a)* Solutions |
5.1: 3* | |
| Apr 13 | ||||||
| Apr 15 | 5.3: 127-133 | 5.3 Fundamental theorem of calculus | ||||
| Apr 16 | Volunteers needed for Math Field Day! Benefits THANKS VERY MUCH to all volunteers!!! | |||||
| Apr 18 | 5 | 5.3 Fundamental theorem of calculus | 5.1: 8(ab), 9* 5.2: 1(abcd*), 4* Solutions |
5.2: 5(ab) | ||
| Apr 20 | 5.4: 136-140 | 5.4 Improper Riemann integration | ||||
| Apr 22 | ||||||
| Apr 25 | 6.1: 154-158 | 6 | Infinite Series of Real Numbers 6.1 Introduction |
5.3: 1(abcde), 3(ab*), 4(a*c*(hint: compare derivatives of L(xq) and qL(x))) Solutions |
5.3: 1(f), 4(b*d*e*) | |
| Integration Bee contest (you'll have to evaluate a few integrals) at 7 PM in S2 109. You will get 10 extra points for participating (or doing this extra assignment) | ||||||
| Apr 27 | 6.2: 160-164 | 6.2 Series with nonnegative terms | ||||
| Apr 29 | 6.3: 165-171 | 6.3 Absolute convergence | ||||
| May 2 | 5.4: 1(ac), 2(a), 4(abcd) | 5.4: 1(bc), 2(b), 4(e)*, 5* 6.1: 1, 2(b), 5(c), 6(ab) Solutions |
5.4: 4(d)* | |||
| 6.4 Alternating series | ||||||
| May 4 | 6.4: 173-176 | |||||
| May 6 | Review (review sheet for test 3) | |||||
| May 9 | Test 3 (covers 5.1 - 6.4), Solutions | 6.2: 7(a) | 6.2: 1(d), 2(c), 8* 6.3: 1(c), 2(c), 6(c), 8(a)* 6.4: 1(b)*, 3(a)* |
Can a function be continuous everywhere but differentiable nowhere?** Do there exist convergent series Σak and Σbk such that Σ(akbk) diverges?* 6.2: 5 6.3: 8(b)* 6.4: 3(b) |
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| May 11 | Review (Part I and review sheet for part II) | |||||
| May 12 | Consultation day. Office hours: 9:20-11:30 | |||||
| May 13 | Consultation day. Those who earned the right to retake one of the tests can do so from 8:00 - 9:05 AM in our regular classroom | |||||
| May 17 | Office hours: 11 AM - 1 PM (Math 171 only), 1 - 2 PM (all classes) | |||||
| May 18 | Part I (problems - take home) of the final due at 8:30 am. 7:30-8:30 am. Part II of the final (definition, example, question, state a theorem, state and prove a theorem - in class). |
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