| Math 447 Schedule Text: Closer and Closer Introducing Real Analysis, by Carol Schumacher. [ Math 447 Home | Office Hours ] |
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| Note: Each section of the text contains two types of problems for you to work, exercises and problems. The exercises in a given section are sprinkled throughout that section. We will use the notation E2.3.4 to refer to Exercise 2.3.4 from Section 2.3. The problems in a given section are located at the end of each section. We will use the notation P2.3.4 to refer to Problem 4 at the end of Section 2.3. | |||||
| Week & Dates |
Reading Assignment | Homework Assignment | Notebook Due Date |
Exam/Quiz Date |
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| Week 1 Aug 31 & Sept 2 |
The Derivative, What does the Derivative Tell Us? Sections 9.1, 9.2, 9.3 |
Notebook(NB): Solutions to all Exercise(E) problems are expected to be in your notebook.
Class: work on your Real Analysis I review poster NB: work on your Real Analysis I review poster |
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| Week 2 Sept 7 & 9 |
The Mean Value Theorem, Monotonicity & the MVT, Darboux's Theorem Section 9.4, 9.5 |
Class: present your Real Analysis I review poster, 9.2.5, 9.2.8, 9.2.11
NB: 8.1.2, 9.2.1, 9.2.4, 9.2.12 Class: 9.4.2, 9.4.3, 9.4.4, 9.4.5 NB: 9.4.7, 9.4.8, 9.4.9 |
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| Week 3 Sept 14 & 16 |
Taylor Polynomials & Taylor's Theorem, Errors in Taylor Approx, Iteration & Cobwebs Section 9.7, 10.1 |
Class: 9.5.1, 9.5.3, 9.5.4
NB: 9.5.2 Class: 9.5.5, 9.7.2 NB: 9.5.6, 9.7.1, 9.7.3 |
Quiz 1 Sept 16 |
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| Week 4 Sept 21 & 23 |
Iteration & Fixed Points, Contractions, The Contraction Mapping Thrm Section 10.1, 10.2 |
Class: worksheet problems
NB: P10.1.2, P10.1.4, P10.1.8 Class: P10.1.5, P10.1.6, P10.1.9, P10.2.1 NB: P10.1.10 |
Sept 23 8.1 - 9.7 NB problems |
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| Week 5 Sept 28 & 30 |
Attracting Fixed Points, Newton's Method, Defining the Integral Sections 10.3, L.1, L.2, 11.1, 11.2 |
Class: P10.2.3, P10.2.4, P10.2.5 NB: P10.2.2, P10.2.6, P10.2.7 Class: In-class exam NB: take home exam |
MIDTERM EXAM 1 Sept 30 |
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| Week 6 Oct 5 & 7 |
The Integral, Arithmetic Order and the Integral, Families of Riemann Sums Sections Excursion I, 11.3, 11.4 |
IJ presents P11.2.3, P11.2.5, P11.2.7 NB: P10.3.2, P11.2.1, P11.2.4 Class: P11.2.6, P11.2.8, P11.3.1 NB: P11.2.2, P11.2.5, P11.2.9 |
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| Week 7 Oct 12 & 14 |
Riemann Sums and Refinements, Cauchy Criteria for the Existence of the Integral Section 11.4 |
Class: P11.3.4, P11.4.1, P11.4.2, P11.4.4
NB: P11.3.3, P11.3.5, P11.3.6 Class: IJ presents Lemma 11.4.8 & Thrm 11.4.9 NB: P11.4.3, P11.4.5 |
Quiz 2 | ||
| Week 8 Oct 19 & 21 |
Existence of the Integral, FUNdamental Theorem of Calculus, Subsequences and Convergence 11.5, 11.6, Excursion G |
IJ finish Thrm 11.4.9, Class: P11.4.6, P11.5.1, P11.5.2
NB: P11.4.7 Class: P11.5.4, P11.5.7 NB: P11.5.5, P11.5.8, P11.5.10 |
Oct 21 10.1 - 11.4 NB problems |
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| Week 9 Oct 26 & 28 |
Subsequences and Convergence, Series, Power Series Sections Excursions G, H, and J |
Class: P11.6.2, P11.6.3, Excursion G.1 prob 3, Excursion G.2 probs 1, 2, 3, 4, 7
NB: P11.6.1, Excursion G.1 probs 1, 2, 4, Excursion G.2 prob 8 Class: Excursion H.1 probs 2, 3, 4, 12 NB: Excursion H.1 probs 7, 9, 10 |
Quiz 3 | ||
| Week 10 Nov 2 & 4 |
Series, Uniform Convergence Excursion H, Review Sections 12.2 |
Class: Excursion H.2 probs 1, 2, Excursion H.3 prob 3, P12.2.1 NB: Excursion H.3 prob 1, P12.2.1 Class: in-class exam NB: take home exam |
MIDTERM EXAM 2 |
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| Week 11 Nov 9 & 11 |
Series of Functions, Interchange of Limit Operations, Integration and Differentiation of Power Series 12.3, 12.4, Excursion J |
Class: IJ presents H2, H3, & review of 12.2 NB: H.3 problems 1, 3, P12.2.5 Class: P12.3.1, P12.3.2, P12.4.3 NB: P12.4.1 |
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| Week 12 Nov 16 & 18 |
Everywhere Continuous Nowhere Differentiable Function, Spaces of Continuous Functions
Excursions K and N.1 |
Class: P12.4.6, P12.4.5, PJ.2.1 NB: P12.4.4, Exercises J.1.4, J.1.6 Class: PJ.1.2, PJ.2.1, PJ.2.2, PJ.2.3, PJ.2.4 NB: PJ.3.1 |
Quiz 4 | ||
| Week 13 Nov 23 Thanksgiving |
Compactness in C(K), Arzela-Ascoli Thrm
Excursion N.2 |
Class: Lemma N.1.1, Thrm N.1.3, Thrm N.2.4 NB: Lemma N.1.4, Thrm N.1.5 |
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| Week 14 Nov 30 & Dec 2 |
Approximations by Polynomials, The Stone Weierstrass Theorem
Excursion N.3 |
Class: Thrm N.2.5, Lemma N.2.6, Thrm N.2.8 NB: Lemma N.2.7, Thrm N.2.5, Lemma N.2.6, Thrm N.2.8 Class: Lemma N.3.3, PN.3.1, PN.3.2, PN.3.3, PN.3.4 NB: PN.3.5, PN.3.6 |
Quiz 5 | ||
| Week 15 Dec 7 & 9 |
Stone Weierstrass, Existence and Uniqueness of DE Solutions, Picard Iteration Excursion O.1, O.2 |
Class: finish problem PN.3.4 (make sure to look up errata for this problem. Steps were assigned in class.), PO.2.1(Wesley), PO.2.2(a) (Ally) NB: Class: PO.2.2(b) (Jonathan) PO.2.2(c) (Heidi), PO.2.4 (Thomas) NB: |
FINAL EXAM Thursday, Dec. 16 2-5 pm |
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