Date |
Topic |
Reading Assignment |
Homework |
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| Monday, January 14 |
Differentiation domains and the definition of the derivative |
* |
* |
| Wednesday, January 16 |
Local linear approximation, differentiation and continuity, differentiation rules |
Sections 9.1 and 9.2. |
Class: Problems 3, 5, 8ac, 11, 12 in Section 9.2
Notebooks: Problems 4, 6, 9, and 10 in Section 9.2 |
| Friday, January 18 |
Finish section 9.2.
Discussion: Why the Mean Value Theorem? |
Section 9.3. |
* |
| * |
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| Monday, January 21 |
Proving the Mean Value Theorem
Corollaries of the Mean Value Theorem |
Section 9.4 |
Class: Problems 1, 2, 3, 4, 5 in Section 9.4
Notebooks: Problems 6, 8, 9 in Section 9.4 |
| Wednesday, January 23 |
Monotonicity and the Mean Value Theorem |
Section 9.5 |
Class: Problems 1 and 3 in Section 9.5
Notebook problems on Sects. 9.2 due. |
| Friday, January 25 |
Darboux's Theorem and the nature of derivative functions |
* |
Class: Problems 4 and 5 in Section 9.5
Notebooks: Problems 2 and 6 in Section 9.5 |
| * |
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| Monday, January 28 |
The Intermediate Value Theorem |
Section 8.1 |
Class: Problems 1 and 2 in Section 8.1.
Notebook: Problem 3 in Section 8.1
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| Wednesday, January 30 |
Introduction to Taylor Polynomials and Taylor's Theorem |
Section 9.7 |
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| Friday, February 1 |
Error in Taylor Polynomial Approximations |
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Notebooks: Problems 1, 2, and 3 in Section 9.7 (Group assignment)
Notebook problems on Sects. 9.4 and 9.5 due |
| * |
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| Monday, February 4 |
Experimenting with iteration and cobweb diagrams. |
Section 10.1 through the description of "cobweb diagrams"---pg 193. (We will work Exercise 10.1.3 in class.) |
Notebooks: Problem 2 in Section 10.1
Group notebook assignment on 9.7 due. And individual write-ups from 8.1. |
| Wednesday, February 6 |
Iteration and Fixed Points |
Rest of Section 10.1 |
Class: Problems 4, 6, and 9 in section 10.1
Notebooks: Problems 5, 8, and 10 in Section 10.1
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| Friday, February 8 |
Finish Section 10.1
Contractions |
Section 10.2 through the top of page 200. |
Class: Problems 1, 3(discussion), and 4 in Section 10.2 |
| * |
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| Monday, February 11 |
The Contraction Mapping Theorem |
Rest of Section 10.2 |
Class: Problem 5 in Section 10.2
Notebooks: Problems 2, 6 and 7 in Section 10.2 |
| Wednesday, February 13 |
More on attracting Fixed Points |
Section 10.3 |
Class: Problem 11 in Section 10.1 and Problems 1 and 2 in Section 10.3 |
| Friday, February 15 |
Iteration and Newton's Method |
Sections L.1 and L.2 |
Class: Problems 1 and 2 in Section L.2.
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| * |
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| Monday, February 18 |
Defining the integral |
Sections 11.1 and 11.2 |
Class: Problems 2, 3, 4 and 6 in Section 11.2 |
| Wednesday, February 20 |
* |
Excursion I---food for thought |
Class: Problems 7 and 8 in Section 11.2
Notebooks: Problems 1, 5, and 9 in Section 11.2
Notebook problems on Sects. 10.1 and 10.2 due |
| Friday, February 22 |
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Class problems from 11.2 Continued. |
| * |
| Monday, February 25 |
Arithmetic, order and the integral |
Section 11.3
Read Section 11.4 through the bottom of pg. 221 (for understanding.) |
Class: Problems 1 and 4 in Section 11.3
Notebooks: Problems 3, 5, and 6 in Section 11.3 |
| Wednesday, February 27 |
Families of Riemann Sums and refinements
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Re-Read Section 11.4 through Lemma 11.4.7 |
Class: Exercises and Problem 1, 2, 4, and 5 in Section 11.4
Notebooks: Problem 3 in Section 11.4 |
| Friday, March 1 |
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Spring Break
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| Monday, March 18 |
Cauchy Criteria for the Existence of the Integral---What are the issues? (Lecture.) |
Rest of Section 11.4 (don't worry about the proofs; ignore Lemma 11.4.8---read and understand the statements of 11.4.9 and 11.4.10!) |
Notebooks: Problems 6 and 7 in Section 11.4 |
| Wednesday, March 20 |
Existence of the Integral |
Section 11.5 |
Class: Problems 1 and 2 in Section 11.5.
Notebooks: Problems 5, 7, 8 and 10 in Section 11.5.
Notebook problems on Sections 11.2, 11.3 & 11.4 number 3 due |
| Friday, March 22 |
The Fundamental Theorem of Calculus |
Section 11.6 |
Class: Problems 2 and 3 in Section 11.6.
Notebooks: Problem 1 in Section 11.6. |
| * |
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| Monday, March 25 |
Subsequences and Convergence |
Excursion G |
Class: Problems 1 in Section G.1 and 1, 2, 3, 4 and 7 in Section G.2. |
| Wednesday, March 27 |
Subsequences and Convergence, cont. |
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Notebook problems from Sections 11.4 numbers 6 and 7, 11.5 and 11.6 due |
| Friday, March 29 |
Relatives of the geometric series---the root and the ratio test. (A quick and dirty discussion.)
Takehome midterm distributed |
Carefully read Excursion H.1- H.3 for big picture review. ASK Questions if you are really rusty. |
** |
| * |
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| Monday, April 1 |
In-class midterm |
| Wednesday, April 3 |
Convergence of Series of Functions
Switching the order of Limiting Processes---discussion of a delicate business. |
Section 12. 3
Read Section 12.4 for big picture. |
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| Friday, April 5 |
Power series---basic definitions
Discussion of Taylor Series.
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Excursion J |
Takehome midterm due by 4 p.m on Thursday, April 4.
Class: Problems 1,3 in Exc. J.1
Notebooks: Problem 4 in Excursion J.1 |
| * |
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| Monday, April 8 |
Integration and differentiation of power series
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Excursion J.2 (again!) |
Class: Problems 1, 2, 3 and 4 in Section J.2
Notebooks: Problem 1 in Excursion J.3.
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| Wednesday, April 10 |
Finish Power Series |
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| Friday, April 12 |
Everywhere continuous, nowhere differentiable. |
Excursion K |
Class: Theorem K.2.1 steps 1 and 2. |
| * |
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| Monday, April 15 |
Everywhere continuous, nowhere differentiable---cont. |
Excursion K |
Class: Theorem K.2.1 steps 3, 4 and 5.
Notebook problems due: Excursion J.1 and J.3 |
| Wednesday, April 17 |
Spaces of Continuous functions |
Excursion N.1 and N.2 |
Class: Lemma N.1.1 and Theorem. N.1.3, Theorem N.2.4
Notebooks: Lemma N.1.4, and Thm. N.1.5 |
| Friday, April 19 |
No Class; Professor Schumacher out of town. |
| * |
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| Monday, April 22 |
Compactness in C(K) |
Excursion N.2 (again!) |
Class: N.2.4, N.2.5, N.2.6, N.2.7 (Assigned in groups.) |
| Wednesday, April 24 |
Compactness in C(K)---continued |
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| Friday, April 26 |
Discussion of Arzela-Ascoli and characterization of compactness in C(K). |
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| * |
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| Monday, April 29 |
Differential Equations: uniqueness and existence of solutions |
Excursion O.1 and O.2 |
Class: Problem 1 in Section O.2
Notebook problems due: Lemma N.1.4 and Thm. N.1.5, Arzela-Ascoli Theorem.
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| Wednesday, May 1 |
Picard Iteration |
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Class: Problems 2 and 3 in Section O.2. |
| Friday, May 3 |
Takehome final distributed |
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Final Examination
In class portion: Monday, May 6 at 1:30 p.m.
Alternate in-class time: 6:30 p.m on Wednesday, May 8
Takehome final due: at 6:30 p.m. on Wednesday, May 8
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