Date 
Topic 
Reading Assignment 
Homework 




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. 
* 
* 



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 
* 



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

Wednesday, January 30 
Introduction to Taylor Polynomials and Taylor's Theorem 
Section 9.7 

Friday, February 1 
Error in Taylor Polynomial Approximations 

Notebooks: Problems 1, 2, and 3 in Section 9.7 (Group assignment)
Notebook problems on Sects. 9.4 and 9.5 due 
* 



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 writeups 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

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 
* 



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.

* 



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 Ifood 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 


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

ReRead 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 



Spring Break

Monday, March 18 
Cauchy Criteria for the Existence of the IntegralWhat are the issues? (Lecture.) 
Rest of Section 11.4 (don't worry about the proofs; ignore Lemma 11.4.8read 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. 
* 



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. 

Notebook problems from Sections 11.4 numbers 6 and 7, 11.5 and 11.6 due 
Friday, March 29 
Relatives of the geometric seriesthe 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. 
** 
* 



Monday, April 1 
Inclass midterm 
Wednesday, April 3 
Convergence of Series of Functions
Switching the order of Limiting Processesdiscussion of a delicate business. 
Section 12. 3
Read Section 12.4 for big picture. 

Friday, April 5 
Power seriesbasic definitions
Discussion of Taylor Series.

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 
* 



Monday, April 8 
Integration and differentiation of power series

Excursion J.2 (again!) 
Class: Problems 1, 2, 3 and 4 in Section J.2
Notebooks: Problem 1 in Excursion J.3.

Wednesday, April 10 
Finish Power Series 


Friday, April 12 
Everywhere continuous, nowhere differentiable. 
Excursion K 
Class: Theorem K.2.1 steps 1 and 2. 
* 



Monday, April 15 
Everywhere continuous, nowhere differentiablecont. 
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. 
* 



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 


Friday, April 26 
Discussion of ArzelaAscoli and characterization of compactness in C(K). 


* 



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, ArzelaAscoli Theorem.

Wednesday, May 1 
Picard Iteration 

Class: Problems 2 and 3 in Section O.2. 
Friday, May 3 
Takehome final distributed 






Final Examination
In class portion: Monday, May 6 at 1:30 p.m.
Alternate inclass time: 6:30 p.m on Wednesday, May 8
Takehome final due: at 6:30 p.m. on Wednesday, May 8
