Date
Topic
Homework Problems
Monday, January 12 Differentiation domains and the definition of the derivative * *
Wednesday, January 14 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 16

Finish section 9.2.
Discussion: Why the Mean Value Theorem?

Section 9.3. *
*
Monday, January 19 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 21 Monotonicity and the Mean Value Theorem Section 9.5 Class: Problems 1 and 3 in Section 9.5
Friday, January 23 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 26 Taylor Polynomials and Taylor's Theorem Section 9.7
Wed., January 28 Error in Taylor Polynomial Approximations   Class: Problem 2 in Section 9.7
Notebooks: Problems 1 and 3 in Section 9.7 (Group assignment)
Friday, January 30

Experimenting with iteration and cobweb diagrams.

Meet in PRCL09 (computer lab in Peirce)

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
Notebook problems on Sects. 9.2, 9.4, and 9.5 due

*
Monday, February 2 Iteration and Fixed Points Rest of Section 10.1 Class: Problems 5, 6, and 9 in section 10.1
Notebooks: Problems 4, 8, and 10 in Section 10.1
Group notebook assignment on 9.7 due
Wednesday, February 4 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
Friday, February 6 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
*
Monday, February 9 More on attracting Fixed Points Section 10.3 Class: Problem 11 in Section 10.1 and Problems 1 and 2 in Section 10.3
Wednesday, February 11 Iteration and Newton's Method Sections L.1 and L.2 Class: Problems 1 and 2 in Section L.2.
Friday, February 13 Defining the integral Sections 11.1 and 11.2 Class: Problems 2, 3, 4 and 6 in Section 11.2
*
Monday, February 16 Defining the integral, cont. 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

Wednesday, February 18 Arithmetic, order and the integral Section 11.3 Class: Problems 1 and 4 in Section 11.3
Notebooks: Problems 3, 5, and 6 in Section 11.3
Friday, February 20

Families of Riemann Sums

Section 11.4 through the bottom of pg. 221 Class: Exercises and Problem 1 in Section 11.4
Notebooks: Problem 3 in Section 11.4
*
Monday, February, 23

Riemann Sums and Refinements

Section 11.4 pgs. 221-Lemma 11.4.7 Class: Problems 2, 4 and 5 in Section 11.4
Wednesday, February 25

Cauchy Criteria for the existence of the integral ---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!)

Notebook problems on Sections 11.2 11.3 and 11.4(so far)

Friday, February 27 Cauchy Criteria for the existence of the integral---lecture cont. ** Notebooks: Problems 6 and 7 in Section 11.4

# Spring Break

Monday, March  16
Existence of the Integral
Section 11.5 Class: Problems 1, 2 and 4 in Section 11.5.
Notebooks: Problems 5, 7, 8 and 10 in Section 11.5.
Wednesday, March 18 The Fundamental Theorem of Calculus Section 11.6 Class: Problems 2 and 3 in Section 11.6.
Notebooks: Problem 1 in Section 11.6.
Friday, March 20

Subsequences and Convergence

Excursion G Class: Problems 3 in Section G.1 and 1, 2, 3, 4 and 7 in Section G.2.
*
Monday, March 23

Subsequences and Convergence, cont.

Wednesday, March 25 Relatives of the geometric series---the root and the ratio test. (A quick and dirty discussion.) Excursion H.3 Notebook problems from Sections 11.4 (remaining), 11.5 and 11.6 due
Friday, March 27 Power series---basic definitions
Excursion J.1 Class: Problems 1 and 3 in Excursion J.1
Notebooks: Problem 4 in Excursion J.1.
*
Monday, March 30 Discussion of Theorem 12.4.4 and problem 6 at the end of Section 12.4
Takehome midterm distributed
Review Section 12.4
Wednesday, April 1 Integration and differentiation of power series Excursion J, Sections 2 & 3 Class: Problems 1, 2, 3 and 4 in Section J.2
Notebooks:
Problem 1 in Excursion J.3.
Friday, April 3
In-class Midterm
*
Monday, April 6
Takehome midterm due; No class. Carol out of town.
Wednesday, April 8 Everywhere continuous, nowhere differentiable. Excursion K Class: Theorem K.2.1 steps 1 and 2.
Friday, April 10 Everywhere continuous, nowhere differentiable---cont.   Class: Theorem K.2.1 steps 3, 4 and 5.
*
Monday, April 13 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

Wednesday, April 15 Compactness in C(K)

Excursion N.2 (again!)

Class: N.2.4, N.2.5, N.2.6, N.2.7, N.2.8. (Arzela-Ascoli)
Friday, April 17 Compactness in C(K)---continued
*
Monday, April 20 Approximation by Polynomials Excursion N.3 Class: Lemma N.3.3 and Problems 1, 2, 3, and 4 in Section N.3
Wednesday, April 22 Approximation by Polynomials (cont.)   Notebook problems due: Lemma N.1.4 and Thm. N.1.5
Friday, April 24 The Stone Weierstrass Theorem Fill in details in the proof outline
*
Monday, April 27 Finish Stone Weierstrass
Wednesday, April 29 Differential Equations: uniqueness and existence of solutions Excursion O.1 and O.2 Class: Problem 1 in Section O.2
Friday, May 1 Picard Iteration Class: Problems 2 and 3 in Section O.2

In-class Final Examination
Monday, May 4th at 9:30 a.m. (Note the late start time)
Takehome final due at noon on Thursday, May 7