Chapter 7: Infinite Series of Functions
WEEK 1 14-18 January Mon 14 7.1 Uniform convergence of sequences Fri 18 7.2 Uniform convergence of seriesWEEK 2 21-25 January Mon 21
Martin Luther King Holiday - no class meeting
Wed 23 Uniform convergence theorems
Fri 25 7.3 Power Series
2.5 Limit superior and limit inferior
WEEK 3 28 January - 1 February Mon 28 7.4 Analytic Functions Wed 30 ... continued Fri 1 Written homework due: § 2.5 #5(a), § 7.2 #3, § 7.4 #3(d).
WEEK 4 4-8 February
Chapter 14: Fourier Series
Mon 4 14.1 Introduction Wed 6 The Dirichlet kernel Fri 8 Written homework due: § 14.1 #6.WEEK 5 11-15 February Mon 11 Riemann-Lebesgue Lemma, preliminaries Wed 13 Dirichlet-Jordan Theorem Fri 15 14.2 Fejer's Theorem
WEEK 6 18-22 February Mon 18 14.3 Mean Square Convergence, Bounds for Fourier Coefficients Fri 22 Oral Exam Completion Date: Riemann-Lebesgue Lemma
WEEK 7 25 February - 1 March
Chapter 9: Topology of Euclidean Spaces
Mon 25 9.1 Interior, Closure, Boundary Fri 1 9.2 Compact sets Written homework due: § 14.1 #4, § 14.3 #6, § 14.4 #2 (b),(c).WEEK 8 4 - 8 March Wed 6 9.3 Connected sets Fri 8 9.4 Continuous functions
WEEK 9 11-15 March Mon 11 9.5 Applications
Chapter 11: Differential Calculus in R^n
Fri 15 11.1 Partial Derivatives and Partial Integrals Written homework due: § 9.1 #5 § 9.4 #7 § 9.4 #8
MARCH 18-22 ***SPRING BREAK***
WEEK 10 25-29 March
WEEK 11 1 - 5 April Mon 1 11.2 Partial derivatives and (total) derivative Wed 3 Written homework due: § 11.1 #9 Fri 5 Midterm Exam II: Chapter 9, Sections 11.1-2.
WEEK 12 8-12 April Mon 8 11.3 Derivative properties; Chain Rule Wed 10 11.4 Mean Value Theorem; Taylor's Formula
WEEK 13 15-19 April Mon 15 11.5 Inverse Function Theorem; Implicit Function Theorem Wed 17 11.6 Optimization Exercises, Chapter 11 §11.2 #6, 10 §11.3 #5, 8 §11.4 #3(a), 12 §11.5 #4, 6 §11.6 #1(a), 3(b)
WEEK 14 22-26 April
National TV Turnoff Week April 22-28
Introduction to Lebesgue Measure and Integration
Fri 26 Written homework due: § 11.3 #11, § 11.4 #7, § 11.5 #8.
WEEK 15 29 April - 3 May
###MAY### EXAM WEEK 6-10 May Tue 7 Final Exam 9:45 - 11:45 AM. Syllabus for final exam:
- Uniform limit of continuous functions is continuous
- Dirichlet-Jordan Theorem
- Bessel inequality
- Heine-Borel Theorem
- "Soft" characterization of continuity
- Mean Value Theorem
- Taylor's Theorem
- 1st and 2nd Derivative Tests
- Outer measure is countably subadditive
- Union of two Lebesgue measurable sets is Lebesgue measurable
