Tentative Schedule
Chapter numbers refer to the text Principles of Mathematical Analysis, 3rd Ed., by Walter Rudin
Chapter 7 -- Sequences and Series of Functions
Jan. 12: Sequences and Series
Jan. 14: Uniform convergence and continuity
Jan. 16: Uniform convergence and integration
Jan. 21: Uniform convergence and differentiation
Jan. 23: Homework discussion
Jan. 26: Equicontinuity
Jan. 28: Arzela-Ascoli Theorem
Jan. 30: Stone-Weierstrass Theorem
Feb. 2: Stone-Weierstrass Theorem
Feb. 4: Stone-Weierstrass Theorem
Feb. 6: Homework discussion
Chapter 8 -- Some Special Functions
Feb. 9: Power Series
Feb. 11: Exponential, logarithm and trigonometric functions
Feb.13: Fourier Series
Feb. 16: Fourier Series
Feb. 18: Review
Feb. 20: First Exam
Chapter 9 -- Functions of Several Variables
Feb. 23: Linear maps
Feb. 25: Linear maps
Feb. 27: Exam discussion
Mar. 2: Differentiation
Mar. 4: Differentiation
Mar. 6: Differentiation
Mar. 16: Higher ordered derivatives
Mar. 18: Higher ordered derivatives
Mar. 20: Contraction mapping and inverse function theorems
Mar. 23: inverse function theorem
Mar. 25: implicit function theorem
Mar. 25*: Rank Theorem
Mar. 37: Differentiation of integrals
Mar. 30: Homework discussion
Apr. 1: Review
Apr. 3: Second Exam (take home -- no class)
Chapter 10 -- Integration of Differential Forms
Apr. 6: Integration on cells
Apr. 8: Mappings
Apr. 8:* Partitions of unity and change of variables
Apr. 10: Differential forms
Apr. 13: Stoke’s Theorem/ closed and exact forms
Apr. 15: Vector calculus
Apr. 20: No class
Apr. 22: No class
Apr. 24: No class
Apr. 27: Homework discussion
*Makeup lectures at 5:00 in WH C103
Apr. 29: Review/ other topics
Apr. 31: Review/ other topics
May 4: Final Exam
