Math 412 -- Mathematical Analysis II, MTH 10:20 - 11:40AM ARC 110 ---- Spring 2019

The instructor is Professor Yanyan Li.


Final Exam: May 13, 2019, 8-11am


Textbook

Principles of Mathematical Analysis, by Walter Rudin, Third Edition


Office Hour

Wed. 10:20--11:40am

Policy

Homework 25% ; Midterm 35%; Final Exam 40% (The in class part is 35%, and the take home part is 5%) (No late homework, drop two lowest for homework)


Syllabus and homework

Date Section Homework
Jan. 24 Chapter 7, Sequences of Functions: Examples, Issues, and Uniform Convergence Homework to be handed in: Page 165, #2,3, 4,6. Homework not handed in: Page 176, #1,5,7.
Jan. 28 Chapter 7, Uniform convergence and continuity, Uniform convergence and integration, Homework to be handed in: Page 166-167, #8, 9, 11, 12. Homework not handed in: P167, #10.
Jan. 31 Chapter 7, Uniform convergence and differentiation Homework to be handed in: Page 166, #7, 10, and two more assigned by Professor Han in class.
Feb. 4 Chapter 7, Equicontinuity Homework to be handed in: Page 167-168, #13, 15, 16, 17.
Feb. 7 Chapter 7, Equicontinuity and Stone-Weisstrass Theorem Homework to be handed in: page 168-169, #19, 20, 23, and one more assigned by Professor Han in class.
Feb. 11 Chapter 8, Power Series, Abel's theorem, Homework to be handed in: Page 196, #1, 2, 3.
Feb. 14 Chapter 8, Exponential and Logarithmic functions, Trigonomic functions Homework to be handed in: Page 196, 4a, 4c, 5a, 5c; Page 197, #6, 7, 9. Homework not handed in: Page 197, #4b, 4d, 5b, 5d; #8.
Feb. 18 Chapter 8, Algebraic completeness of the complex field, Fourier Series Homework to be handed in: Page 197-198, #10, 11, 12(a), 12(b).
Feb. 21 Chapter 8, Fourier Series Homework to be handed in: Page 198, #12(c), 12(d), 12(e), Page 199, #14, 15.
Feb. 25 Chapter 6, Riemann-Stieltjes integrals, definition and existence of the integral Homework to be handed in: Page 138, #1, 3, 5, 7. Homework not handed in: Page 138, #2, 4.
Feb. 28 Chapter 6, Properties of the integral Homework to be handed in: Page 138, #6, 8, 9, 10.
March 4 Class canceled due to weather Class canceled due to weather
March 7 Exam 1
March 11 Chapter 6, Properties of integrals Homework to be handed in: Page 140, #11, 12; Page 138, #2, 4.
March 14 Chapter 6, Integration and differentiation, Rectifiable curves Homework to be handed in: Page 141-142, #13, 15, 17, 18. Homework not handed in: Page 141, #16, 19.
March 25 Chapter 9, Linear transformations and Differentiation Homework to be handed in: Page 239, #8-11. Homework not handed in: Page 239, #1-7.
March 28 Chapter 9, Differentiation Homework to be handed in: Page 239-240, # 12, 13, 14, 15.
April 1 Chapter 9, The contraction principle, the Inverse Function Theorem Homework to be handed in: Page 241-242, #17, 19, 21, 23. Homework not handed in: Page 241, #16.
April 4 Chapter 9, Derivatives of higher order, Differential of integrals Homework to be handed in: Page 241-242, #18, 24, 27, 28. Homework not handed in: Page 241-242, #22, 26.
April 8 Chapter 9 Homework to be handed in: Page 141, #16, 19; Page 197-198, #8, 13.
April 11 Chapter 10. Integration, Primitive Mappings Homework to be handed in: Page 288-289, #1-4.
April 15 Chapter 10, Partition of Unity, Change of Variables, Differential Forms Homework to be handed in: Page 290, #9-12.
April 18 Chapter 10, Differential Forms Homework to be handed in: Page 289-291, #5, 6, 13, 15.
April 22 Chapter 10, Simplexes and Chains, Stokes' Theorem, Closed Forms and Exact Forms Homework to be handed in: Page 293-294, #16, 18, 20, 21.
April 25 Chapter 10, Closed Forms and Exact Forms, Poincare Lemma Homework to be handed in: Page 290-292, #22, 24, 27, 28.
April 29 Chapter 10, Vector Analysis Homework handed in: Page 297, #23, 25, 26, 31.
May 2 Chapter 10, Vector Analysis, partial review Homework not handed in: Page 296-297, #30. Prepare for the Final Exam
May 6 Partial review Prepare for the Final Exam