Real Analysis II
Send me email at leader@rose-hulman.edu.
MA490 Real Analysis II is a course in integration theory that is intended for those who will be studying pure or applied mathematics in graduate school and wish to insure adequate preparation in analysis. We will review the Riemann integral and then cover the Generalized Riemann integral (a.k.a. the Henstock-Kurzweil, Denjoy, or Perron integral), the Riemann-Stieltjes integral (integration dg(x) for cases other than g(x)=x) and its relation to probability density functions, and an introduction to the Lebesgue integral.
Grading: Weekly homework, two midterms, one presentation to the class. No final exam.
Texts: A Garden of Integrals, Frank E. Burk; The Integrals of Lebesgue, Denjoy, Perron, and Henstock, Russell A. Gordon; The Origins of Cauchy's Rigorous Calculus, Judith A. Grabiner
Prerequisite: MA366.
Class will not meet the week of Jan. 7.
HW:
Assignment 1: Burk #3.2.1,3.3.2,3.4.1,3.4.2,3.7.1,3.8.1; Grabiner Ch. 1-3 Due 13 Dec. Assignment 2: Burk #4.2.1,4.3.1,4.3.2; Handout 1 A,B,C; Grabiner Ch. 4 Due 18 Dec. Assignment 3: Burk #4.5.2,4.6.1; Handout 2 D,E,F,G; Grabiner Ch. 5 Due 21 Dec. Assignment 4: Burk #5.5.1; Gordon #1.1,1.4; Handout 3 H,I,J; Grabiner Ch. 6, Conclusion, Appendix Due 15 Jan. Assignment 5: Burk #5.7.2,6.1.1,6.2.2; Gordon #2.5,3.1,3.2 Due 22 Jan. Assignment 6: Handout 4 Due 4 Feb. Assignment 7: Handout 5 Due 11 Feb. Assignment 8: Handout 6 Due 18 Feb.
Maintainer: leader@rose-hulman.edu.