Spring 2015, Math 500, Real Analysis

Course Information

  • Course Coverage: This course intends to cover some basic topics of real analysis at the undergraduate level: the real number system, limits and sequences, sequences and series of functions, continuity and differentiability of functions, Riemann integrals. Tentatively, we will cover Chapter 1 to Chapter 6.
  • Time: MWF 11:00 --- 11:50 AM
  • Location: Snow Hall 301
  • Text: Elementary Analysis, the theory of Calculus, (2nd edition), By Kenneth A. Ross
  • Prerequisite: Math 223 and Math 290
  • Instructor: Shuanglin Shao
  • Office: Snow Hall 615
  • Email: slshao@ku.edu
  • Office Hour: MWF: 1:00 --- 2:00 PM, or by appointment.

Grade Policy

  • Homework: There will be 10 homework. Each homework consists of roughly 20 problems; only 3 of them will be graded, which will be decided after you turn in homework. The lowest homework grade will be dropped.
  • Quizzes: There will be 5 quizzes in class; the date will be announced one week in advance in class or by email.
  • Midterm: There will one midterm of 50 minutes in class on March 11, 2015.
  • Final Exam: There is a comprehensive final exam on May 11, 10:30 AM --- 1:00 PM. The location is 301 Snow Hall.
  • Grade Percentage: homework (30 %) + midterm (20 %) + quizzes (10 %) + final (40 %).

Homework

  • Homework 1.(due by Feb. 2nd in class.): #1.1 ,#1.7, #1.12, #2.3, #2.7, #3.1, #3.5, #3.8, #4.3, #4.4, #4.5, #4.9, #4.10, #4.12, #4.14, #4.16, #5.4. Solutions to homework 1 (PDF)
  • Homework 2.(due by Feb. 16th in class;rescheduled to be due by Feb. 20th in class.): #7.3(b)(d)(f)(h)(j)(l)(n)(p)(r)(t); #7.4, #8.2(b)(d), #8.4, #8.5(a)(b), #8.6, #8.8; #9.4, #9.5, #9.9, #9.11, #9.15, #9.18, #10.1, #10.3, #10.6, #10.7, #10.9, #10.12. Solutions to homework 2 (PDF)
  • Homework 3.(due by March 9th in class.extended to March 13 in class): #11.2, # 11.3, # 11.6, #11.8, # 11.11, # 14.1, # 14.2, # 14.5, # 14.6, # 14.8, # 14.12, # 14.13, # 14.14, # 15.1, # 15.2, # 15.3, # 15.6, # 15.7. Solutions to homework 3 (PDF)
  • Homework 4.(due by March 30th in class.): #17.1, #17.4,# 17.9 (a), # 17.10 (b), # 17.11, # 17.13(a), # 18.1, #18.2,#18.4,#18.5,#18.8,#18.12. Solutions to homework 4 (PDF)
  • Homework 5.(due by April 1st in class.): #19.1, #19.2 (a)(b), #19.3(a), #19.4, #19.6, #19.7, #19.9; #20.1, #20.2, #20.5, #20.6, #20.11, #20.11, #20.12, #20.16, #20.17, #20.20. Solutions to homework 5 (PDF)
  • Homework 6.(due by April 10th in class.): #23.1(b)(d)(f)(h), # 23.2, #23.4, #23.5, #23.6; #28.1 (a)(c)(e), #28.2, #28.3, #28.4 ,#28.7, #28.11, #28.12, #28.14, #28.16 Solutions to homework 6 (PDF)
  • Homework 7.(due by April 13th in class.): #29.1(a)(c)(e), #29.2, #29.3, #29.4, #29.7, #29.9, #29.11, #29.18. Solutions to homework 7 (PDF)
  • Homework 8.(due by April 20th in class.): #32.1, #32.2, #32.3, #32.4, #32.6. Solutions to homework 8 (PDF)
  • Homework 9.(due by April 27th in class.): # 33.1, # 33.2, # 33.4, # 33.5, # 33.7. Solutions to homework 9 (PDF)
  • Homework 10.(due by May 4th in class.): # 34.1, # 34.2, # 34.5, # 34.6, # 34.7, # 34.11. Solutions to homework 10 (PDF)