Professor Alexandru I. Suciu MATH 3150 · Real Analysis Fall 2016

## Course Information

 Course MATH 3150 · Real Analysis Instructor Alex Suciu Course Web Site www.northeastern.edu/suciu/MATH3150/analysis.fa16.html Time and Place Monday & Wednesday 2:50pm-4:30pm, in 266 Ryder Hall Office 435 LA – Lake Hall Phone (617) 373-3899 Email a.suciu@neu.edu Office Hours Monday & Wednesday 4:40-5:40pm or by appointment, in 435 Lake Hall Prerequisites MATH 2321 (Calculus 3 for Science and Engineering) and MATH 2331 (Linear Algebra) Textbook An Introduction to Classical Real Analysis, Karl R. Stromberg, AMS Chelsea Publishing, 2015 Course Description Provides the theoretical underpinnings of calculus and the advanced study of functions. Emphasis is on precise definitions and rigorous proof. Topics include the real numbers and completeness, continuity and differentiability, the Riemann integral, the fundamental theorem of calculus, inverse function and implicit function theorems, and limits and convergence. Grade Based on problem sets (40%), midterm exam (20%), and final exam (40%). It is expected that you will work on the problem sets together; however, they must be written up separately.

## Homework assignments

• Homework 1:  Chapter 1, Problems 6, 10, 18, 23, 25, and one more: Given two subsets A, B of R, show that inf(A+B) = inf(A)+inf(B), where A+B={a+b : aA and bB}.  Due Monday, September 19.   Solutions to Homework 1
• Homework 2:  Chapter 2 (pp. 84-86): Problems 2(b)-(c), 7, 8, 15, 18(b).  Due Monday, October 3.   Solutions to Homework 2.
• Homework 3:  Chapter 2 (pp. 86-87): Problems 21, 24, 28 and Chapter 3 (p. 111): Problems 2, 3.  Due Wednesday, October 19.
• Homework 4:  Chapter 3 (pp. 119-121): Problem 1 (for f_1 and f_2 with S_1, S_2, S_4, only compute the limits, not the iterated limits), Problems 6 and 8; and Chapter 3 (pp. 124-125): Problems 9 and 17.  Due Monday, November 7.
• Homework 5:  Chapter 3 (pp. 111-113): Problems 4, 14, 16; (p. 120): Problem 2; (p. 124): Problem 1.  Due Wednesday, November 16.
• Homework 6:  Chapter 3 (p. 144): Problems 1(a-b), 2, 4; Show that the sequence in Example (3.111)-(d) is NOT uniformly convergent;   Chapter 4 (p. 183): Problem 4.   Due Wednesday, November 30.   Solutions to Homework 6.
• Homework 7:   Chapter 4 (pp. 183-187): Problems 5, 17, 21 (a,e,i); (p. 198): Problem 3 (a,b); (p. 215): Problem 2.  Due Friday, December 10.

## Course Materials and Exams

• Review session: Monday December 12, from 3:00pm to 5:00pm, in 509 Lake Hall.
• Final exam: Wednesday December 14, at 3:30-5:30pm, in Hastings Suite 104.

 Department of Mathematics Office: 435 Lake Hall Messages: (617) 373-2450 Northeastern University Phone: (617) 373-3899 Fax: (617) 373-5658 Boston, MA, 02115 Email: a.suciu@neu.edu Directions