Professor Alexandru I. Suciu
MATH 3150 · Real Analysis
Fall 2011

* Course Information

Course MATH 3150 · Real Analysis: Sec. 1, CRN 15304
Instructor Alex Suciu
Course Web Site    www.northeastern.edu/suciu/MATH3150/analysis.fa11.html
Time and Place Monday & Wednesday 2:50pm-4:30pm, in 165 Richards Hall
Office 435 LA – Lake Hall
Phone (617) 373-3899
Email a.suciu@neu.edu
Office Hours Mon, Tue, Wed 4:40-5:30pm, in 435 LA
Teaching Assistant Gufang Zhao.  Email: zhao.g@husky.neu.edu Phone: x-5673.
Office hours: Tue 10:30am-12:00Noon and Th 9:30am-11:00am, in 537NI.
Prerequisites MATH 2321 (Calculus 3 for Science and Engineering) and MATH 2331 (Linear Algebra)
Textbook Elementary Classical Analysis, Second Edition, Jerrold E. Marsden and Michael J. Hoffman, W. H. Freeman 1993. ISBN: 0716721058
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 (50%), midterm exam (20%), and final exam (30%). It is expected that you will work on the problem sets together; however, they must be written up separately.

* Class Materials

Homework assignments

HMW Due date Sections Pages Problems
1 Sept. 21 Introduction 21 8(a)
1.2: Completeness 45 2, 5
1: Exercises 97-100 4, 7, 33
2 Oct. 3 1.4: Cauchy sequences 51-52 2, 5
1.5: Cluster points 56 3
1: Exercises 98-100 9, 15, 32
3 Oct. 12 1.6: Euclidean spaces 63-64 3, 5
1.7: Norms, inner products, and metrics 70 1, 4
1: Exercises 98-100 12(b,c), 30
4 Oct. 19 2.1 Open sets 108 4, 6
2.2: Interior of a set 110 4
2: Exercises 143-144 1(c,e,f,g,h), 3, 10(a,b,c)
5 Nov. 9 3.1 Compactness 155 2, 3
3.2: Heine-Borel 157 4, 5
3: Exercises 173-176 30, 37(a)
6 November 16 3.4: Path-connected sets 162 3
3.5: Connected sets 164 4
4.1 Continuity 181 1(b), 2
4.2: Images of continuous maps 184 4a
4.3: Operations on continuous maps 187 3
7 November 28 4.4: Boundedness of continuous functions 191 3
4.5: Intermediate value theorem 193 2
4.6: Uniform continuity 196 2
4: Exercises 232 6(b), 7, 12(c)
8 December 7 4.7 Differentiation 203 5
4.8: Integration 210-211 7, 8
4: Exercises 235-236 29, 31, 42

Handouts

Midterm exam (Wednesday, October 26, 2011)

  • Practice problems from Chapter 1 (pp. 97-100):   1, 15, 24, 27

  • Practice problems from Chapter 2 (pp. 143-148):   2, 4, 6, 7, 12, 13, 16, 18, 19, 26, 28, 29, 31, 34, 38, 42, 43, 52

  • Review session: Tuesday, October 25, at 8:00pm in 509 LA

Final exam (December 15, 2011, at 1:00pm, in 119 Dodge Hall)

  • Practice problems from Chapter 3 (pp. 172-176):   15, 22, 29, 30, 32, 35, 37

  • Practice problems from Chapter 4 (pp. 231-236):   3, 6, 7, 9, 12(b, d), 15, 18, 21, 23*, 28, 29, 30(a), 34*, 39, 40, 41, 43, 45

  • Practice exam: Final Exam from Spring 2011, with solutions

  • First review session: Monday December 12, at 5:00pm-6:30pm, in 544 Nightingale

  • Second review session: Tuesday December 13, at 5:00pm-6:30pm, in 235 Ryder

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
Home Started:   September 2, 2011
Last modified:   December 16, 2011
URL:  www.northeastern.edu/suciu/MATH3150/analysis.fa11.html