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

## Course Information

 Course MATH 3150 · Real Analysis: Sec. 2, CRN 35831 Instructor Alex Suciu Course Web Site www.math.neu.edu/~suciu/MATH3150/analysis.sp11.html Time and Place Tuesday & Friday 9:50am-11:30am, in 128 Ryder Hall Office 441 LA – Lake Hall Phone (617) 373-4456 Email a.suciu@neu.edu Office Hours Tuesday & Friday 11:40am-12:40pm, Thursday 4:40-5:40pm, in 441 Lake Hall Teaching Assistant Yinbang Lin.  Email: lin.yinb@husky.neu.edu Phone: x-7055. Office hours:  Tue 12:30pm-2:00pm and Th 2pm-3:30pm, in 551NI. 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 Solutions
1 Jan. 21 1.1: Number systems 35 5 Solutions to HMW 1
1.2: Completeness 45 1, 2, 3, 4
1: Exercises 97-100 2, 3, 33
2 Jan. 28 1.3: Least Upper Bounds 48 4 Solutions to HMW 2
1.4: Cauchy sequences 51-52 2, 4, 5
1.5: Cluster points 56 1
1: Exercises 98 9
3 Feb. 4 1.6: Euclidean spaces 63-64 3, 5 Solutions to HMW 3
1.7: Norms, inner products, and metrics 70 1, 3, 4
1: Exercises 98 12(b,c)
4 Feb. 15 2.1 Open sets 108 4, 6 Solutions to HMW 4
2.2: Interior of a set 109 2
2.3: Closed sets 112 2
2.5: Closure of a set 117 2
2.6: Boundary of a set 120 2
5 Feb. 22 2.7 Sequences 123 3
2.8: Completeness 125 4
2.9: Series 129 1, 4
2: Exercises 143-149 28, 34
6 March 18 3.1 Compactness 155 2, 3 Solutions to HMW 6
3.2: Heine-Borel 157 4, 5
3.5: Connected sets 164 4
3: Exercises 173 6
7 March 29 4.1 Continuity 181 1b
4.2: Images of continuous maps 184 4a
4.3: Operations on continuous maps 187 3
4.6: Uniform continuity 196 2
3: Exercises 176 37a
4: Exercises 232 12c
8 April 8 4.7 Differentiation 203 5 Solutions to HMW 8
4.8: Integration 210-211 2, 7, 8
4: Exercises 235-236 31, 42
9 April 19 6.1 Differentiable mappings 330 2
6.2: Matrix representation 334 2
6.4: Conditions for differentibility 344 1, 4
6.6: Product rule and gradients 352 4
6: Exercises 386 13(a,b)

### Midterm exam (February 25, 2011)

• Practice problems from Chapter 1 (pp. 97-102):   1, 7, 15, 24

• Practice problems from Chapter 2 (pp. 143-149):   1, 2, 4, 7, 10, 12, 13, 16, 18, 19, 26, 29, 31, 42, 43, 52(b,c,f)

• Midterm exam, with solutions

### Final exam (April 25, 2011, at 10:30am)

• 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, 9, 15, 23*, 34*, 40, 41, 45

• Practice problems from Chapter 6 (pp. 383-389):   5, 13(c), 16, 18, 35, 38, 40

 Department of Mathematics Office: 441 Lake Hall Messages: (617) 373-2450 Northeastern University Phone: (617) 373-4456 Fax: (617) 373-5658 Boston, MA, 02115 Email: a.suciu@neu.edu Directions