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Professor Alexandru I. Suciu
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MATH 3150 · Real Analysis
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Spring 2011
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Course Information
Course
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MATH 3150 · Real Analysis:
Sec. 2, CRN 35831
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Instructor
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Alex Suciu
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Course Web Site
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www.northeastern.edu/suciu/MATH3150/analysis.sp11.html
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Time and Place
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Tuesday & Friday 9:50am-11:30am, in 128 Ryder Hall
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Office
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441 LA – Lake Hall
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Phone
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(617) 373-4456
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Email
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a.suciu@neu.edu
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Office Hours
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Tuesday & Friday 11:40am-12:40pm, Thursday 4:40-5:40pm, in 441 Lake Hall
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Teaching Assistant
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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.
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Prerequisites
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MATH 2321 (Calculus 3 for Science and Engineering) and MATH 2331 (Linear Algebra)
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Textbook
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Elementary Classical Analysis, Second Edition,
Jerrold E. Marsden and Michael J. Hoffman, W. H. Freeman 1993. ISBN: 0716721058
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Course Description
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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.
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Grade
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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.
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Class Materials
Homework assignments
HMW
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Due date
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Sections
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Pages
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Problems
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Solutions
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1
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Jan. 21
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1.1: Number systems
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35
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5
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Solutions to HMW 1
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1.2: Completeness
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45
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1, 2, 3, 4
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1: Exercises
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97-100
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2, 3, 33
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2
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Jan. 28
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1.3: Least Upper Bounds
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48
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4
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Solutions to HMW 2
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1.4: Cauchy sequences
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51-52
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2, 4, 5
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1.5: Cluster points
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56
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1
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1: Exercises
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98
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9
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3
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Feb. 4
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1.6: Euclidean spaces
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63-64
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3, 5
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Solutions to HMW 3
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1.7: Norms, inner products, and metrics
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70
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1, 3, 4
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1: Exercises
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98
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12(b,c)
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4
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Feb. 15
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2.1 Open sets
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108
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4, 6
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Solutions to HMW 4
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2.2: Interior of a set
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109
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2
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2.3: Closed sets
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112
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2
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2.5: Closure of a set
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117
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2
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2.6: Boundary of a set
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120
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2
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5
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Feb. 22
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2.7 Sequences
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123
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3
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2.8: Completeness
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125
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4
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2.9: Series
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129
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1, 4
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2: Exercises
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143-149
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28, 34
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6
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March 18
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3.1 Compactness
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155
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2, 3
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Solutions to HMW 6
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3.2: Heine-Borel
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157
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4, 5
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3.5: Connected sets
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164
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4
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3: Exercises
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173
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6
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7
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March 29
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4.1 Continuity
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181
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1b
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4.2: Images of continuous maps
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184
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4a
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4.3: Operations on continuous maps
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187
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3
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4.6: Uniform continuity
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196
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2
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3: Exercises
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176
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37a
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4: Exercises
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232
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12c
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8
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April 8
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4.7 Differentiation
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203
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5
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Solutions to HMW 8
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4.8: Integration
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210-211
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2, 7, 8
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4: Exercises
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235-236
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31, 42
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9
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April 19
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6.1 Differentiable mappings
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330
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2
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6.2: Matrix representation
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334
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2
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6.4: Conditions for differentibility
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344
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1, 4
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6.6: Product rule and gradients
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352
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4
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6: Exercises
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386
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13(a,b)
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Midterm exam (February 25, 2011)
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Practice problems from Chapter 1 (pp. 97-102):
1, 7, 15, 24
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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)
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Midterm exam, with solutions
Final exam (April 25, 2011, at 10:30am)
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Practice problems from Chapter 3 (pp. 172-176):
15, 22, 29, 30, 32, 35, 37
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Practice problems from Chapter 4 (pp. 231-236):
3, 6, 9, 15, 23*, 34*, 40, 41, 45
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Practice problems from Chapter 6 (pp. 383-389):
5, 13(c), 16, 18, 35, 38, 40
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Final Exam
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