Week
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Date
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Topic
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Homework (Solution)
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1
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Sept. 4
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Organization; Review I: Limit of Sequences and Functions: Definitions
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Sept. 5
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Review II: Understanding Limit of Sequences
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Sept. 6
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2
|
Sept. 9
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Sept. 11
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Sept. 12
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Review VI: Properties of Riemann Integrals
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Homework 1 (Solution)
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Sept. 13
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Review VII: Example: Additive functions
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3
|
Sept. 16
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Sept. 18
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Sept. 19
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Geometry of R^N III: Square matrices and linear transformations
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Homework 2 (Solution)
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Sept. 20
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4
|
Sept. 23
|
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Sept. 25
|
Topology of R^N II: More on open and closed sets
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Sept. 26
|
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Homework 3 (Solution)
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Sept. 27
|
Topology of R^N IV: More compactness
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5
|
Sept. 30
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Oct. 2
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Oct. 3
|
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Homework 4 (Solution)
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Oct. 4
|
Differentiability IV: Properties and Applications
|
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6
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Oct. 7
|
Implicit and Inverse Functions I: Linear Functions
|
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Oct. 9
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Implicit and Inverse Functions II: R^2 case
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Oct. 10
|
Implicit and Inverse Functions III: General case
|
Homework 5 (Solution)
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Oct. 11
|
Implicit and Inverse Functions IV: Applications
|
Midterm Practice Problems
|
7
|
Oct. 16
|
Review for Midterm I
|
|
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Oct. 17
|
Review for Midterm II
|
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Oct. 18
|
Midterm
|
Midterm Solution
|
8
|
Oct. 21
|
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|
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Oct. 23
|
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Oct. 24
|
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Homework 6 (Solution)
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Oct. 25
|
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9
|
Oct. 28
|
The plan
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Oct. 30
|
Measure Theory I: Simple Graphs
|
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Oct. 31
|
Measure Theory II: Zero measure sets
|
Homework 7 (Solution)
|
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Nov. 1
|
Measure Theory III: Measurability
|
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10
|
Nov. 4
|
Riemann Integration I: Integration of simple functions
|
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Nov. 6
|
Riemann Integration II: Riemann integration
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Nov. 7
|
Riemann Integration III: Riemann integrability
|
Homework 8 (Solution)
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Nov. 8
|
Riemann Integration IV: More on integrability
|
|
11
|
Nov. 13
|
Fubini I: The theorem
|
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Nov. 14
|
Fubini II: Calculation of double integrals
|
Homework 9 (Solution)
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Nov. 15
|
Fubini III: Calculation of triple integrals
|
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12
|
Nov. 18
|
Change of Variables I: The theorem and sketch of proof
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Nov. 20
|
Change of Variables II: Double integrals
|
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Nov. 21
|
Change of Variables III: Triple integrals
|
Homework10 (Solution)
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Nov. 22
|
Change of Variables IV: More applications
|
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13
|
Nov. 25
|
Numbers I: N
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Nov. 27
|
Numbers II: Q and Cuts
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Nov. 28
|
Numbers III: R
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Nov. 29
|
Numbers IV: Properties of R
|
Final Practice Problems with Solution
|
14
|
Dec. 2
|
Review for Final I: Calculation
|
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Dec. 4
|
Review for Final II: Concepts
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