Week

Date

Topic

Homework (Solution)

1

Sept. 4

Organization; Review I: Limit of Sequences and Functions: Definitions



Sept. 5

Review II: Understanding Limit of Sequences



Sept. 6



2

Sept. 9




Sept. 11




Sept. 12

Review VI: Properties of Riemann Integrals

Homework 1 (Solution)


Sept. 13

Review VII: Example: Additive functions


3

Sept. 16




Sept. 18




Sept. 19

Geometry of R^N III: Square matrices and linear transformations

Homework 2 (Solution)


Sept. 20



4

Sept. 23




Sept. 25

Topology of R^N II: More on open and closed sets



Sept. 26


Homework 3 (Solution)


Sept. 27

Topology of R^N IV: More compactness


5

Sept. 30




Oct. 2




Oct. 3


Homework 4 (Solution)


Oct. 4

Differentiability IV: Properties and Applications


6

Oct. 7

Implicit and Inverse Functions I: Linear Functions



Oct. 9

Implicit and Inverse Functions II: R^2 case



Oct. 10

Implicit and Inverse Functions III: General case

Homework 5 (Solution)


Oct. 11

Implicit and Inverse Functions IV: Applications

Midterm Practice Problems

7

Oct. 16

Review for Midterm I



Oct. 17

Review for Midterm II



Oct. 18

Midterm

Midterm Solution

8

Oct. 21




Oct. 23




Oct. 24


Homework 6 (Solution)


Oct. 25



9

Oct. 28

The plan



Oct. 30

Measure Theory I: Simple Graphs



Oct. 31

Measure Theory II: Zero measure sets

Homework 7 (Solution)


Nov. 1

Measure Theory III: Measurability


10

Nov. 4

Riemann Integration I: Integration of simple functions



Nov. 6

Riemann Integration II: Riemann integration



Nov. 7

Riemann Integration III: Riemann integrability

Homework 8 (Solution)


Nov. 8

Riemann Integration IV: More on integrability


11

Nov. 13

Fubini I: The theorem



Nov. 14

Fubini II: Calculation of double integrals

Homework 9 (Solution)


Nov. 15

Fubini III: Calculation of triple integrals


12

Nov. 18

Change of Variables I: The theorem and sketch of proof



Nov. 20

Change of Variables II: Double integrals



Nov. 21

Change of Variables III: Triple integrals

Homework10 (Solution)


Nov. 22

Change of Variables IV: More applications


13

Nov. 25

Numbers I: N



Nov. 27

Numbers II: Q and Cuts



Nov. 28

Numbers III: R



Nov. 29

Numbers IV: Properties of R

Final Practice Problems with Solution

14

Dec. 2

Review for Final I: Calculation



Dec. 4

Review for Final II: Concepts

