Math 217: Honors Advanced Calculus I (Fall 2013)



Instructor / Office / Phone #

Xinwei Yu / 527 CAB / (780)4925731

Email ;  Webpage

xinwei2@ualberta.ca ;  http://www.math.ualberta.ca/~xinweiyu

Location / Time 

CAB269/ MWF 10am - 10:50am; R 5pm - 5:50pm

Office Hours

MWF 11am - 12pm; R 3:30pm - 4:50pm.

MF 12pm - 2pm (share with Math 314)

Online Discussion

A joint forum for Math 217 and Math 314 has been set up on Piazza; 

You are encouraged to send me your questions, comments, and advice through email.




Current HW: No More HW


Draft Lecture Note Week 13 (Nov.25 - Nov. 29)



Your Position in Class (After HW10)

How to calculate: Round(Midterm + Average of 7 best HW grades)


Important dates.

Download course syllabus. 

Course Material

Homeworks: 

Homework Solutions: 


Plan of Lectures and Notes

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

Review III: Continuity and Differentiability


2

Sept. 9

Review IV: Taylor Expansion



Sept. 11

Review V: Riemann Integrals in R



Sept. 12

Review VI: Properties of Riemann Integrals
Homework 1 (Solution)


Sept. 13

Review VII: Example: Additive functions


3

Sept. 16

Geometry of R^N I: Definitions and Properties



Sept. 18

Geometry of R^N II: Linear functions and matrices



Sept. 19

Geometry of R^N III: Square matrices and linear transformations
Homework 2 (Solution)


Sept. 20

Geometry of R^N IV: Geometric Objects in R^N


4

Sept. 23

Topology of R^N I: Limits and Continuity; Open/closed sets.



Sept. 25

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



Sept. 26

Topology of R^N III: Compactness
Homework 3 (Solution)


Sept. 27

Topology of R^N IV: More compactness


5

Sept. 30

Differentiability I: Definitions



Oct. 2

Differentiability II: Partial Derivatives



Oct. 3

Differentiability III: Geometric Meanings of the Differential
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

Higher Derivatives I: Higher Order Partial Derivatives



Oct. 23

Higher Derivatives II: Taylor Expansion



Oct. 24

Higher Derivatives III: Unconstrained Optimization
Homework 6 (Solution)


Oct. 25

Higher Derivatives IV: Constrained Optimization


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



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