Math 117 Fall 2014


Instructor / Office / Phone # Xinwei Yu / 527 CAB / (780)4925731
Email ;  Webpage xinwei2@ualberta.ca ;  http://www.math.ualberta.ca/~xinweiyu
Location / Time  SAB 331 MWF 10a - 10:50a; AF 1 13 R 1p - 1:50p
Office Hours M 11-12, W 13 - 14:45, R 10:30 - 12, F 11 - 12; Or by appointment


Your Position in Class

Last Updated: Dec. 1, 2014 (Homework 9 included)

To calculate your term mark: Add up your best 7 homework marks, divide by 4; Average your best 2 midterms;

Add the two numbers up and round. 

Important Dates:
Course Syllabus

Course Material

Week
 Dates
 Lecture Notes/Review Problems/Midterms Assigned Readings in
textbooks
HC: Dr. Bowman's book
314: 314 Notes
 Homeworks
1
 9/3-5
 Introduction; Number Theory;
Integers and Rationals
Homework 1 (Solutions)
2
 9/8-12
 Sqrt(2); e; Pi; Sup and Inf
 HC 1.B, 1.H, 1.I, 1.J
Optional: HC 1.C;
Homework 2 (Solutions)
3
 9/15-19
 Sets; Sets (cont.); Functions; Functions (cont.)
Midterm 1 Review Problems (Updated Dec. 9)
 314: Sets & Functions 1, 2.1, 3 ("Open & Close Sets" is optional; 3.4 is optional)
HC: 1.A, 1.G, 3.A, 3.B
4
 9/22-26
 Proof; Induction and Binomial Theorem; Logic
Midterm 1 (Solutions)
 314: Proof & Logic
HC: 1.E, 1.F
 Homework 3 (Solutions)
5
 9/29 - 10/3
 Definitions of Limits for Sequences;
Cont.
Definitions of Limits for Functions;
Limits for Functions not Defined on all of R
 HC: 2.A, 2.B, 3.C,
Homework 4 (Solutions)
6
 10/6 - 10
 Comparison; Operations;
Operations cont.;
Cauchy & Squeeze;
Relations between function and sequence limits; Left/right limits
 314: Limit & Continuity 3.
HC: 2.E, 3.D
 Homework 5 (Solutions)
7
 10/15 - 17
 Accumulation Points;
Limsup and Liminf;
Cont.;
Midterm 2 Review Problems
(Updated Dec. 9)
 It's time to read through 314: Limit & Continuity and HC Sections 2 & 3 (except the continuity parts).

8
 10/20 - 24
 Definition of infinite series;
Review Problems;
More Review Problems;
Midterm 2 (Solutions)
Homework 6 (Solutions)
9
 10/27 - 31
 Continuity;
More on continuity;
Intermediate Value;
Max/Min;
 HC: 3.E -- 3.G.
314: Limit & Continuity Sections 5, 6. 		Homework 7 (Solutions)
10
 11/3 - 7
 Differentiation;
More on Differentiation;
Still More on Differentiation;
Max/Min; MVT
 HC: 4.A -- 4.D, 4.F, 4.I, 4.J;
314: Differentiation Sections 1 -- 3.
Homework 8 (Solutions)
11
 11/12 - 14
 Riemann Integration: Definitions;
Riemann Integration: Properties;
Fundamental Theorems of Calculus
Midterm 3 Review Problems
(Updated Nov. 19)
 HC: 5.A -- 5.E;
314: Integration.
12
 11/17 - 21
 L'Hospital;
Higher Derivatives;
Review, Q&A.
Midterm 3 (Solutions)
 HC: 4.F;
314: Differentiation 3.2, 3.3, 4.1. 		Homework 9 (Solutions)
13
 11/24 - 28
 Taylor Expansion;
Taylor Expansion (cont.);
Taylor Expansion (Appications);
Power Series;
 HC: 4.G;
314: Differentiation 4.2.
14
 12/1 - 3
 Final Review 1: Integration
Final Review 2: Other Stuff
Final Review Problems
(Updated Dec. 9)


Possible Reference Books and Courses
The following books are around the level of 117-118 (could be slightly higher or lower).
The list will be constantly updated.
If you find some book that is really helpful, please let me know so everyone (in this class or in future classes) could benefit.
You are also welcome to review/rate these books!

Note: The correct way of using this list is to pick a book and work through it.

Calculus Texts: The following are calculus textbooks.
  1. Analysis of Functions of a Single Variable: A Detailed Development by Lawrence Baggett (http://spot.colorado.edu/~baggett/analysis.html)
  2. Applied Mathematics: Body and Soul by K. Eriksson, D. Estep and C. Johnson. The whole Volumes 1 - 3 cover 117 - 317. 117 - 118 is roughly Volume 1 and part of Volume 2.
  3. A Guide to Real Variables by Steven Krantz (eaccess through UA library);
  4. Calculus by Michael Spivak: Will be put on reserve at Cameron library (together with solutions to all the exercises there).
  5. Differential & Integral Calculus by Richard Courant;
  6. Introduction to Real Analysis by William F. Trench (http://ramanujan.math.trinity.edu/wtrench/misc/index.shtml)
  7. Math131AH of UCLA by Terence Tao (http://www.math.ucla.edu/~tao/resource/general/131ah.1.03w/)
  8. Mathematical Analysis: A Straightforward Approach by K. G. Binmore.
  9. Practical Analysis in One Variable by Donald Estep. 
  10. Principles of Mathematical Analysis by Walter Rudin. This book is at a slighly higher level.
Books and web courses that could be helpful: The following books are kind of "complementary" to 117.
  1. Calculus: Single Variable by Robert Ghrist of UPenn: https://www.coursera.org/course/calcsing. Note that although this is a calculus course around the same level as 117, the emphasis is quite different. Therefore though it will definitely help you understand calculus, it may or may not help you directly regarding exams.
  2. Counterexamples in Calculus by Sergiy Klymchuk (eaccess through UA library); 
  3. Introduction to Mathematical Thinking by Keith Devlin on Coursera: https://www.coursera.org/course/maththink.
  4. The Calculus: A Genetic Approach by Otto Toeplitz. This is also a calculus textbook, but with a emphasis on how concepts reach their current forms through history.
Further readings: If you are interested in calculus/analysis.
  1. http://www.classicalrealanalysis.com: The free books here will cover every topic in undergraduate calculus/real analysis.