## Math 118 Winter 2015

 Instructor / Office / Phone # Xinwei Yu / 527 CAB / (780)4925731 Email ;  Webpage xinwei2@ualberta.ca ;  http://www.math.ualberta.ca/~xinweiyu Location / Time SAB 326 MWF 10a - 10:50a; AF 1 13 R 1p - 1:50p Office Hours M 11-12:30, W 13 - 14:30, R 11 - 12; Or by appointment

Last Updated: Mar. 29, 2015 (HW1 - 8 & Mid1, Mid2)

Important Dates:
• Midterms (Temporary): Fridays in class. Feb. 6, Mar. 13.
• Final Exam (Temporary, check beartracks for final date/time/location): TBA.
• Deferred Exam: Saturday May 2, 2015 @ TBA. You need to register at 8:30am.

Course Material

 Week Dates Lecture Notes/Review Problems/Midterms Assigned Readings in textbooks HC: Dr. Bowman's book Homeworks 1 1/5 - 9 Lecture 1: Indefinite integral; Lecture 2: Simple calculations; Lecture 3: Integration by substitution (change of variables) Lecture 4: Integration by substitution II. HC: 7.A Homework 1 (Due Jan. 15 3p) Solutions 2 1/12 - 16 Lecture 5: Integration by substitution III. Lecture 6: Integration by parts; Lecture 7: Integration by parts II; Lecture 8: The method of partial fractions; HC: 7.B - D Homework 2 (Due Jan. 22 3p) Solutions 3 1/19 - 23 Lecture 9: The method of partial fractions II; Lecture 10: Hermite's method; Partial fractions in counting; Lecture 11: Integration of trig functions; Lecture 12: Integration of functions involving roots; HC: 7.E - G Homework 3(Due Jan. 29 3p) Solutions 4 1/26 - 30 Lecture 13: The theorems of Chebyshev and Liouville; Lecture 14: Integration by substitution and by parts for definite integrals; Lecture 15: Evaluation of definite integrals: Examples; Lecture 16: Evaluation of definite integrals: Tricks; Homework 4 (Due Feb. 5 3p) Solutions 5 2/2 - 6 Review Problems for Midterm 1Lecture 17: Review for Midterm; Lecture 18: More Review for Midterm; Lecture 19: Yet Another Review for Midterm; Midterm 1 Midterm 1 Solutions 6 2/9 - 13 Improper Integrals: Definition; Improper Integrals: Properties; Improper Integrals: Properties cont; Improper Integrals: Tests and Applications. Homework 5 Solutions 7 2/23 - 27 Infinite Series of Functions; Uniform Convergence I; Uniform Convergence II; Continuity, Integrability, and Differentiability; For more on this topic, please check out lecture notes of weeks 1--4 of Math 317 Winter 2014 here. Homework 6 Solutions 8 3/2 - 6 Power Series; Examples of Power Series; An Example of Trigonometric Series; Nowhere Differentiable Functions; Homework 7 Solutions 9 3/9 - 13 Review Problems for Midterm 2 Review for Midterm 2 I: Improper integration; Review for Midterm 2 II: Series of functions; Review for Midterm 2 III. Midterm 2 Midterm 2 Solutions 10 3/16 - 20 Optimization: Theory Optimization: Theory & Examples More Examples Convex and Concave Functions HC: 4.B, 4.D, 4.E, 4.H Homework 8 Solutions 11 3/23 - 27 Arc Length of Curves Area of Plane Regions Volume Surface Area HC: Chapter 8. 12 3/30 - 4/2 Calculus and Prime Numbers Calculus and Irrationality Hilbert's 3rd Problem 13 4/8 - 4/10 Review for Final I: Optimization & Convexity Review for Final II: Curves, Area, Volume Review for Final III: Cont and Q&A Review Problems for Final

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.