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.
- Analysis of Functions of a Single Variable: A Detailed Development by Lawrence Baggett (http://spot.colorado.edu/~baggett/analysis.html)
- 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.
- A Guide to Real Variables by Steven Krantz (eaccess through UA library);
- Calculus by Michael Spivak: Will be put on reserve at Cameron library (together with solutions to all the exercises there).
- Differential & Integral Calculus by Richard Courant;
- Introduction to Real Analysis by William F. Trench (http://ramanujan.math.trinity.edu/wtrench/misc/index.shtml)
- Math131AH of UCLA by Terence Tao (http://www.math.ucla.edu/~tao/resource/general/131ah.1.03w/)
- Mathematical Analysis: A Straightforward Approach by K. G. Binmore.
- Practical Analysis in One Variable by Donald Estep.
- 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.
- 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.
- Counterexamples in Calculus by Sergiy Klymchuk (eaccess through UA library);
- Introduction to Mathematical Thinking by Keith Devlin on Coursera: https://www.coursera.org/course/maththink.
- 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.
- http://www.classicalrealanalysis.com: The free books here will cover every topic in undergraduate calculus/real analysis.