Next: The Contrapositive and the Divergence Test
Textbooks
In the lists below, items are arranged in alphabetical order by author last name.
Most calculus textbooks cover everything on infinite series that is in the ISM. As of 2011, the calculus textbooks used at UBC that cover infinite series are
- Adams, R, and Essex, C. Calculus, A Complete Course. Pearson 2011.
- Briggs, B, and Cochran, L. Calculus, Early Transcendentals. Pearson, 2010.
- Stewart, J. Calculus, Early Transcendentals. Thomson Brooks/Cole, 2011.
Students learning infinite series may wish to refer to one of these texts to help their learning.
Open Textbooks from the Web
When this module was developed, most of the open textbooks that were found on the web did not cover enough of the content on the IST or did so at a level that was more advanced than what was needed. However, Calculus by Gilbert Strang may be of use to students.
- Strang, Gilbert. Calculus, MIT OpenCourseWare. The first year calculus textbook, Calculus, freely available on the MIT OpenCourseWare website may be of interest for students looking for additional instruction and/or exercises to work on. Chapter 10 of Calculus covers most of the concepts that are in the ISM, but not infinite sequences. Answers (but not complete solutions) to odd-numbered problems are available.
- Download Chapter 10 of Calculus (PDF, 2.1 MB)
- Download Solutions to All Odd-Numbered Problems in Calculus (2.5 PDF)
Calculus is under a Creative Commons (CC BY-NC-SA 3.0) license.
Course Notes from the Web
Dawkins, Paul, Calculus II.
A chapter on sequences and series of Dawkins' Calculus II notes provides exercises, additional examples and instruction on infinite sequences and series. The notes cover areas that are not ISM, including the formal definition of limit, the root test, and the binomial series.
- Download Infinite Sequences and Series from Paul's Online Math Notes (PDF, 1.0 MB, used with permission)
- View the online version of the Sequences and Series Chapter
Ikenaga, Bruce, Notes on Calculus
These course notes are also relatively brief and cover the formal definition of a limit which students are not expected to know. But the notes otherwise contain examples that students may find helpful.
- Download Notes on Calculus from Bruce Ikenaga's website (PDF, 1.0 MB, used with permission)
- Visit Bruce Ikenaga's Bruce's Notes on Calculus website
UBC Math 101 Course Notes
These online notes are no longer being maintained, but contain lessons on Taylor Polynomials and infinite series that are very readable. There are no additional exercises, but students may find the additional examples helpful.
Other Open Textbooks
The UBC Mathematics Department can't maintain an exhaustive database of all the available resources on infinite sequences and series that can be found on the internet. But those who discover or are aware of useful other sources that they would recommend are encouraged to contact the lead developer of the ISM, Greg Mayer, who can see about adding additional resources to the ISM.
Next: The Contrapositive and the Divergence Test
