Office hours: Wednesdays 10:10 am - 12 pm in Pierce 2416 or by appointment

Email: mouille@math.ucr.edu

Homework and midterm solutions:

• Chapter 5

• Chapter 6

• Chapter 8

• Midterm

Useful links:

• All the Mathematics You Missed: But Need to Know for Graduate School - This is good resource for helping organize all the math you've learned in your head and for pointing attention to the topics where your background is lacking. It won't help you learn what you didn't know already, but it will help you figure out what you should read about before going to graduate school to study mathematics.

• Terrence Tao: Problem solving strategies in analysis - Some of the tips are meant for a graduate-level course in real analysis, but a lot of it is useful for studying advanced calculus.

• Examples illustrating concepts from the course:

  • Weierstrass's function - It's continuous everywhere but differentiable nowhere.

  • Volterra's function - It's differentiable everywhere, its derivative is bounded everywhere, but it isn't integrable.

  • Discontinuous derivatives - See the answer by Mark McClure for three great examples where derivatives exist everywhere but are discontinuous at certain points.

• LaTeX - a high-quality mathematical and scientific typesetting system

  • Wikibooks LaTeX/Math - the resource for LaTeX that I find most useful

  • LaTeX symbol list - a more extensive resource

• GeoGebra - A great tool for creating graphs and other math illustrations (I used it to make the image at the top of the page). There are even options to embed your pictures into TeX documents. Download it for your computer or mobile devices, or use the in-browser version.