Math 521 and 522 form our Advanced Calculus sequence. They are devoted to a rigorous development of calculus, in one variable for the first course, and in several variables, for the second course. The first set of notes form the basis for my Math 521 course.
Introduction to Analysis in One Variable
Here is some supplementary material for this One Variable text (extra exercises, etc.).
Supplementary Material for Math 521 Text
The following deals with multivariable analysis. I use this as a text for Math 522.
Introduction to Analysis in Several Variables
Here is some supplementary material for this Math 522 text (extra exercises, etc.).
Supplementary Material for Math 522 Text
Here is a more elementary text on multivariable calculus, designed for Math 233H.
These texts devote some space to computing various quantities using power series. Here are some complementary results on using power series efficiently to compute natural logarithms.
Calculating natural logarithms
Linear algebra is a useful tool in multivariable calculus. Here is an introduction to this subject. Linear Algebra
The following notes contain introductory material on differential equations. Further ODE notes can be found on the Math 524 web page and the Math 653 web page.
Due to the corona virus emergency, Math 521 was conducted online, March 23 — April 24, 2020. The following file includes worksheets for each class day in this interval. Each sheet covers what would in happier circumstances be one lecture. Each sheet is arranged as a set of 5 or 6 exercises. Students could cover each sheet on the assigned day, with text in hand, in order to do the exercises.
A somewhat similar situation has led me to provide worksheets for Math 522, in Spring 2023.
A deep subject like calculus deserves a deep philosophical underpinning. Here are the
Nine Gates to the Revelation of the Mysteries of Calculus