The Textbook

This book for this course is the second volume of Calculus: Dynamic Mathematics. This course, along with the previous course, Magnet Calculus I, comprise what is traditionally considered the undergraduate calculus course sequence in most colleges and universities (probably called “Calculus I, II, and III”).

The main feature of the book is that no idea is presented without some motivation for that idea, either through an example or an application. In other words, students discover the reasons why calculus describes what it does. 

The begins with some of the remaining BC topics (vectors, polar, parametric equations) before moving into an introduction to linear algebra. Linear algebra gets a superficial treatment in most calculus books, but it is unique and interesting in its own right, and that is reflected in this book. The linear algebra chapter takes students from three-dimensional vectors to determinants to eigenvalues to orthogonal matrices.

The next two chapters comprise the traditional multivariable topics of partial differentiation, multiple integrals, line integrals, and surface integrals. Applications are introduced, as well as theory. The next chapter is on the convergence of infinite series, and the final chapter is a short chapter on techniques for solving differential equations.

The 2011-2012 school year was the first year of implementation for this course, although I taught Multivariable Calculus for four years prior.

The Syllabus

The syllabus corresponds to chapters and section in the textbook.
“Calculus: Dynamic Mathematics Volume Two” Second edition

444 pp., with answers to problems and an index. Hardcover: $39.95 
PDF: $23.95