We will approach this subject in a novel way, by looking at the subject both physically and historically. We will begin with Newton and the early problem of planetary motion and possibly end with Einstein. At the same time we will look at the mathematical structure underlying the applications of calculus. You are expected to be familiar with the calculus you have seen in MAT 161, 162 and 261, though we will spend some time reviewing and going deeper into the theory and applications from the latter course.

Learning Outcomes

After successfully completing the course, students should

• state and apply key theorems, prove special cases of each theorem, and prove some of the lemmas used in their proofs (e.g., Chain Rule, Taylor's Theorem, Implicit Function Theorem, Fubini's Theorem, Green's, Gauss' and Stokes' Theorems);

• further the basic knowledge in the analysis of functions of several variables (partial derivatives, total differential, local extremes, integration in two and three dimensions);

• develop ability to solve problems, working in groups;

• be able to compute line and surface integrals of vector functions using differential forms;

• have greater appreciation of the place of calculus in mathematics and related sciences.

Group Work: Some of the problems appear in groups and the computations can become tedious. Therefore, to relieve you of some of this, you will be assigned a group project. This will involve using the computing facilities. This will count 10% of your grade.

Exams and Grades: Exams and Grades: There will be a two regular exams and a final exam. The exams will cover the basic material up to the date of the exam. The tentative dates for the exams are below.

Your final grade will be based on the following:

More information will be posted on the web related to the topics we are studying. Links can be found with summaries to the material, study suggestions, homework assignments, etc. These will be accessible through the instructor's homepage at