Course Description
This is an honors version of Math 240. It will cover the material in greater depth than that course, with more challenging problems and more attention to definitions and to the reasons behind the results. The course assumes familiarity with the material in Math 116. The precise sequence of topics within each semester will differ somewhat between the Math 114240 sequence and the Math 116260 sequence; but over the course of the two semesters, the honors sequence will cover the usual material and more. Students who wish to take further mathematics courses beyond Math 116 and 260 will be prepared to take either of two sequences in analysis/advanced calculus (Math 360361 or Math 508509), and either of two sequences in abstract and linear algebra (Math 370371 or Math 502503).
Textbook:
Tom Apostol, Calculus, volumes I and II, second edition. On reserve at MPA library, DRL 3N1.
Topics covered:

Linear spaces. Volume II, Chapter 1 (= Volume I, Chapter 15).

Linear transformations and matrices. Volume II, Chapter 2 (= Volume I, Chapter 16).

Determinants. Volume II, Chapter 3.

Eigenvalues and eigenvectors. Volume II, Chapter 4.

Eigenvalues of operators on Euclidean spaces. Volume II, Chapter 5.

Introduction to dierential equations. Volume I, Chapter 8.

Linear dierential equations. Volume II, Chapter 6.

Systems of dierential equations. Volume II, Chapter 7.