Course Description
This is an honors version of Math 2400. 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 1610. The precise sequence of topics within each semester will differ somewhat between the Math 14102400 sequence and the Math 16102600 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 1160 and 2600 will be prepared to take either of two sequences in analysis/advanced calculus (Math 36003610 or Math 50805090), and either of two sequences in abstract and linear algebra (Math 37003710 or Math 50205030).
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.