Course Description
This is an honors version of Math 1410. 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. Like Math 1410, the course assumes familiarity with the material in Math 1300 and Math 1400. Math 1610 is followed by Math 2600, an honors version of Math 2400. 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 1610 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:

Foundations  theory and review (selections from volume I):
(a) real numbers, order completeness, complex numbers. Introduction, Part 3; Chapter 9.
(b) integration. Chapter 1.
(c) limits and continuity. Chapter 3.
(d) differentiation. Chapter 4.
(e) relation between integration and differentiation. Chapter 5 (first part).

Vector algebra. Volume I, Chapter 12.

Applications of vector algebra to analytic geometry. Volume I, Chapter 13.

Calculus of vectorvalued functions. Volume I, Chapter 14.

Calculus of scalar and vector fields. Volume II, Chapter 8.

Applications of differential calculus. Volume II, Chapter 9 (second half).

Line integrals. Volume II, Chapter 10.

Multiple integrals. Volume II, Chapter 11.

Surface integrals. Volume II, Chapter 12.
Home pages: including homework
Math 1610 Old Final Exams
 Fall 2009: Final Exam
 Fall 2008: Final Exam