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 1410-2400 sequence and the Math 1610-2600 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 3600-3610 or Math 5080-5090), and either of two sequences in abstract and linear algebra (Math 3700-3710 or Math 5020-5030).

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 vector-valued 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

• Fall 2008
• Fall 2009

Math 1610 Old Final Exams

• Fall 2009: Final Exam
• Fall 2008: Final Exam