This is an honors version of Math 114. 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 114, the course assumes familiarity with the material in Math 103 and Math 104. Math 116 is followed by Math 260, an honors version of Math 240. The precise sequence of topics within each semester will differ somewhat between the Math 114-240 sequence and the Math 116-260 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 360-361 or Math 508-509), and either of two sequences in abstract and linear algebra (Math 370-371 or Math 502-503).
Tom Apostol, Calculus, volumes I and II, second edition. On reserve at MPA library, DRL 3N1.
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.
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