Course Description
A more rigorous and extensive treatment of differential calculus. Topics include the real numbers, the least upper bound property, limits, continuity, differentiability, and applications. Students with a strong background and interest in mathematics are encouraged to take this course; prior experience with calculus is not required.
Athena Title
Differ Calc Theory Hon
Equivalent Courses
Not open to students with credit in MATH 2400
Prerequisite
Permission of Honors
Semester Course Offered
Not offered on a regular basis.
Grading System
A - F (Traditional)
Course Objectives
In addition to learning the customary computational skills in calculus, the student will be exposed to mathematics as mathematicians view it. Students will learn to write proofs and think more rigorously about mathematics, and will come to grips with challenging concepts and problems. In that regard, this course is an excellent preparation for students considering a career in law, medicine, or the sciences.
Topical Outline
1. Numbers, inequalities, rigorous review of algebra, and proofs by induction. 2. Functions and their graphs. 3. Limits, including delta-epsilon definition and many concrete examples. 4. Continuity and the three hard theorems. 5. Differentiation: the rules and applications to related rates problems and maximum/minimum problems. 6. The theory of differentiation: local and global behavior, Mean Value Theorem, Cauchy Mean Value Theorem and L'Hopital's Rule; the second derivative and convexity; curve sketching. 7. Inverse functions; review of inverse trigonometric functions. 8. Brief introduction to antidifferentiation.
General Education Core
CORE I: FoundationSyllabus