| Course ID: | MATH 2400H. 4 hours. |
| Course Title: | Differential Calculus with Theory (Honors) |
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. |
| Oasis Title: | Differ Calc Theory Hon |
| Duplicate Credit: | 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. |