421 - The Theory of Single Variable Calculus
Prerequisites:
Math 234 or cons inst. Open to Fr.
Frequency:
Fall (I), Spring (II)
Student Body:
Math majors and students who need a proof-based course on Calculus
Credits:
3. (N-A) Recent Texts:
Calculus, by M. Spivak
Course Coordinator:
Andreas Seeger Background and Goals:
This course covers material in first and second semester calculus but it is intended to teach math majors to write and understand proofs in mathematics in general and in calculus in particular. The course is designated as writing intensive course.
Alternatives:
The Honors Calculus Sequence Math 275-276. Students who took Math 275-276 cannot get credit for Math 421.
Subsequent Courses:
Math 521 and other upper level courses Course Content:
- Functions, sets and graphs
- Epsilon and delta definitions and proofs for limits
- Continuos functions and related theorems
- Differentiable functions. Proofs of the rules of differentiation and related theorems
- Chain Rule
- Inverse functions
- The Riemann integral. The Fundamental Theorem of Calculus.
- Taylor approximation
- Transcendental functions (optional).