Math 421 - The Theory of Single Variable Calculus

• Prerequisites: Math 234 or consent of instructor. A student cannot enroll in Math 421 if he or she took the Honors Calculus sequence
• 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 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. A student cannot get credit for Math 421 if they took Math 275-276.
• Alternatives: N/A
• Subsequent Courses: Math 521 and other upper level courses

Content coverage:

• 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.
• Transcendental functions (optional.)
• Taylor approximation (optional.)
• Uniform convergence and power series (optional.)
• Implicit function theorem in two variables (optional.)