Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 421: The Theory of Single Variable Calculus

Student Body: 

Math majors and students who need a proof-based course on Calculus

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.


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).
3. (N-A)
MATH 234 or graduate or professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, WI  53706

(608) 263-3054

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