Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 221: Calculus and Analytic Geometry I

Student Body: 

Students preparing for major study in mathematics, the physical sciences, computer sciences, or engineering. Some biological sciences and economics programs require Math 221-222.


Background and Goals: 

This course covers differential and integral calculus, plane analytic geometry, applications; transcendental functions,etc. The Math 221-222 sequence is the first two semesters of the standard three-semester calculus sequence, completed with 234, which is normally required for all higher level math courses and should be taken by those preparing for major study in mathematics, the physical sciences, computer sciences, or engineering. It is also recommended for students in the social and life sciences who may want a more substantial introduction to calculus than is offered in the Math 211-213 sequence.


Math 114 and Math 221 are equivalent to Math 171 and Math 217.

Subsequent Courses: 

Math 222.

Course Content: 
  • Coordinates, lines, circles
  • Functions and graphing, trig functions
  • Limits, intuitively and with an idea of how they can be formalized, including limits at infinity and infinite limits, trig limits
  • Derivatives, Chain rule, Leibniz notation, higher order derivatives, implicit differentiation, related rates, approximations
  • Applications of the derivative
  • Antiderivatives, indefinite integrals and introduction to differential equations
  • Sums, areas and the definite integral. Fundamental Theorem of Calculus.
  • Integration by substitution, applications of the integral: areas and volumes.
  • Transcendental functions, limits involving logs, exp and powers. Optional: Hyperbolics functions.
5. (L&S credit type: C, r)
MATH 114 or (MATH 112 and 113) or placement into MATH 221 . MATH 211 or MATH 213 does not fulfill the requisite.

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

(608) 263-3054

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