Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 213: Calculus and Introduction to Differential Equations

Student Body: 

Students in social sciences and finance.  Mainly they are students looking to *leave* their program in the business school.  It has been a long time since many have taken a mathematics course.

Background and Goals: 

This course is a sequel to Math 2ll for students, primarily in social sciences and finance, who need to develop more techniques than are covered in Math 211. Math 211 is also suitable preparation for Math 213. Students in Math 213 whose calculus background is not very recent will need to review and work problems in elementary calculus. Some class time is assigned for this, but students should be prepared to put considerable effort into review. A unique characteristic of this course, along with Math 211, is the lack of trigonometry. Apparently, this is due to a request by the business school.


Students in the physical sciences or who will eventually wish to take higher level mathematics courses should *NOT* take this course, but should go through the sequence 221-222-234.

Subsequent Courses: 

None. Students wishing to take subsequent courses should not take this course.

Course Content: 
  • Review of techniques of single-variable calculus: Functions, graphs, definition of derivative, rules for calculating derivatives, exponential and logarithmic functions, maximum - minimum problems, indefinite and definite integrals, the fundamental theorem of calculus, techniques of integration.
  • Some business applications of single-variable calculus: Optimization problems, supply and demand, elasticity of demand, consumers' surplus.
  • Multivariable calculus: Functions of two variables, limits, partial derivatives, local linearity and the chain rule, implicit differentiation, maximum - minimum problems and business applications, constrained maximum - minimum problems and business applications.
  • Taylor approximation: Taylor polynomials, the mean value theorem, Taylor's theorem with remainder, Taylor series and representation of functions by power series.
  • First-order differential equations: Exponential growth and decay, separable equations, linear differential equations, qualitative properties, applications in economics and business.
  • A bit of probability.
3. Students may not receive full degree credit for both Math 222 and 213 or both Math 234 and 213. (r-N-I)
Math 211 or 221. Closed to students with credit for Math 222, 223, or 234

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

(608) 263-3054

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