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Advanced Calculus

Debra J. Woods
Organization: University of Illinois at Urbana-Champaign
Department: Department of Mathematics
Education level


The courseware is in the form of an interactive/electronic textbook. Students will have to purchase a copy of Mathematica to take the course.

This is an introductory study of vector calculus and functions of several variables.

Calculus&Mathematica is a complete, modern calculus course developed recently at the University of Illinois and Ohio State University. The course, which is based on an interactive electronic text written as a series of Mathematica notebooks, fully integrates the numeric, symbolic and graphic capabilities of Mathematica as tools to explore calculus concepts, methods and applications. As such, it differs markedly in content emphasis and organizational style as well as in its underlying pedagogy from "traditional" calculus courses. Calculus&Mathematica (C&M) is a college-level course that is taught at a number of universities and high schools throughout the country.

NetMath courses have been taught at a distance from the University of Illinois Campus for the past 6 years.

Students are each assigned a mentor to help them through the course, answer questions, and grade their homework assignment.

Topics include:
  • Directional derivatives
  • Jacobians
  • Change of variables in multiple integrals
  • Maxima and minima
  • Line and surface integrals
  • Theorems of Gauss, Green, and Stokes
  • Infinite series
  • Uniform convergence

*Mathematics > Calculus and Analysis > Calculus