Course Description

This course could be called Generalizations of Fundamental Theorem of Calculus. We will define integration over surfaces and curves and we will relate those integrals in a fashion similar to the Fundamental Theorem of Calculus. The whole material has been developed for direct applications in physics and engineering.

Prerequisites

  • Definition of Riemann integral.
  • Some techniques of integration and differentiation.
  • Polar coordinates.
  • Curves, tangent (velocity) vectors to curves.
  • Partial derivatives.
  • Linear maps and their matrices.
  • Using determinants for computing area/volume of parallelopipeds.
  • Using determinants of matrices of linear maps for computing the area of the image of a region under that linear map.

Text:

Calculus Early Transcendentals, by C. Henry Edwards and David E. Penney
The text is required and is available at the bookstore. We will cover material from chapters 13, 14 and some review from chapter 11.

Grades:    

Grades will be based on the following components:
  • Homeworks: 16%
  • Two midterms: 22% each
  • Final Exam: 40%