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.


  • 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.


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

Students with Documented Disabilities    

Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is made. Students should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066, URL: