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Advanced Calculus: Course Outline (MAT 401)

Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis.

Course Outline

  • Algebraic and order properties of R, the completeness property, cluster points, open and closed sets in R
  • Sequences, the limit of a function, limit theorems 
  • Boundedness theorem, maximum-minimum theorem and the intermediate value theorem; uniform continuity 
  • The mean value theorem
  • Taylor’s theorem, Limit and continuity of functions of two and three variables
  • Partial derivatives 
  • Differentiable functions, regions in the x-y plane, iterated integrals, double integrals, change in the order of integration, transformation of double integrals 
  • Jordan curve, regular region, line integral
  • Green’s theorem, independence of the path, surface integrals 
  • Gauss theorem. 

Text Books

Reference Books

Other Books (Full Text)