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.
- 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.