Calculus of Several Real Variables

This course introduces the very important subject called the calculus of several real variables, which has important applications in science and engineering. The modern world would have been impossible without it. We introduce and discuss the subject in a non-traditional way taking the vector approach in most places. We start with the basics of Vectors, study continuity and partial derivatives, study multiple integrals and their applications and end with the stokes Theorem and Gauss divergence theorem.INTENDED AUDIENCE: Any Interested LearnersPREREQUISITES: Calculus of One Real Variable

Week 1: Vectors and MatricesWeek 2: Functions of several variables and partial derivativesWeek 3: IFT, Taylor’s Theorem, Maxima and MinimaWeek 4: Lagrange Multiplier RuleWeek 5: Multiple IntegralsWeek 6: Line IntegralsWeek 7: Surface IntegralsWeek 8: Green’s Theorem Strokes Theorem and Gauss Divergence Theorem