Calculus Iii

AY2018/2019 Semester 1

Calculus III is a core Mathematics course that extends concepts and techniques developed in Calculus I and Calculus II to the case of functions of several real variables. In other words, we try to do the same things as in Calculus I and II, but in higher dimensions. In this course, we shall discuss the notions of limits, continuity, derivatives and integrals of real-valued and vector-valued functions of many variables. Most of the time, extending these familiar notions from one to several variables requires some degree of ingenuity, and we are going to have to spice up the material from Calculus I and II with a little bit of geometry and linear algebra. Techniques learned in Calculus III are essential for financial analysts, engineers, and for further study in mathematics. Content Parametric equations, polar coordinates. Vector-valued functions, calculus of vector-valued functions. Functions of more than one variable, limits, continuity, partial derivatives, differentiability and total differential, chain rule, directional derivatives, gradients, Lagrange multipliers. Double integrals, area of a surface, triple integrals. Line integrals, Green's Theorem, surface integrals, Gauss' divergence theorem, Stokes' Theorem.