Course Description: | This course covers vectors, differential calculus of curves in R3 and surfaces, Taylor series for functions of two variables, critical points, local maxima and minima, Lagrange multipliers, integral calculus for functions of several variables using various co-ordinate systems, conservative vector fields and line integrals, Green's Theorem in the plane, divergence and curl, surface integrals, Stokes' Theorem, and Gauss' divergence Theorem. Students analyze complex numbers, simple mapping problems, differentiation theory for complex functions, Cauchy Riemann equations, analytic functions, the elementary functions, Integration Theory for complex functions, Cauchy's Theorem and the Cauchy integral formulae, Taylor series and Laurent Series, residues, and evaluate real integrals and trigonometric integrals using residues. |