Engineering Mathematics II

Differential equations of first order, separable equations. Linear differential equations of higher order, homogeneous and nonhomogeneous equations. Numerical solutions of differential equations. Runge-Kutta method, boundary-value problems. Differential calculus of functions of several variables, Taylor series approximation. Jacobians, maxima and minima of a function, Method of Lagrange multipliers. Functions of a complex variable, differential complex calculus. Complex integration, Cauchy's theorem. Complex series, Taylor and Laurent series. Residue theorem.