gradient, divergence and curl of a vector point function and related identities;

evaluation of line, surface and volume integrals using Gauss, Stokes and Green's theorems and their verification;

analytic functions and complex integration;

Fourier series, integral, and transform;

PDE in heat, wave, and Laplace equations.

compute vector differential calculus (knowing the physical meaning of gradient, divergence, and curl operators);

compute vector integral calculus (knowing divergence theorem and Stoke's theorem);

represent complex numbers algebraically and geometrically;

apply the concept and consequences of analyticity and the Cauchy-Riemann equations and of results on harmonic and entire functions including the fundamental theorem of algebra;

evaluate complex contour integrals directly and by the fundamental theorem, apply the Cauchy integral theorem in its various versions, and the Cauchy integral formula;

represent functions as Taylor, power and Laurent series, classify singularities and poles, find residues and evaluate complex integrals using the residue theorem;

understand how partial differential equations arise in the mathematical description of heat flow and vibration;

demonstrate the ability to solve initial boundary value problems;

express and explain the physical interpretations of common forms of PDEs;

be acquainted with applications of partial differential equations in various disciplines of study.

P. V. O'Neil, Advanced Engineering Mathematics, CENGAGE Learning, 8th Ed, 2018.

Dennis G. Zill, Advanced Engineering Mathematics, Jones & Bartlett Learning, 7th Ed, 2017.