ME-642 Advanced Mathematics for Mechanical Engineering

ME-642 Advanced Mathematics for Mechanical Engineering 

Credit Hours = 3

COURSE CONTENT

Review of general Mathematical techniques in Mechanical Engineering, Partial Differential Equations and Fourier Methods: Applications of PDEs and boundary-value problems, Heat equation, Linearity and homogeneity, Separation of variables and Fourier series, Fourier transforms Sturm Liouville problems and special functions. Complex analysis, Differentiation and integration over a complex domain, wave equation. Airy’s function, equation of diffusion and Taylor series applications, similarity solutions. Perturbation Theory and Asymptotic Approximations:   Perturbation theory for algebraic equations, Regular perturbation theory, Asymptotic and uniformity, Stretched-time and two-time methods. Numerical Analysis: Numerical solution of non-linear equation through iteration, numerical integration and differentiation, Solution of linear systems, Gauss elimination, least square method, matrix eigen value problem.

RECOMMENDED BOOKS

1. Zill D.G, Wright W.S, Advanced Engineering Mathematics, 7thEdition, Jones & Bartlett, 2020
2. Erwin Kreyszig, Herbert Kreyszik, Advanced Engineering Mathematics, 10thedition, John Wiley and sons, 2019
3. Bender C.M and Steven A.O, Advanced Mathematical Methods for Scientist and Engineers: Asymptotic Methods & Perturbation theory, 1st Edition, Springer, 2010