Focus of the course is on the state-of-the-art computational modeling techniques used in disciplines such as structural mechanics, fluid mechanics, heat transfer and electromagnetics. Emphasis is on the numerical solution methods of partial differential equations and their use in computational analysis and simulations for engineering design. There will be a number of case studies and examples to enhance the lectures with examples. Topics covered are: basic numerical methods for root-finding, solution of linear system of equations and ordinary-differential equations, finite-difference solution of parabolic, elliptic and hyperbolic partial- differential equations and finite-element solution of elliptic PDEs such as Poisson equation in 1D.