This book strives to provide a concise introduction to computational engineering by introducing a wider range of numerical methods commonly used in computational modelling and scientific computing. These methods include finite difference methods, finite volume methods, finite element methods, virtual bee algorithms, and cellular automata. It also covers a wide spectrum of advanced topics in engineering applications, and these advanced topics include elasticity, heat conduction, reaction-diffusion system, optimisation, stochastic cellular automata, combustion, consolidation, heat transfer of carbon nanotubes, and pattern formation. The accompanied concise Matlab programs, no more than 100 lines each, demonstrate how each numerical method works. The animation and visualization of the results provide a first hand experience to the readers, especially for undergraduates and graduates, to master the fundamentals of the numerical methods. These Matlab programs can also be modified by the readers to carry out their own modelling and simulations. This book can serve as an introductory textbook and prepare the readers to learn more advanced topics in scientific computing.