This textbook is intended for graduate and undergraduate students interested in engineering computation and programming using MATLAB. The purpose of this textbook is to strengthen the reader's mathematical foundation and application capability, so that the reader can master the basic concepts and methods of engineering computations, and improve the ability to use computer-aided tools for mathematical modeling and numerical analysis of engineering problems. After an introduction in the first chapter, this textbook provides a detailed introduction to basic matrix analysis, MATLAB syntax and programming techniques in the second to fourth chapters. Then, in the fifth to eighth chapters, some upgraded contents are presented about the application of engineering computations based on MATLAB programming, including advanced operations of matrix analysis, data visualization, interpolation and curve fitting, optimization algorithms and engineering application etc. Particularly, the optimization has been emphasized from basic linear programming, single-variable minimization, multi-variable optimization, unconstrained and constrained optimization, multi-objective optimization, as well as basic concept and codes on topology optimization in engineering. At the same time, this textbook also provides plenty of application examples from engineering, which will be greatly attractive to readers.