Engineering analysis involves the application of scientific analytic principles and processes to reveal the properties and state of the system, device or mechanism under study. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. This text introduces numerical methods that an engineer should know and shows how to develop, analyze, and use them. Complete MATLAB programs for most of the worked examples are introduced in this book. This thorough and practical book is primarily intended for new graduate students in engineering and physical science. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods. We derive basic algorithms in root finding, matrix algebra, integration and interpolation, ordinary and partial differential equations. We assume students are already familiar with the basics of matrix algebra, differential equations, and vector calculus. Students should have already studied a programming language, and be willing to learn MATLAB.