Using MATLAB throughout, this textbook presents a clear, solid introduction to the theory and application of computational methods for the practical use in everyday computing. It prepares graduate students taking doctoral examinations on numerical analysis and provides a solid foundation in numerical analysis for more specialized topics, such as finite element theory and advanced numerical linear algebra. The text features interval computing in numerical analysis, including coverage of interval arithmetic, interval computation, and interval algorithms. It also includes many analytical and computational exercises to illustrate how the theory and methods can be best applied.