In a modern programming environment such as MATLAB® it is possible, through simple commands, to perform advanced calculations on a personal computer, To use this powerful tool, students do not need to understand algorithmic details, but they do need a familiarity with numerical methods and the properties of algorithms. This text, for an introductory course in scientific computation at an advanced undergraduate level, is a revision and translation of a Swedish work by Eldén and Wittmeyer-Koch. It offers an introduction to basic ideas in numerical analysis including classical algorithms for solutions of nonlinear equations and linear systems of algebraic equations as well as ordinary differential equations plus methods for error analysis, interpolation, integration and approximation. Moreover, the text covers important applications in science and engineering such as floating point computer arithmetic and standard functions, splines, finite elements and discrete cosine transform. The authors focus on simplicity and readability in order to help students prepare for more complex mathematical software; they also offer useful materials on their personal Web site homepages. Useful end of chapter questions on theory and computer exercises make this a valuable tool for students as well as professionals