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A First Course in Numerical Methodsis aimed at undergraduate and postgraduate students of all engineering disciplines and the students of mathematics and other science disciplines, to enable them to gain practical knowledge of modern techniques in scientific computing. Avoiding encyclopedic and heavily theoretical exposition, the book provides an in-depth treatment of fundamental issues and methods, the reasons behind the success and failure of numerical software, and fresh and easy-to-follow approaches and techniques. Focuses on current methods, issues, and software while providing a comprehensive theoretical foundation, enabling those who need to apply the techniques to successfully design solutions to nonstandard problems. Illustrates algorithms using the programming environment of MATLAB, with the expectation that the reader will gradually become proficient in it while learning the material covered in the book. Provides a variety of exercises within each chapter and review questions aimed at self-testing. The book takes an algorithmic approach, focusing on techniques that have a high level of applicability to engineering, computer science, and applied mathematics. Table of Contents List of Figures List of Tables Preface 1. Numerical Algorithms 2. Roundoff Errors 3. Nonlinear Equations in One Variable 4. Linear Algebra Background 5. Linear Systems: Direct Methods 6. Linear Least Squares Problems 7. Linear Systems: Iterative Methods 8. Eigenvalues and Singular Values 9. Nonlinear Systems and Optimization 10. Polynomial Interpolation 11. Piecewise Polynomial Interpolation 12. Best Approximation 13. Fourier Transform 14. Numerical Differentiation 15. Numerical Integration 16. Differential Equations Bibliography Index