'Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. NUMERICAL MATHEMATICS AND COMPUTING, 7E, also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors.
' More Accessible: Computer codes and other material are now included on the text websitegiving you and your students easy access without tedious typing. Matlab, Mathematica, and Maple computer codes and the ¿Overview of Mathematical Software appendix are all now available online. Visual Learning: Because concrete codes and visual aids are helpful to every reader, the authors have added even more figures and numerical examples throughout the textensuring students gain solid understanding before advancing to new topics. Comprehensive, Current and Cutting Edge: Completely updated, the new edition includes new sections and material on such topics as the modified false position method, the conjugate gradient method, Simpsons method, and more. Hands-On Applications: Giving students myriad opportunities to put chapter concepts into real practice, additional exercises involving applications are presented throughout. References: Citation to recent references reflects the latest developments from the field. Appendices: Reorganized and revamped, new appendices offer a wealth of supplemental material, including advice on good programming practices, coverage of numbers in different bases, details on IEEE floating-point arithmetic, and discussions of linear algebra concepts and notation. UPDATED! The Solving Systems of Linear Equations chapter has been moved earlier in the text to provide more clarity throughout the text. NEW! Exercises, computer exercises, and application exercises have been added to the text. NEW! A section of Fourier Series and Fast Fourier Transforms has been added. The first two chapters in the previous edition on Mathematical Preliminaries, Taylor Series, Oating-Point Representation, and Errors have been combined into a single introductory chapter to allow instructors and students to move quickly. Some sections and material have been re-moved from the new edition such as the introductory section on numerical integration. Some material and many bibliographical items have been moved from the textbook to the website. The two chapters, in the previous edition, on Ordinary Differential Equations have been combined into one chapter. Many of the pseudocodes from the text have been programmed in MATLAB, Mathematica, and Maple and appear in the website so that they are easily accessible. More figures and numerical examples have been added.
'1. INTRODUCTION. Preliminary Remarks. Review of Taylor Series. 2. FLOATING-POINT REPRESENTATION AND ERRORS. Floating-Point Representation. Loss of Significance. 3. LOCATING ROOTS OF EQUATIONS. Bisection Method. Newton's Method. Secant Method. 4. INTERPOLATION AND NUMERICAL DIFFERENTIATION. Polynomial Interpolation. Errors in Polynomial Interpolation. Estimating Derivatives and Richardson Extrapolation. 5. NUMERICAL INTEGRATION. Lower and Upper Sums. Trapezoid Rule. Romberg Algorithm. 6. ADDITIONAL TOPICS ON NUMERICAL INTEGRATION. Simpson's Rule and Adaptive Simpson's Rule. Gaussian Quadrature Formulas. 7. SYSTEMS OF LINEAR EQUATIONS. Naive Gaussian Elimination. Gaussian Elimination with Scaled Partial Pivoting. Tridiagonal and Banded Systems. 8. ADDITIONAL TOPICS CONCERNING SYSTEMS OF LINEAR EQUATIONS. Matrix Factorizations. Iterative Solutions of Linear Systems. Eigenvalues and Eigenvectors. Power Method. 9. APPROXIMATION BY SPLINE FUNCTIONS. First-Degree and Second-Degree Splines. Natural Cubic Splines. B Splines: Interpolation and Approximation. 10. ORDINARY DIFFERENTIAL EQUATIONS. Taylor Series Methods. Runge-Kutta Methods. Stability and Adaptive Runge-Kutta and Multistep Methods. 11. SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. Methods for First-Order Systems. Higher-Order Equations and Systems. Adams-Bashforth-Moulton Methods. 12. SMOOTHING OF DATA AND THE METHOD OF LEAST SQUARES. Method of Least Squares. Orthogonal Systems and Chebyshev Polynomials. Other Examples of the Least-Squares Principle. 13. MONTE CARLO METHODS AND SIMULATION. Random Numbers. Estimation of Areas and Volumes by Monte Carlo Techniques. Simulation. 14. BOUNDARY-VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS. Shooting Method Shooting Method Algorithm. A Discretization Method. 15. PARTIAL DIFFERENTIAL EQUATIONS. Parabolic Problems. Hyperbolic Problems. Elliptic Problems. 16. MINIMIZATION OF FUNCTIONS. One-Variable Case. Multivariate Case. 17. LINEAR PROGRAMMING. Standard Forms and Duality. Simplex Method. Approximate Solution of Inconsistent Linear Systems. APPENDIX A. ADVICE ON GOOD PROGRAMMING PRACTICES. Programming Suggestions. APPENDIX B. REPRESENTATION OF NUMBERS IN DIFFERENT BASES. Representation of Numbers in Different Bases. APPENDIX C. ADDITIONAL DETAILS ON IEEE FLOATING-POINT ARITHMETIC. More on IEEE Standard Floating-Point Arithmetic. APPENDIX D. LINEAR ALGEBRA CONCEPTS AND NOTATION. Elementary Concepts. Abstract Vector Spaces. ANSWERS FOR ED PROBLEMS. BIBLIOGRAPHY. INDEX.
'E. Ward Cheney Ward Cheney is Professor of Mathematics at the University of Texas at Austin. His research interests include approximation theory, numerical analysis, and extremum problems. David R. Kincaid David Kincaid is Senior Lecturer in the Department of Computer Sciences at the University of Texas at Austin. Also, he is the Interim Director of the Center for Numerical Analysis (CNA) within the Institute for Computational Engineering and Sciences (ICES).
