Numerical Methods: Fundamentals and Applications

Description

Written in an easy-to-understand manner, this comprehensive textbook brings together both basic and advanced concepts of numerical methods in a single volume. Important topics including error analysis, nonlinear equations, systems of linear equations, interpolation and interpolation for Equal intervals and bivariate interpolation are discussed comprehensively. The textbook is written to cater to the needs of undergraduate students of mathematics, computer science, mechanical engineering, civil engineering and information technology for a course on numerical methods/numerical analysis. The text simplifies the understanding of the concepts through exercises and practical examples. Pedagogical features including solved examples and unsolved exercises are interspersed throughout the book for better understanding. Cover Front Matter Numerical Methods: Fundamentals and Applications Copyright Dedication Contents Preface Acknowledgments 1 Number Systems 2 Error Analysis 3 Nonlinear Equations 4 Nonlinear Systems and Polynomial Equations 5 Systems of Linear Equations 6 Eigenvalues and Eigenvectors 7 Eigenvalues and Eigenvectors of Real Symmetric Matrices 8 Interpolation 9 Finite Operators 10 Interpolation for Equal Intervals and Bivariate Interpolation 11 Splines, Curve Fitting, and Other Approximating Curves 12 Numerical Differentiation 13 Numerical Integration 14 First Order Ordinary Differential Equations: Initial Value Problems 15 Systems of First Order ODEs and Higher Order ODEs: Initial and Boundary Value Problems 16 Partial Differential Equations: Finite Difference Methods Appendix A. Comparison of Analytical and Numerical Techniques Appendix B. Numerical Techniques and Computer Appendix C. Taylor Series Appendix D. Taylor Series Appendix E. Taylor Series Appendix F. Greek Letters Index