Numerical methods : fundamentals and applications

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. Chapter 1 Number Systems Chapter 2 Error Analysis Chapter 3 Nonlinear Equations Chapter 4 Nonlinear Systems and Polynomial Equations Chapter 5 Systems of Linear Equations Chapter 6 Eigenvalues and Eigenvectors Chapter 7 Eigenvalues and Eigenvectors of Real Symmetric Matrices Chapter 8 Interpolation Chapter 9 Finite Operators Chapter 10 Interpolation for Equal Intervals and Bivariate Interpolation Chapter 11 Splines, Curve Fitting, and Other Approximating Curves Chapter 12 Numerical Differentiation Chapter 13 Numerical Integration Chapter 14 First Order Ordinary Differential Equations: Initial Value Problems Chapter 15 Systems of First Order ODEs and Higher Order ODEs: Initial and Boundary Value Problems Chapter 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 Linear and Nonlinear Appendix E Graphs of Standard Functions Appendix F Greek Letters Index Written in a lucid manner, this textbook gives an in-depth discussion of basic and advanced concepts of numerical methods. C programming codes are included in the textbook for better understanding of concepts. Pedagogical features including solved examples and unsolved exercises are interspersed throughout the book for better understanding.