Elements of Numerical Analysis
- 2nd
- Delhi Cambridge University Press 2015
- 759
Numerical analysis deals with the manipulation of numbers to solve a particular problem. This book discusses in detail the creation, analysis and implementation of algorithms to solve the problems of continuous mathematics. An input is provided in the form of numerical data or it is generated as required by the system to solve a mathematical problem. Subsequently, this input is processed through arithmetic operations together with logical operations in a systematic manner and an output is produced in the form of numbers. Covering the fundamentals of numerical analysis and its applications in one volume, this book offers detailed discussion on relevant topics including difference equations, Fourier series, discrete Fourier transforms and finite element methods. In addition, the important concepts of integral equations, Chebyshev Approximation and Eigen Values of Symmetric Matrices are elaborated upon in separate chapters. The book will serve as a suitable textbook for undergraduate students in science and engineering.
Provides an in-depth coverage of topics like moving grid method, hyperbolic equation of first order and finite difference methods Includes a separate chapter on Fourier series, discrete Fourier transform and fast Fourier transform Presents applications of interpolation, splines, ordinary differential equations and minimum functional theorem
Preface 1. Errors in computation 2. Linear equations and eigenvalue problem 3. Nonlinear equations 4. Interpolation 5. Numerical differentiation 6. Numerical integration 7. Ordinary differential equations 8. Splines and their applications 9. Method of least squares and Chebyshev approximation 10. Eigenvalues of symmetric matrices 11. Partial differential equations 12. Finite element method 13. Integral equations 14. Difference equations 15. Fourier series, discrete Fourier transform and fast Fourier transform 16. Free and moving boundary problems: a brief introduction