Elements of Numerical Analysis

ISBN-13: 9781107500495 / Angielski / Miękka / 2015 / 774 str.

Radhey S. Gupta

Opis

Numerical Analysis deals with 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 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 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 in separate chapters. It serves as a textbook for undergraduate students in science and engineering across all major universities in India.

Spis treści

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; Appendices; Index.