Elements of Numerical Analysis

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.

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.

Radhey S. Gupta is former professor and head in the Department of Mathematics at Indian Institute of Technology, Roorkee. He also served as Director at the Trinity Institute of Higher Education (Guru Gobind Singh Indraprastha University), New Delhi. Gupta was a visiting professor at Asian Institute of Technology, Bangkok and University of Florence, Italy. He has more than thirty-five years of experience in teaching and research in the field of numerical analysis with specialization in moving boundary problems.