(Ebook) Introduction to Numerical Analysis 1st Edition by DC Sanyal, K Das ISBN 9789380673370 938067337X

(Ebook) Introduction to Numerical Analysis 1st Edition by DC Sanyal, K Das ISBN 9789380673370 938067337X

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ISBN 10: 938067337X
ISBN 13: 9789380673370
Author: DC Sanyal, K Das

a clear and structured foundation in the theory and practical applications of numerical methods. The book introduces students and practitioners to essential techniques for solving mathematical problems that cannot be addressed analytically, covering topics such as error analysis, solutions of linear and nonlinear equations, interpolation, numerical differentiation and integration, and numerical solutions of ordinary differential equations. With a balance between mathematical rigor and computational approaches, the authors emphasize algorithmic development and the implementation of methods for real-world problems. Designed for undergraduates in mathematics, engineering, and computer science, the text serves as both a learning resource and a reference for applying numerical techniques in scientific and engineering contexts.

(Ebook) Introduction to Numerical Analysis 1st Edition Table of contents:

Part I: Foundations of Numerical Analysis

1. Introduction to Numerical Methods

   • Nature and scope of numerical analysis

   • Approximation vs. exact solutions

   • Applications in science and engineering

2. Errors in Numerical Computation

   • Sources and types of errors

   • Propagation and control of errors

   • Significant digits and stability

Part II: Algebraic and Transcendental Equations

3. Solution of Nonlinear Equations

   • Bisection method

   • Regula-Falsi method

   • Newton-Raphson method

   • Secant method and convergence

4. Systems of Linear Equations

   • Gauss elimination method

   • Gauss-Jordan method

   • LU decomposition

   • Iterative methods: Jacobi, Gauss-Seidel

Part III: Interpolation and Approximation

5. Interpolation with Equal Intervals

   • Newton’s forward and backward interpolation

   • Error analysis

6. Interpolation with Unequal Intervals

   • Divided differences

   • Newton’s general interpolation formula

   • Lagrange interpolation formula

7. Curve Fitting and Approximation

   • Method of least squares

   • Polynomial approximation

   • Chebyshev polynomials

Part IV: Numerical Differentiation and Integration

8. Numerical Differentiation

   • Using interpolation polynomials

   • Error estimation

9. Numerical Integration

   • Trapezoidal rule

   • Simpson’s 1/3 and 3/8 rules

   • Romberg integration

   • Gaussian quadrature

Part V: Differential Equations

10. Numerical Solution of Ordinary Differential Equations (ODEs)

• Euler’s method

• Modified Euler method

• Runge-Kutta methods

• Predictor-corrector methods

11. Systems of ODEs and Higher-Order ODEs

• Reduction techniques

• Numerical schemes

Part VI: Advanced Topics

12. Numerical Solution of Partial Differential Equations (PDEs)

• Finite difference methods

• Elliptic, parabolic, and hyperbolic equations

13. Eigenvalue Problems

• Power method

• Jacobi method

• Applications

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Tags: DC Sanyal, K Das, Numerical Analysis, Introduction