## Table of Contents

**Chapter 1 Solution of Algebraic and Transcendental Equations **

1.1 Introduction

1.2 Gauss Elimination Method (Direct Method)

*Solved Problems 1.1 to 1.2 *

1.3 Gauss-Jordan Method (Direct Method)

*Solved Problems 1.3 to 1.6 *

1.4 Inverse of a Matrix by Gauss-Jordan Method (Direct Method)

*Solved Problems 1.7 to 1.10 *

1.4.1 Errors

1.5 Iterative Method

1.5.1 Gauss-Jacobi Iterative Method

*Solved Problems 1.11 to 1.13 *

1.5.2 Gauss-Seidel Iterative Method

*Solved Problems 1.14 to 1.15 *

1.6 Method of Successive Approximation (Simple Iteration Method)

*Solved Problems 1.16 to 1.19 *

1.7 Newton-Raphson Iterative Method

*Solved Problems 1.20 to 1.24 *

1.7.1 Criterion for Convergence in Newton-Raphson Method

*Solved Problems 1.25 to 1.27 *

1.8 EigenValue of a Matrix by Power Method

*Solved Problems 1.28 to 1.32 *

1.9 Thomas Algorithm for Tridiagonal System of Equations

*Solved Problems 1.33 to 1.35 *

*Exercise *

*Multiple-Choice Questions *

*Exercise Problems *

** **

**Chapter 2 Interpolation and Approximation **

2.1 Introduction

2.2 Lagrange’s Interpolation Formula for Equal as Well as Unequal Intervals

*Solved Problems 2.1 to 2.3 *

2.2.1 Inverse Interpolation

*Solved Problem 2.4 *

2.3 Difference Operators

2.4 Newton’s Forward Interpolation Formula

2.5 Newton’s Backward Interpolation Formula

*Solved Problems 2.5 to 2.9 *

2.6 Newton’s Divided Difference Formula for Interpretation

*Solved Problems 2.10 to 2.12 *

*Multiple-Choice Questions *

*Exercise Problems *

* *

**Chapter 3 Numerical Differentiation and Integration **

3.1 Introduction

3.2 Newton’s Forward Formula for Differentiation

3.3 Newton’s Backward Formula for Differentiation

*Solved Problems 3.1 to 3.3 *

3.4 Numerical Differentiation for Unequal Intervals

*Solved Problems 3.4 to 3.7 *

3.5 Numerical Integration

3.5.1 Trapezoidal Rule

3.5.2 Simpson’s 1/3 Rule

3.5.3 Simpson’s 3/8 Rule

*Solved Problems 3.8 to 3.15 *

3.6 Romberg Integration

*Solved Problem 3.16 *

3.7 Double Integration

*Solved Problems 3.17 to 3.23 *

3.8 Two-Point and Three-Point Gaussian Quadrature Formula

*Solved Problems 3.24 to 3.30 *

*Multiple-Choice Questions *

*Exercise Problems *

**Chapter 4 Numerical Solution of Ordinary Differential**

**Equations **

4.1 Introduction

4.2 Taylor Series Method

*Solved Problems 4.1 to 4.4*

4.2.1 Point wise Method in Taylor’s Series

*Solved Problem 4.5 *

4.3 Euler’s Method

*Solved Problems 4.6 to 4.8 *

4.4 Modified Euler’s Method

*Solved Problems 4.9 to 4.10 *

4.5 Runge*−*Kutta Method of Fourth Order

*Solved Problems 4.11 to 4.13 *

4.5.1 Runge*−*Kutta Method for Simultaneous First Order Differential Equation

*Solved Problems 4.14 to 4.15 *

4.5.2 Runge*−*Kutta Method for Second Order Differential Equation

*Solved Problem 4.16 *

4.6 Multi Step Methods

4.6.1 Milne’s Predictor-Corrector Method

*Solved Problems 4.17 to 4.20 *

4.6.2 Adams*−*Bashforth Predictor-Corrector Method

*Solved Problem 4.21 *

*Multiple-Choice Questions *

*Exercise Problems *

**Chapter 5 Numerical Solution of Partial Differential**

**Equation **

5.1 Introduction

5.2 Classification

*Solved Problems 5.1 to 5.3 *

5.3 Difference Quotient

5.4 Finite Difference Formula for Two-Dimensional Heat Equation

*Solved Problems 5.4 to 5.7 *

5.5 Poisson Equation

*Solved Problems 5.8 to 5.9 *

5.6 One-Dimensional Wave Equation *− *Numerical Solution

(Hyperbolic Equation)

*Solved Problems 5.10 to 5.13 *

5.7 One-Dimensional Heat Equation

5.7.1 Finite Difference Solution of One-Dimensional Heat Equation

5.7.2 Explicit Method

*Solved Problems 5.14 to 5.15 *

5.7.3 Implicit Method

5.8 Crank Nicolson Method

*Solved Problems 5.16 to 5.17 *

*Multiple-Choice Questions *

*Exercise Problems *