Cover -- Preface -- Contents -- Chapter 1 Solution of Equations and Eigen Value Problems -- 1.1 Solution of Algebraic and Transcendental Equations -- 1.1.1 Introduction -- 1.1.2 Initial Approximation for an Iterative Procedure -- 1.1.3 Method of False Position -- 1.1.4 Newton-Raphson Method -- 1.1.5 General Iteration Method -- 1.1.6 Convergence of the Iteration Methods -- 1.2 Linear System of Algebraic Equations -- 1.2.1 Introduction -- 1.2.2 Direct Methods -- 1.2.2.1 Gauss Elimination Method -- 1.2.2.2 Gauss-Jordan Method -- 1.2.2.3 Inverse of a Matrix by Gauss-Jordan Method -- 1.2.3 Iterative Methods -- 1.2.3.1 Gauss-Jacobi Iteration Method -- 1.2.3.2 Gauss-Seidel Iteration Method -- 1.3 Eigen Value Problems -- 1.3.1 Introduction -- 1.3.2 Power Method -- 1.4 Answers and Hints -- Chapter 2 Interpolation and Approximation -- 2.1 Introduction -- 2.2 Interpolation with Unevenly Spaced Points -- 2.2.1 Lagrange Interpolation -- 2.2.2 Newton's Divided Difference Interpolation -- 2.3 Interpolation with Evenly Spaced Points -- 2.3.1 Newton's Forward Difference Interpolation Formula -- 2.3.2 Newton's Backward Difference Interpolation Formula -- 2.4 Spline Interpolation and Cubic Splines -- 2.5 Answers and Hints -- Chapter 3 Numerical Differentiation and Integration -- 3.1 Introduction -- 3.2 Numerical Differentiation -- 3.2.1 Methods Based on Finite Differences -- 3.2.1.1 Derivatives Using Newton's Forward Difference Formula -- 3.2.1.2 Derivatives Using Newton's Backward Difference Formula -- 3.2.1.3 Derivatives Using Divided Difference Formula -- 3.3 Numerical Integration -- 3.3.1 Introduction -- 3.3.2 Integration Rules Based on Uniform Mesh Spacing -- 3.3.2.1 Trapezium Rule -- 3.3.2.2 Simpson's 1/3 Rule -- 3.3.2.3 Simpson's 3/8 Rule -- 3.3.2.4 Romberg Method (Integration) -- 3.3.3 Integration Rules Based on Non-Uniform Mesh Spacing.

3.3.3.1 Gauss-Legendre Integration Rules -- 3.3.4 Evaluation of Double Integrals -- 3.3.4.1 Evaluation of Double Integrals Using Trapezium Rule -- 3.3.4.2 Evaluation of Double Integrals by Simpson's Rule -- 3.4 Answers and Hints -- Chapter 4 Initial Value Problems for Ordinary Differential Equations -- 4.1 Introduction -- 4.2 Single Step and Multi Step Methods -- 4.3 Taylor Series Method -- 4.3.1 Modified Euler and Heun's Methods -- 4.4 Runge-Kutta Methods -- 4.5 System of First Order Initial Value Problems -- 4.5.1 Taylor Series Method -- 4.5.2 Runge-Kutta Fourth Order Method -- 4.6 Multi Step Methods and Predictor-Corrector Methods -- 4.6.1 Predictor Methods (Adams-Bashforth Methods) -- 4.6.2 Corrector Methods -- 4.6.2.1 Adams-Moulton Methods -- 4.6.2.2 Milne-Simpson Methods -- 4.6.2.3 Predictor-Corrector Methods -- 4.7 Stability of Numerical Methods -- 4.8 Answers and Hints -- Chapter 5 Boundary Value Problems in Ordinary Differential Equations and Initial and Boundary Value Problems in Partial Differential Equations -- 5.1 Introduction -- 5.2 Boundary Value Problems Governed by Second Order Ordinary Differential Equations -- 5.3 Classification of Linear Second Order Partial Differential Equations -- 5.4 Finite Difference Methods for Laplace and Poisson Equations -- 5.5 Finite Difference Method for Heat Conduction Equation -- 5.6 Finite Difference Method for Wave Equation -- 5.7 Answers and Hints -- Bibliography -- Index.