Cover -- Preface to the Third Edition -- Preface to the First Edition -- Contents -- Chapter 1. Errors -- 1.1 Introduction -- 1.2 Significant digits -- 1.3 Rounding off numbers -- 1.4 Errors -- 1.5 Relative error and the number of correct digits -- 1.6 General error formula -- 1.7 Application of errors to the fundamental operations of arithmetic -- Exercise 1.1 -- Chapter 2. Solution of Algebraic and Transcendental Equations -- 2.1 Introduction -- 2.2 Graphical solution of equations -- Exercise 2.1 -- 2.3 Method of bisection -- Exercise 2.2 -- 2.4 The Iteration Method -- Exercise 2.3 -- 2.5 Newton-Raphson method or Newton iteration method -- Exercise 2.4 -- Exercise 2.5 -- 2.6 Generalised Newtons' method for multiple roots -- Exercise 2.6 -- 2.7 Regula-Falsi method -- 2.8 Muller's Method -- Exercise 2.7 -- Chapter 3. Finite Differences -- 3.1 Introduction -- 3.2 Forward difference operator -- 3.3 The operator E -- 3.4 The operator D -- 3.5 Backward differences -- 3.6 Factorial polynomial -- 3.7 Error propagation in a difference table -- 3.8 Central Differences -- 3.9 Mean Operator -- 3.10 Separation of Symbols -- 3.11 Herchel's Theorem -- Exercise 3.1 -- Chapter 4 Interpolation with Equal Intervals -- 4.1 Introduction -- 4.2 Missing Values -- 4.3 Newton's Binomial Expansion Formula -- 4.4 Newton's Forward Interpolation Formula -- 4.5 Newton-Gregory Backward Interpolation Formula -- 4.6 Error in the Interpolation Formula -- Exercise 4.1 -- Chapter 5 Interpolation with Unequal Intervals -- 5.1 Introduction -- 5.2 Newton's General Divided Differences Formula -- Exercise 5.1 -- 5.3 Lagrange's Interpolation Formula -- Exercise 5.2 -- 5.4 Inverse Interpolation -- Exercise 5.3 -- Chapter 6 Central Difference Interpolation Formulae -- 6.1 Introduction -- 6.2 Gauss Forward Interpolation Formula -- 6.3 Gauss Backward Interpolation Formula.

6.4 Bessel's Formula -- 6.5 Stirling's Formula -- 6.6 Laplace-Everett Formula -- Exercise 6.1 -- Chapter 7 Inverse Interpolation -- 7.1 Introduction -- 7.2 Method of Successive Approximations -- 7.3 Method of Reversion Series -- Exercise 7.1 -- Chapter 8 Numerical Differentiation -- 8.1 Introduction -- 8.2 Derivatives Using Newton's Forward Interpolation formula -- 8.3 Derivatives Using Newton's Backward Interpolation formula -- 8.4 Derivatives Using Stirling's Formula -- Exercise 8.1 -- Chapter 9 Numerical Integration -- 9.1 Introduction -- 9.2 General Quadrature Formula for Equidistant Ordinates -- 9.3 Trapezoidal Rule -- 9.4 Simpson's One-third Rule -- 9.5 Simpson's Three-eighth's Rule -- 9.6 Weddle's Rule -- Exercise 9.1 -- 9.7 Newton-Cotes Formula -- 9.8 Derivation of Trapezoidal Rule, and Simpson's Rule from Newton-Cotes Formula -- 9.9 Boole's Rule -- 9.10 Romberg Integration -- Exercise 9.2 -- 9.11 Double Integration -- 9.12 Euler-Maclaurin Summation Formula -- Exercise 9.3 -- Chapter 10 Numerical Solution of Ordinary Differential Equations -- 10.1 Introduction -- 10.2 Taylor's Series Method -- 10.3 Euler's Method -- 10.4 Modified Euler's Method -- Exercise 10.1 -- 10.5 Predictor-Corrector Methods -- 10.6 Milne's Method -- 10.7 Adams-Bashforth-Moulton Method -- Exercise 10.2 -- 10.8 Runge-Kutta Method -- Exercise 10.3 -- 10.9 Picard's Method of Successive Approximation -- Exercise 10.4 -- Chapter 11 Solution of Linear Equations -- 11.1 Matrix Inversion Method -- Exercise 11.1 -- 11.2 Gauss-Elimination method -- Exercise 11.2 -- 11.3 Iteration Methods -- Exercise 11.3 -- Exercise 11.4 -- 11.4 Crout's Triangularisation Method (Method of Factorisation) -- Exercise 11.5 -- Chapter 12 Curve Fitting -- 12.1 Introduction -- 12.2 The straight line -- 12.3 Fitting a straight line -- 12.4 Fitting a parabola -- 12.5 Exponential function y = aebx.

Exercise 12.1 -- Chapter 13 Eigen Values and Eigen Vectors of a Matrix -- 13.1 Introduction -- 13.2 Method for the largest Eigen value (Power Method) -- 13.3 Cayley-Hamilton theorem -- Exercise 13.1 -- Chapter 14 Regression Analysis -- 14.1 Regression Analysis -- 14.2 Correlation -- 14.3 Coefficient of Correlation (r) -- 14.4 Scatter Diagram -- 14.5 Calculation of r (Correlation Coefficient) (Karl Pearson's formula) -- 14.6 Regression -- 14.7 Regression Equation -- 14.8 Curve of Regression -- 14.9 Types of Regression -- 14.10 Regression Equations (linear fit) -- 14.11 Angle Between two lines of regression -- 14.12 Solved Examples -- 14.13 Multilinear Linear Regression -- 14.14 Uses of Regression Analysis -- Exercise 4.1 -- Bibliography -- Index.