Cover -- Preface -- Contents -- Chapter 1. Errors and Floating Point -- 1.1 Introduction -- 1.2 Accuracy of Numbers -- 1.3 Errors -- 1.4 A General Formula for Error -- 1.4.1 Error in Addition of Numbers -- 1.4.2 Error in Subtraction of Numbers -- 1.4.3 Error in Product of Numbers -- 1.4.4 Error in Division of Numbers -- 1.4.5 Inverse Problem -- 1.4.6 Error in Evaluating xk -- 1.5 Error in Series Approximation -- Problem Set 1.1 -- 1.6 Some Important Mathematical Preliminaries -- 1.7 Floating Point -- 1.8 Floating Point Arithmetic and their Computation -- 1.8.1 Arithmetic Operations on Floating Point Numbers -- Problem Set 1.2 -- Chapter 2. Algebraic and Transcendental Equation -- 2.1 Introduction -- 2.2 Methods for Finding the Root of an Equation -- 2.2.1 Direct Methods -- 2.2.2 Iterative Methods -- 2.3 Order (or Rate) of Convergence of Iterative Methods -- 2.4 Bisection (or Bolzano) Method -- 2.4.1 Procedure for the Bisection Method to Find the Root of the Equation f (x) = 0 -- 2.4.2 Order of Convergence of Bisection Method -- Problem Set 2.1 -- 2.5 False Position Method (or Regula Falsi Method) -- 2.5.1 Procedure for the False Position Method to Find the Root of the Equation f (x) = 0 -- 2.5.2 Order (or Rate) of Convergence of False Position Method -- Problem Set 2.2 -- 2.6 Iteration Method (Method of Successive Approximation) -- 2.6.1 Procedure For Iteration Method To Find The Root of The Equation f(x) = 0 -- 2.6.2 Rate of Convergence of Iteration Method -- Problem Set 2.3 -- 2.7 Newton-Raphson Method (or Newton's Method) -- 2.7.1 Procedure for Newton Raphson Method to Find the Root of the Equation f (x) = 0 -- 2.7.2 Order (or Rate) of Convergence of Newton-Raphson Method -- Problem Set 2.4 -- 2.8 Secant Method -- 2.8.1 Procedure for Secant Method to Find the Root of f(x)=0 -- 2.8.2 Rate or Order of Convergence of Secant Method.

2.9 Methods for Complex Roots -- 2.10 Muller's Method -- 2.11 Lin Bairstow Method -- 2.12 Quotient Difference Method -- Problem Set 2.5 -- Chapter 3. Calculus of Finite Differences -- 3.1. Introduction -- 3.2 Finite Differences -- 3.3 Argument and Entry -- 3.4 Differences -- 3.4.1 Forward or Leading Differences -- 3.4.2 Backward or Ascending Differences -- 3.4.3 Central Differences -- 3.4.4 Other Difference Operators -- 3.4.5 Properties of Operators -- 3.4.6 Relation between Different Operators -- Problem Set 3.1 -- 3.5 Fundamental Theorem on Differences of Polynomial -- 3.6 Estimation of Error By Difference Table -- 3.7 Technique to Determine The Missing Term -- Problem Set 3.2 -- 3.8 Separation of Symbols -- 3.9 Factorial Notations -- 3.10 Reciprocal Factorial Notation -- 3.11 Method of Representing Polynomial in Factorial Notations -- 3.11.1 Direct Method -- 3.11.2 Method of Synthetic Division -- 3.12 Errors in Polynomial Interpolation -- 3.13. Differences of Zeros -- Problem Set 3.3 -- Chapter 4. Interpolation with Equal Interval -- 4.1 Introduction -- 4.2 Newton's Gregory Formula for Forward Interpolation -- Problem Set 4.1 -- 4.3 Newton's Gregory Formula for Backward Interpolation -- Problem Set 4.2 -- 4.4 Central Difference Formulae -- 4.4.1 Gauss Forward Difference Formula -- 4.4.2 Gauss Backward Difference Formula -- 4.4.3 Stirling's Formula -- 4.4.4 Bessel's Interpolation Formula -- 4.4.5 Laplace-Everett's Formula -- Problem Set 4.3 -- Gauss Backward -- Problem Set 4.4 -- Stirling's Formula -- Problem Set 4.5 -- 4.5 Bessel's -- Problem Set 4.6 -- 4.6 Laplace Everetts -- Problem Set 4.7 -- Chapter 5. Interpolation with Unequal Interval -- 5.1 Introduction -- 5.2 Lagrange's Interpolation Formula -- Problem Set 5.1 -- 5.3 Errors in Polynomial Interpolation -- 5.3.1 Error in Lagrange's interpolation formula -- 5.3.2 Inverse Interpolation.

5.3.3 Expression of Function as a Sum of Partial Fractions -- Problem Set 5.2 -- 5.4 Divided Difference -- 5.4.1 Properties of Divided Differences -- 5.4.2. Relation Between Divided Differences and Ordinary Differences -- 5.5 Newton's Divided Difference Formula -- Problem Set 5.3 -- 5.6. Hermite's Interpolation Formula -- Problem Set 5.4 -- 5.7. Some Related Terms -- 5.7.1 Some Remarkable Points about Chosen Different Interpolation Formulae -- 5.7.2 Approximation of Function -- 5.7.3 Spline Interpolation -- 5.7.4 Cubic Spline Interpolation for Equally and Unequally Spaced Values -- Problem Set 5.5 -- Chapter 6. Numerical Differentiation and Integration -- 6.1 Introduction -- 6.2 Numerical Differentiation -- 6.2.1 Derivation Using Newton's Forward Interpolation Formula -- 6.2.2 Derivatives Using Newton's Backward Difference Formula -- 6.2.3 Derivatives Using Stirling's Formula -- 6.2.4 Derivative Using Newton's Divided Difference Formula -- Problem Set 6.1 -- 6.3 Numerical Integration -- 6.4 General Quadrature Formula -- 6.5 Trapezoidal Rule -- 6.6 Simpson's One-third Rule -- 6.7 Simpson's Three-eight Rule -- 6.8 Boole's Rule -- 6.9 Weddle's Rule -- 6.10 Euler-Maclaurin's Formula -- Problem Set 6.2 -- Chapter 7. Numerical Solution of Ordinary Differential Equation -- 7.1 Introduction -- 7.2 Taylor's Method -- 7.3 Picard's Method of Successive Approximations -- 7.4 Euler's Method -- 7.5 Euler's Modified Method -- Problem Set 7.1 -- 7.6 Runge-Kutta Method -- 7.7 Milne's Predictor-Corrector Method -- Predictor-Corrector Methods -- Milne's Method -- 7.8 Automatic Error Monitoring -- Convergence of a Method -- 7.9 Stability in the Solution of Ordinary Differential equation -- Problem Set 7.2 -- Chapter 8. Solution of Simultaneous Linear Equation -- 8.1 Introduction -- 8.2 Gauss-Elimination Method -- 8.3 Gauss-Elimination with Pivoting Method.

8.4 Ill-Conditioned System of Equations -- 8.5 Iterative Refinement of The Solution by Gauss elimination Method -- 8.6 Iterative Method for Solution of Simultaneouslinear Equation -- 8.6.1 Jacobi's Method or Gauss-Jacobi Method -- 8.6.2 Guass-Seidel Method -- Problem Set 8.1 -- Chapter 9. Curve Fitting -- 9.1 Introduction -- 9.2 Principle of Least Squares -- 9.2.1 Fitting of Straight Line -- 9.2.2 Fitting of Parabola -- 9.2.3 Change of Scale -- 9.2.4 Fitting of an Exponential Curve -- 9.2.5 Fitting of the Curve y=ax+bx2 -- 9.2.6 Fitting of the Curve y = ax+b/x -- 9.2.7 Fitting of the Curve -- Problem Set 9.1 -- 9.3 Regression -- 9.3.1 Dependent and Independent Variables -- 9.3.2 Line of Regression -- 9.3.3 Regression Line of y on x -- 9.3.4 Regression Line of x on y -- 9.3.5 To obtain the Equation of Line of Regression of y on x -- 9.3.6 To Obtain the Equation of Line of Regression of x on y -- 9.3.7 Another Form of Equations of Lines of Regression -- 9.3.8 Some Properties of Regression Coefficients -- 9.4 Error of Prediction -- 9.5 Multiple Linear Regression -- Problem Set 9.2 -- Chapter 10. Time Series and Forecasting -- 10.1 Introduction -- 10.2 Times Series Graph -- 10.3 Component of Time Series -- 10.4 Analysis of Time Series -- 10.4.1 Analysis of Trend or Secular Trend -- 10.4.2 Analysis of Seasonal Variation -- 10.4.3 Analysis of Cyclical Fluctuation or Cyclic Variations -- 10.4.4 Analysis of Irregular of Random Movements -- 10.5 Importance of Time Series -- Problem Set 10.1 -- 10.6 Forecasting -- 10.7 Forecasting Modes -- 10.7.1 Additive Model -- 10.7.2 Multiplicative Model -- 10.8 Types of Forecasting and Forecasting Methods -- 10.9 Smoothing of Curve -- Chapter 11. Statistical Quality Control -- 11.1 Introduction -- 11.1.1 Difference between Diagrams and Graphs -- 11.1.2 Types of Diagrams -- 11.1.3 Rules for Drawing Diagrams.

11.2 Line Diagram -- 11.3 Bar Diagram -- 11.4 One Dimensional Diagram -- 11.5 Two Dimensional Diagrams -- 11.6 Three Dimensional Diagrams -- 11.7 Pictograms -- 11.8 Cartograms -- 11.9 Graphic Representation of Data -- 11.9.1 Graphs of Frequency Distribution -- 11.9.2 Graphs of Time-Series -- 11.10 Statistical Quality Control -- 11.10.1 Causes of Variation -- 11.10.2 Types of Quality Control -- 11.11 Control Charts -- 11.12 3-σ Control Limits -- 11.13 Types of Control Chart -- 11.13.1 Control Chart for Variable -- 11.13.2 Control Chart for Attributes -- Problem Set 11.1 -- Chapter 12. Testing of Hypothesis -- 12.1 Introduction -- 12.2 Some Important Definitions -- 12.3 Understanding the Type of Test -- 12.4 Procedure for Testing of Hypothesis -- 12.5 Standard Error -- 12.6 Test of Significance for Large Samples -- Problem Set 12.1 -- 12.7 Test of Significance for Small Samples -- 12.7.1 Chi-Square (χ2) Test -- 12.7.2 Student's t-distribution -- 12.7.3 Snedecor's Variance Ratio Test or F-test -- 12.7.4 Fisher's Z-test -- Problem Set 12.2 -- Chapter 13. Computer Programming in 'C' Language -- 13.1 Introduction -- Elements of Real Programming Languages -- Computer Representation of Numbers -- Characters, Strings, and Numbers -- Compiler Terminology -- Basic Data Types and Operators -- Arithmetic Operators -- Assignment Operators -- Function Calls -- Statements And Control Flow -- Boolean Expressions -- Array Initialization -- Arrays of Arrays ("Multidimensional" Arrays) -- Functions and Program Structure -- Function Basics -- Character Input and Output -- Assignment Operators -- Increment and Decrement Operators -- Strings -- The C Preprocessor -- Pointers and Arrays -- Null Pointers -- 13.2 Algorithm for Bisection Method -- 13.3 Programming for Bisection Method -- 13.4 Algorithm for False Position Method -- 13.5 Programming for False Position Method.

13.6 Algorithm for Iteration Method.