Contents

• 1. Error & Solutions of Algebraic, Transcendental Equations

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  Objectives, Introduction, Accuracy of Numbers, Exact and Approximate Numbers, Significant Digits, Accuracy and Precision, Error, Sources of Errors, Inhernet Error, Numerical Errors (Procedural Errors), Truncation Errors, Absolute Error, Relative Error, Percentage Error, Illustrative Examples, Exercise 1.1, Algebraic and Transcendental Equations, Solution of Algebraic and Transcendental Equations, Direct Method, Graphical Method, Iterative Method, Bisection Method, Newton-Raphson Method, Geometrical Meaning of Newton-Raphson Method, Rate of Convergence of Newton Raphson Method, Direct Iteration Method, Illustrative Examples, Exercise 1.2, Regula Falsi Method or Method of False Position, The Secant Method (Chord Method), Convergence of Secant Method, Polynomial Equations, Graffe’s Root Squaring Method, Synthetic Division, Birge-Vieta Method, Lin-Bairstow’s Method or Method for Complex Root, Exercise 1.3.
   
  2. Solution of Simultaneous Algebraic Equations

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  Objectives, Introduction, Solution of Simultaneous Linear Algebraic Equations, Non-Homogeneous System, Direct Method, Matrix Inversion Method, Gauss Elimination Method, Partition Method, Eigen Value and Eigen Vector, Power Series Method, Exercise 2.1, Finite Difference and Interpolation, Finite Difference Calculus, Forward Differences, Backward Differences, Central Differences, Other Difference Operators, Relation between Difference Operators, Exercise 2.2, Errors in Polynomial Interpolation, Newton Gregory Forward Interpolation Formula, Newton-Gregory Backward Interpolation Formula, Central Difference Interpolation Formula, Lagrange’s Interpolation Formula for Unequal Spaced Points, Divided Differences and Their Properties, Illustrative Examples, Exercise 2.3.
   
  3. Numerical Differentiation, Integration & Solution to Ordinary Differential Equations

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  Objectives, Introduction, Numerical Differentiation, Illustrative Examples, Maximum and Minimum Value of a Tabulated Function, Numerical Integration, Trapezoidal Rule, Simpson’s 1/3 Rule, Simpson’s 3/8 Rule, Boole’s Rule, Weddle’s Rule, Exercise 3.1, Solution of Ordinary Differential Equation, Taylor’s Series Method, Picard’s Method, Euler’s Method, Modified Euler’s Formula, Runge-Kutta Method of Fourth Order, Milne’s Predictor Corrector Method, Adams-Moulton (OR Adams-Bashforth Method), Illustrative Examples, Exercise 3.2.
   
  4. Fundamental Concepts of Probability and Statistics

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  Objectives, Introduction, Frequency Distribution, Measures of Central Tendency, Measures of Dispersion, Skewness, Kurtosis, Coefficient of Dispersion and Coefficient of Variation, Moments of A Frequency Distribution, Moment About Origin, Moment About Mean or Central Moment, Moment About an Arbitrary Point, Karl Pearson b and g Coefficients, Probability, The Axiomatic Definition of Probability, Conditional Probability, Independent Events, Random Variable, Probability Distribution of Random Variable, Expectation, Variance, Moment Generating Function (mgf), Binomial Distribution, Mean and Variance of Binomial Distribution, Moments, Moment Generating Function and Recurrence Relation for Moments, Mode of the Binomial Distribution, Fitting of Binomial Distribution (Recurrence Relation for the Probabilities of Binomial Distribution), Poisson Distribution, Mean and Variance of Poisson Distribution, Moments, Moment Generating Function and Recurrence Relation for Moments, Mode of Poisson Distribution, Fitting of Poisson Distribution, Normal Distribution, Standard Form of the Normal Distribution, Normal Probability Integral (Area Under the Standard Probability Curve), Mean and Variance of Normal Distribution, Moment Generating Function of Normal Distribution, Recurrence Relation for Even Order Central Moments, Fitting of Normal Distribution, Exercise.
   
  5. Statistical Sampling Study

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  Objectives, Introduction, Parameter and Statistic, Parameter Estimation, Unbiased Estimator, Confidence Interval and Confidence Limits, Hypothesis Testing, Critical Region, Critical Values, Level of Significance, Errors in Testing of Hypotheses, Central Limit Theorem, Sampling Distribution of a Statistic, Sampling Distribution of Proportions, Sampling Distribution of Mean, Sampling Distribution of Difference of Mean, Test of Significance for the Difference of Standard Deviations, Illustrative Examples, Exercise.
   
  6. Exact Sampling Distributions

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  Objectives, Introduction, Student’s t-Distribution, Test of Significance of the Difference between Sample Mean and Population Mean, t-Test for Difference of Means, Paired t-Test for Difference of Means, Chi-Square Distribution, Chi-Square test of Goodness of Fit, ?2-Test of Independence of Attributes, Snedecor’s F-Distribution, F-test for Equality of Population Variances, Illustrative Examples, Exercise.
   
  7. Correlation and Regression

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  Objectives, Introduction, Bivariate Distribution, Correlation, Measure of Correlation: Karl Pearson Coefficient of Correlation, Rank Correlation, Correlation of Bivariate Frequency Distribution, Curve Fitting, Principle of Least Squares, Fitting of a Straight Line, Regression, Linear Regression, Lines of Regression, Angle Between Two Lines of Regression, Standard Error of Estimate or Residual Variance, Coefficient of Determination, Multiple Regression, Curvilinear Regression, Multiple and Partial Correlation, Multiple Correlation Coefficient, Partial Correlation Coefficient, Illustrative Examples, Exercise.
   
  Appendix
  P. Paper