1. Finite Differences and Interpolation
Introduction, Finite Difference Calculus, Forward Differences, Backward Differences, Central Differences, Other Difference Operators, Relation Between Difference Operators, Exercise 1 (A), 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, Numerical Differentiation, Maximum and Minimum Value of a Tabulated Function, Numerical Integration, Illustrative Examples, Exercise 1 (B).
2. Ordinary Differential Equations & Difference Equations
Introduction, Picard’s Method, Euler’s Method, Modified Euler’s Formula, Runge-Kutta Method of Fourth Order, Milne’s Predictor Corrector Method, Illustrative Examples, Exercise 2 (A), Difference Equations, Linear Difference Equation, Particular Integral, Illustrative Examples, Exercise 2 (B).
3. Algebraic & Transcendental Equations
Introduction, Algebraic and Transcendental Equations, Solution of Algebraic and Transcendental Equations, Illustrative Examples, Solution of Simultaneous Linear Algebraic Equations, Illustrative Examples, Exercise 3 (B), Curve Fitting, Principle of Least Squares, Fitting of a Straight Line, Fitting a Parabola, Exercise 3 (C).
4. Special Functions: Bessel Functions and Legendre Polynomial
Intorudction, Bessel’s Equation and ITS Solution, Recurrence Relations for Jn(x), Illustrative Examples, Exercise 4 (A), Orthogonal Properties of Bessel Functions, Transformation of Bessel's Equation, Generating Function for Jn(x), Integral Form of Jn(x), Illustrative Examples, Exercise 4 (B), Legendre's Differential Equation and its Solution, Rodrigue's Formula, Generating Function for Pn(x), Orthogonal Properties of Legendre Polynomials, Recurrence Relations, Illustrative Examples, Exercise 4 (C).
5. Elementary Probability Theory
Introduction, Events and Sample Space, Algebra of Events, Exhaustive Events, Mutually Exclusive Events, Equally Likely Events, Partition of the Sample Space S, Probability, The Axioms of Probability, Conditional Probability, Independent Events, Illustrative Examples, Exercise 5 (A), Baye’s Theorem, Illustrative Examples, Exercise 5 (B).
6. Theoretical Probability Distributions
Introduction, Random Variable, Discrete Random Variable, Continuous Random Variable, Probability Distribution of a Discrete Random Variable, Probability Mass Function, Probability Distribution of a Continuous Random Variable, Probability Density Function, Expectation, Binomial Distribution, Mean and Variance of Binomial Distribution, Fitting of Binomial Distribution (Recurrence Relation for the Probabilities of Binomial Distribution), Illustrative Examples, Exercise 6 (A), Poisson Distribution, Mean and Variance of Poisson Distribution, Fitting of Poisson Distribution, Illustrative Examples, Exercise 6 (B), Normal Distribution, Standard Form of the Normal Distribution, Normal Probability Integral (Area Under the Standard Probability Curve), Mean and Variance of Normal Distributio, Fitting of Normal Distribution, Illustrative Examples, Exercise 6 (C).
7. Correlation and Regression
Introduction, Bivariate Distribution, Correlation, Measure of Correlation: Karl Pearson Coefficient of Correlation, Rank Correlation, Regression, Linear Regression, Lines of Regression, Angle Between two Lines of Regression, Illustrative Examples, Exercise 7 (A).
8. Calculus of Variations
Introduction, Definitions, Euler’s Equation, Isoperimetric Problems, Illustrative Examples, Exercise 8 (A).
9. Z-Transforms
Introduction, Definition, Properties of Z-Transforms, Linearity, Change of Scale or Damping Rule, Shifting Property, Multiplication by n, Division by n, Initial Value Theorem, Final Value Theorem, Illustrative Examples, Exercise 9 (A), Region of Convergence (R.O.C.), Inverse Z-Transform, Partial Fraction Method, Convolution Property for Z-Transform, Convolution Theorem for Casual Sequence, Solution of Difference Equations, Illustrative Examples, Exercise 9 (B).
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