Syllabus Numerical and Statistical Methods - [302041] Credits Examination Scheme Theory 3 In-Semester 30 Marks Tutorial 1 End-Semester 70 Marks Term Work 25 Marks Unit 1 Roots of Equation and Simultaneous Equations Roots of Equation : Bracketing method and Newton-Raphson method Solution of simultaneous equations : Gauss Elimination Method with Partial pivoting, Gauss-Seidel method, Thomas algorithm for Tri-diagonal Matrix. (Chapters - 1, 2) Unit 2 Numerical Solution of Differential Equations Ordinary Differential Equations [ODE] : Taylor series method, Euler Method, Runge-Kutta 4th order. Simultaneous equations using Runge-Kutta 2nd order method. Partial Differential Equations [PDE] : Finite difference method, Simple Laplace method, PDE’s Parabolic explicit solution, Elliptic explicit solution. (Chapters - 3, 4) Unit 3 Numerical Integration Numerical Integration (1D) : Trapezoidal rule, Simpson’s 1/3rd Rule, Simpson’s 3/8th Rule, Gauss Quadrature2-point and 3-point method. Double Integration : Trapezoidal rule, Simpson’s 1/3rd Rule. (Chapter - 5) Unit 4 Curve Fitting and Regression Analysis Curve Fitting : Least square technique- first order, power equation, exponential equation and quadratic equation. Regression Analysis : Linear regression, Nonlinear regression, Multiple regressions, Polynomial regression. Lagrange’s interpolation, Numerical interpolation and differentiation using Newton’s forward method, inverse interpolation (Lagrange’s method only). (Chapters - 6, 7) Unit 5 Statistics Measures of central tendency : mean, median, mode. Measurement of variability and dispersion : Standard deviation, standard error, variance, range. Measure of shape : skewness, kurtosis Statistical diagram : scattered diagram, histogram, pie charts and measure of association between two variables. Correlation : Karl Pearson’s Coefficient of correlation and its mathematical properties, Spearman’s Rank correlation and its interpretations. (Chapter - 8) Unit 6 Probability and Linear Algebra Probability : Joint, conditional and marginal probability, Bayes’ theorem, independence, theorem of total probability, expectation and variance, random variables. Probability distributions : Binomial, Poisson, Geometric, Uniform, Exponential, Gamma, Normal and Chi square. Linear algebra : Review of matrix operations, vector and vector spaces, linear mapping. (Chapter - 9)
