Numerical & Statistical Methods for SPPU 19 Course (TE - SEM V - MECH- 302041)  (Paperback, Anup Goel, Dr. J. S. Chitode)

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 - 2, 3) Unit 2 : Numerical Solution of Differential Equations Ordinary Differential Equations [ODE] : Taylor series method, Euler Method, Runge-Kutta 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 - 4, 5) Unit 3 : Numerical Integration Numerical Integration (1D) : Trapezoidal rule, Simpson’s 1/3rd Rule, Simpson’s Rule, Gauss Quadrature 2-point and 3-point method. Double Integration : Trapezoidal rule, Simpson’s 1/3rdRule. (Chapter - 6) 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 - 7, 8) 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 - 9) 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 - 10)