MCSE-004 Numerical and Statistical Computing
(3 Credits)
Syllabus
Block-1
Numerical Computing-I
Unit 1
Floating Point Arithmetic and Errors
·
Floating Point Representation
·
Sources of Errors
·
Propagated Errors
Unit 2
Solution of Non-Linear Equations
·
Bisection Method
·
Regula-Falsi Method
·
Secant Method
·
Newton-Raphson Method
·
Successive Iteration Method
Unit 3
Solution of Linear Algebraic Equations
Direct Method
·
Gauss Elimination Method (without and with Pivoting)
·
LU-Decomposition Method
Iterative Method
·
Jacobi Method
·
Gauss Seidel Method
·
Successive Over Relaxation Method
Block-2
Numerical Computing-II
Unit 1
Interpolation
·
Differences – Forward and Backward Differences
·
Newton
’s – Forward and Backward Difference
Formulas
·
Lagrange’s Interpolation
Unit 2
Numerical Integration
·
Newton
–
Cotes
Formulas
·
Composite Formulas
·
Gaussian Quadrature
Unit 3
Numerical Solution of ODE
·
Euler’s Method
·
Runge Kutta Method
Block-3
Statistical Computing
Unit 1
Probability Distribution
·
Discrete Distribution
·
Binomial Distribution
·
Poisson Distribution
Continuous Distribution
·
Uniform Distribution
·
Exponential Distribution
·
Normal Distribution
·
Chi-square Distribution
Unit 2
Pseudo Random Number Generation
·
Uniform Distribution
o
Method of Generation (Discrete Case)
o
Inversion Method (Exponential Distribution)
o
Acceptance and Rejection
Unit 3
Regression
·
Linear Regression Model
o
Least Square for Parameter Estimation
o
Goodness-of-Fit
o
Residual Analysis
·
Non-Linear Regression