Numerical and Statistical Methods Syllabus

Unit	Details
I	Mathematical Modeling and Engineering Problem Solving: Simple Mathematical Model, Conservation Laws and Engineering Problems Approximations and Round-Off Errors: Significant Figures, Accuracy and Precision, Error Definitions, Round-Off Errors Truncation Errors and the Taylor Series: The Taylor Series, Error Propagation, Total Numerical Errors, Formulation Errors and Data Uncertainty
II	Solutions of Algebraic and Transcendental Equations: The Bisection Method, The Newton-Raphson Method, The Regula-falsi method, The Secant Method Interpolation: Forward Difference, Backward Difference, Newton’s Forward Difference Interpolation, Newton’s Backward Difference Interpolation, Lagrange’s Interpolation.
III	Solution of simultaneous algebraic equations (linear) using iterative methods: Gauss-Jordan Method, Gauss-Seidel Method. Numerical differentiation and Integration: Numberical differentiation, Numerical integration using Trapezoidal Rule, Simpson’s 1/3rd and 3/8th rules Numerical solution of 1st and 2nd order differential equations: Taylor series, Euler’s Method, Modified Euler’s Method, Runge-Kutta Method for 1st and 2 nd Order Differential Equations.
IV	Least-Squares Regression: Linear Regression, Polynomial Regression, Multiple Linear Regression, General Linear Least Squares, Nonlinear Regression Linear Programming: Linear optimization problem, Formulation and Graphical solution, Basic solution and Feasible solution.
V	Random variables: Discrete and Continuous random variables, Probability density function, Probability distribution of random variables, Expected value, Variance. Distributions: Discrete distributions: Uniform, Binomial, Poisson, Bernoulli, Continuous distributions: uniform distributions, exponential, (derivation of mean and variance only and state other properties and discuss their applications) Normal distribution state all the properties and its applications

Numerical and Statistical Methods Practicals

Practical No	Details
1	Iterative Calculation
a	Program for iterative calculation
b	Program to calculate the roots of a quadratic equation using the formula.
c	Program to evaluate 𝑒𝑥 using infinite series
2	Solution of algebraic and transcendental equations:
a	Program to solve algebraic and transcendental equation by bisection method.
b	Program to solve algebraic and transcendental equation by false position method.
c	Program to solve algebraic and transcendental equation by Secant method.
d	Program to solve algebraic and transcendental equation by Newton Raphson method.
3	Interpolation
a	Program for Newton’s forward interpolation
b	Program for Newton’s backward interpolation
c	Program for Lagrange’s interpolation
4	Solving linear system of equations by iterative methods
a	Program for solving linear system of equations using Gauss Jordan method.
b	Program for solving linear system of equations using Gauss Seidel method
5	Numerical Differentiation
a	Programing to obtain derivatives numerically.
6	Numerical Integration
a	Program for numerical integration using Trapezoidal rule
b	Program for numerical integration using Simpson’s 1/3rd rule.
c	Program for numerical integration using Simpson’s 3/8th rule.
7	Solution of differential equations
a	Program to solve differential equation using Euler’s method
b	Program to solve differential equation using modified Euler’s method
c	Program to solve differential equation using Runge-kutta 2nd order and 4th order methods.
8	Regression
a	Program for Linear regression.
b	Program for Polynomial Regression
c	Program for multiple linear regression
d	Program for non-linear regression
9	Random variables and distributions
a	Program to generate random variables.
b	Program to fit binomial distribution.
c	Program to fit Poisson distribution.
10	Distributions
a	Program for Uniform distribution.
b	Program for Bernoulli distribution
c	Program for Negative binomial distribution

Numerical and Statistical Methods Reference Books