Course Details

Subject {L-T-P / C} : MA2005 : Numerical Methods { 3-0-0 / 3}

Subject Nature : Theory

Coordinator : Jugal Mohapatra

Syllabus

Module 1 (7 hours)
Definitions, Sources, Propagation of errors, floating-point arithmetic, and rounding errors. Root finding of nonlinear equations: Bisection method, secant and Regula-Falsi methods, Newton's method, fixed-point iterations.

Module 2 (7 Hours)
Finite differences, Polynomial interpolation, Lagrange, Newton, forward/backward interpolation.

Module 3 (7 Hours)
Numerical integration, trapezoidal, Simpson's rules, Newton-Cotes formula, Gaussian quadrature.

Module 4 (5 hours)
IVP: Euler and modified Euler methods, Runge-Kutta methods.

Module 5 (10 hours)
Numerical methods in linear algebra: Gauss elimination, LU factorization, matrix inversion Linear systems: Solution by iteration Matrix
Eigenvalue problems, Inclusion of matrix Eigenvalues, Eigenvalues by iteration.

Course Objectives

Course Outcomes

CO1: Understand and apply various numerical methods for solving mathematical problems.
CO2: Analyze the accuracy, efficiency, and stability of numerical algorithms.
CO3: Implement numerical methods using programming languages and software tools.
CO4: Students will learn how to apply, analyze, and implement various iterative methods.
CO5: Students will be equipped to handle a wide variety of real-world computational problems involving linear systems of equations, whether in engineering, physics, data science, or other domains.

Essential Reading

Supplementary Reading