Course

UNIT 1Modelling, Computers and Error Analysis: Mathematical Modelling, Programming and Software, Approximations and Round off errors, Truncation errors and the Taylor series.UNIT 2Algebraic Equations and Curve Fitting: Bracketing Methods, Open Methods, Roots of Polynomials, Gauss Elimination, LU Decomposition and Matrix Inversion, Special Matrices and Gauss-Seidel, Least- Squares Regression, Interpolation, Fourier ApproximationsUNIT 3Numerical Integration and Differentiation: The Trapezoidal Rule, Simpson’s Rules, Open Integration Formulas, Multiple Integrals, Gauss Quadrature, Improper Integrals, Richardson Extrapolation, Derivatives of Unequally Spaced Data, Derivatives and Integrals for Data with Errors, Partial DerivativesUNIT 4Ordinary Differential Equations: Euler’s Method, Runge-Kutta Methods, System of Equations, Stiffness, Multistep Methods, General Methods for Boundary-Value Problem, Eigenvalue ProblemsUNIT 5Partial Differential Equations: The Laplace Equation, Solution Technique, Boundary Conditions, The Control Volume Approach, The Heat Conduction Equation, Explicit Methods, Parabolic Equations in Two Spatial Dimensions

Course Objectives: This course delves into a broad array of topics centered on numerical methods and their applications, spanning mathematical modeling, algebraic equation solving, curve fitting, numerical integration, as well as ordinary and partial differential equations.Course outcomes:At the end of the that students can expect after completing this course:CO1: Model real-world problems using mathematical and computational methods, understanding the inherent errors in numerical computations.CO2: Analyze and solve ordinary and partial differential equations using various numerical techniques.CO3: Perform curve fitting, interpolation, and regression analyses to interpret and model data effectively.CO4: Apply learned techniques to a variety of scientific and engineering applications, including computational fluid dynamics, heat conduction, and other physical simulations.

Text Book1. Steven Chapra, Raymond Canale, Numerical Methods for Engineers, 7th Ed., McGraw-Hill Higher Education, 2015.Reference Books 1. V. Rajaraman, Computer Oriented Numerical Methods, PHI LEARNING PVT LTD, 2016.