Modelling, Computers and Error Analysis: Mathematical Modelling, Programming and Software, Approximations and Round off errors, Truncation errors and the Taylor series.

Unit 2

Algebraic 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 Approximations

Unit 3

Numerical 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 Derivatives

Unit 4

Ordinary Differential Equations: Euler’s Method, Runge-Kutta Methods, System of Equations, Stiffness, Multistep Methods, General Methods for Boundary-Value Problem, Eigenvalue Problems

Unit 5

Partial 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

Text Books

1. Steven Chapra, Raymond Canale, Numerical Methods for Engineers, 7th Ed., McGraw-Hill Higher Education, 2015.

References

1. V. Rajaraman, Computer Oriented Numerical Methods, PHI LEARNING PVT LTD, 2016.