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.

Broad range of numerical methods for solving mathematical problems that arise in science and engineering.

approximate a function using various interpolation techniques, numerical integration.

derive appropriate numerical methods to solve linear systems of equations.

to find the numerical solution of initial value problems and boundary value problems

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.

K. E. Atkinson, Introduction to Numerical Analysis, John Wiley , 2nd Edition.

R. L. Burden, J. Douglas Faires, Numerical Analysis, Cengage Learning.

C. F. Gerald and P. O. Wheatley, Applied Numerical Analysis, Pearson Education India , 2007.

Erwin Kreyszig, Advanced Engineering Mathematics, Wiley 10th edition.