Syllabus

(10 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. Methods based on 2nd degree as Chebyshev, Mullers

(7 Hours)
Finite differences, Polynomial interpolation, Lagrange, Newton, forward/backward interpolation. Splines, Hermite interpolation

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

(8 hours)
IVP: Euler and modified Euler methods, Runge-Kutta methods. Multi-step methods

(8 hours)
Numerical methods in linear algebra: Solution by iteration methods, Jacobi, Seidel, SOR
Eigenvalue problems, Inclusion of matrix Eigenvalues, Eigenvalues by iteration.

Introduce fundamental concepts of numerical methods and their role in solving mathematical problems where analytical solutions are difficult or impossible

Develop an understanding of error analysis, stability, and convergence of numerical algorithms.

Provide practical skills in applying numerical techniques to problems in algebra, calculus, differential equations, and applied sciences.

Train students to implement numerical algorithms using computational tools (MATLAB/Python).

Explain sources of errors (truncation, round-off) and assess their impact on numerical solutions.

Apply root-finding methods and analyze their convergence.

Use interpolation and approximation techniques (Lagrange, Newton, spline methods) for data fitting and function approximation.

Perform numerical differentiation and integration with appropriate quadrature rules.

Develop and implement numerical algorithms using MATLAB/Python for scientific problems.

R. L. Burden, J. Douglas Faires, Numerical Analysis, Cengage Learning , 2011

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

K. E. Atkinson & W. Han, Theoretical Numerical Analysis: A Functional Analysis Framework, Springer , 2009

S.D. Conte, Carl de Boor, Elementary Numerical Analysis: An Algorithmic Approach Updated with MATLAB, SIAM , 2018