Week 1: Introduction to Numerical analysis, Importance of error and their calculations, Examples
Week 2: Root Finding Method of non-linear equations, Bisection Method, Newton Raphson Method,
Secant method, Regula- Falsi method, Practical examples.
Week 3: Curve fitting method, linear and non-linear fitting, Linear interpolation, Lagrange interpolation
method, Newton Interpolation formula, Practical examples.
Week 4: Numerical differentiation, central difference methods, higher order derivatives, errors, practical examples.
Week 5: Numerical integration, Simpson’s 1/3 rd rule, Simpson’s 3/8 th rule, local and global error analysis
Week 6: Eigenvalue problems, Heun’s method, Euler’s method, Runge Kutta Method, Gerschgorin disc theorem ,
Jacobi method, Practical examples
Week 7: Simulation Techniques, Random numbers, Monte Carlo Method, Importance Sampling, Metropolis Algorithm,
Heat- bath algorithm, practical Examples
Week 8: Molecular dynamics, interaction and forces in molecular systems, MD and Verlet algorithm, correlations,