Applied Numerical Methods (MAT3005)
Credits : 4
Topics Included: System of Linear Equations and Eigen Value Problems: Gauss –Seidel iteration method. Convergence analysis of iterative methods, LU Decomposition -Tri diagonal system of equations, Thomas algorithm, Eigen values of a matrix by Power and Jacobi methods.
Topics Included: Interpolation: Finite difference operators, Newton’s forward, Newton’s Backward, Central differences, Stirling’s interpolation, Lagrange’s interpolation, Inverse Interpolation, Newton’s divided difference, Interpolation with cubic splines.
Topics Included: Numerical Differentiation and Integration: Numerical differentiation with interpolation polynomials, maxima and minima for tabulated values, Trapezoidal rule, Simpsons 1/3rd and 3/8th rules. Romberg’s method. Two and Three point Gaussian quadrature formula.
Topics Included: Numerical Solution of Ordinary Differential Equations: First and second order differential equations, Fourth order Runge, Kutta method. Adams Bashforth-Moulton predictor-corrector methods. Finite difference solution for the second order ordinary differential equations.
Topics Included: Numerical Solution of Partial Differential Equations: Classification of second order linear partial differential equations, Laplace equation, Gauss-Seidal method, One dimensional heat equation, Schmidt explicit method, Crank-Nicolson implicit method, One dimensional wave equation, Explicit method.
Videos to Watch: According to the playlist 6.1
Topics Included: Vibrational Methods: Introduction to calculus of variations, Definition of functional , Extremals of functional of a single dependent variable and its first derivative, Functional involving higher order derivatives Functional involving several variables Isoperimetric problems, Galerkins method.
Topics Included: Contemporary Issues: Industry Expert Lecture