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# NOTE:

MODULE 1

Topics Included: Algebraic and Transcendental Equations: General iterative method, rates of convergence, Secant method, Newton, Raphson method System of non-linear equations by Newton’s method.

Videos to Watch: According to the playlist 1.1 to 1.6  MODULE 2

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.

Videos to Watch: According to the playlist 2.1 to 2.6  MODULE 3

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.

Videos to Watch: According to the playlist 3.1 to 3.5  MODULE 4

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.

Videos to Watch: According to the playlist 4.1 to 4.5  MODULE 5

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.

Videos to Watch: According to the playlist 5.1 to 5.11  MODULE 6

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  MODULE 7

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.

Videos to Watch: According to the playlist 7.1 to 7.4  MODULE 8

Topics Included: Contemporary Issues: Industry Expert Lecture  