NOTES
UNIT 1:
Module 1: Numerical Methods – 1: (8 hours): Solution of polynomial and transcendental equations – Bisection method, Newton-Raphson method and Regula-Falsi method. Finite differences, Relation between operators, Interpolation using Newton’s forward and backward difference formulae. Interpolation with unequal intervals: Newton’s divided difference and Lagrange’s formulae.
UNIT 2:
Module 2: Numerical Methods – 2: (6 hours): Numerical Differentiation, Numerical integration: Trapezoidal rule and Simpson’s 1/3rd and 3/8 rules. Solution of Simultaneous Linear Algebraic Equations by Gauss’s Elimination, Gauss’s Jordan, Crout’s methods, Jacobi’s, Gauss-Seidal, and Relaxation method.,
UNIT 3:
Module 3: Numerical Methods – 3: (10 hours): Ordinary differential equations: Taylor’s series, Euler and modified Euler’s methods. RungeKutta method of fourth order for solving first and second order equations. Milne’s and Adam’s predicator-corrector methods. Partial differential equations: Finite difference solution two dimensional Laplace equation and Poission equation, Implicit and explicit methods for one dimensional heat equation (BenderSchmidt and Crank-Nicholson methods), Finite difference explicit method for wave equation.
UNIT 4:
Module 4: Transform Calculus: (8 hours): Laplace Transform, Properties of Laplace Transform, Laplace transform of periodic functions. Finding inverse Laplace transform by different methods, convolution theorem. Evaluation of integrals by Laplace transform, solving ODEs by Laplace Transform method, Fourier transforms.
UNIT 5:
Module 5: Concept of Probability: (8 hours): Probability Mass function, Probability Density Function, Discrete Distribution: Binomial, Poisson’s, Continuous Distribution: Normal Distribution, Exponential Distribution.
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