Mathematics-III
BT-301-
Unit 1Numerical Methods – 1
Solution of polynomial and transcendental equations · Bisection method · Newton-Raphson method · 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 · Lagrange's formulae
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Unit 2Numerical Methods – 2
Numerical Differentiation · Numerical integration · Trapezoidal rule · Simpson's 1/3rd rule · Simpson's 3/8 rule · Solution of Simultaneous Linear Algebraic Equations by Gauss's Elimination · Gauss's Jordan · Crout's methods · Jacobi's · Gauss-Seidal · Relaxation method
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Unit 3Numerical Methods – 3
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 predictor-corrector methods · Partial differential equations · Finite difference solution two dimensional Laplace equation · Poisson equation · Implicit and explicit methods for one dimensional heat equation (Bender-Schmidt and Crank-Nicholson methods) · Finite difference explicit method for wave equation
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Unit 4Transform Calculus
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
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Unit 5Concept of Probability
Probability Mass function · Probability Density Function · Discrete Distribution · Binomial · Poisson's · Continuous Distribution · Normal Distribution · Exponential Distribution