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BT-401 · Mathematics-III/Official Syllabus

Mathematics-III (BT-401) - Official Syllabus

1
Unit 1

Module – 1 : Numerical Methods

  • 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.
2
Unit 2

Module – 2 : Numerical Methods

  • 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.
3
Unit 3

Numerical Methods

  • Ordinary differential equations:Taylor’s series
  • Euler and modified Euler’s methods.
  • Runge Kutta 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 Poisson equation
  • Implicit and explicit methods for one dimensional heat equation (BenderSchmidt and Crank-Nicholson methods)
  • Finite difference explicit method for wave equation.
4
Unit 4

Module – 4 : Transform 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.
5
Unit 5

Module – 5 : Concept of Probability

  • Probability Mass function Probability Density Function
  • Discrete Distribution: Binomial
  • Poisson’s Continuous
  • Distribution:Normal Distribution Exponential Distribution.
6
Unit 6

== END OF UNITS==

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