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BT-301 · Mathematics-III/Official Syllabus

Mathematics-III (BT-301) - Official Syllabus

1
Unit 1

MODULE-1 :Numerical 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.
2
Unit 2

MODULE-2 : Numerical Methods -2 :

  • 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,
  • Relaxation method
3
Unit 3

MODULE-3 : Numerical 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 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 (Bender-Schmidt 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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