System Modelling Techniques - II (ICT-110), formerly known as Applied Mathematics II (BS-112), covers probability and statistics, complex analysis and contour integration, Laplace transforms and Fourier analysis, and partial differential equations with engineering applications.
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Probability concepts, conditional probability, Bayes' theorem, discrete and continuous random variables, probability distributions (Binomial, Poisson, Normal), mathematical expectation and variance, correlation and regression, sampling distributions, confidence intervals, hypothesis testing, and engineering applications.
Complex functions, analytic functions, Cauchy-Riemann equations, harmonic functions and Laplace equation, exponential, trigonometric, hyperbolic and logarithmic functions, Euler's formula, De Moivre's theorem, general power and principal value, singularities and zeros, line integrals, Cauchy's integral theorem and formula, Taylor and Laurent series, residue theorem, and evaluation of definite real integrals using residues.
Laplace transforms: definition, properties, transforms of derivatives and integrals, shifting theorems, unit step function, Dirac delta function, inverse Laplace transforms, convolution theorem, solution of ordinary differential equations; Fourier analysis: Fourier series, functions of arbitrary period, half-range expansions, Sturm-Liouville problems, introduction to Fourier transforms and engineering applications.
Basic concepts of partial differential equations, wave equation, heat equation, method of separation of variables, D'Alembert's solution, Laplace equation in two dimensions, boundary value problems, Fourier series solutions, and engineering applications.