SYSTEM MODELING TECHNIQUES 2

About the work

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Subject syllabus

Exactly what you would be recording.

**Unit I**
Probability concepts, Conditional probability, Bayes' theorem, Random variables, Discrete and continuous probability distributions, Binomial, Poisson and Normal distributions, Mathematical expectation and variance, Correlation and regression, Sampling distributions, Confidence intervals, Tests of hypotheses for means and proportions, Engineering applications.

**Unit II**
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 (without proof), General power and principal value, Singularities and zeros, Line integrals in the complex plane, Cauchy's integral theorem, Cauchy's integral formula, Taylor and Laurent series, Residue theorem, Evaluation of definite real integrals using residues.

**Unit III**
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.

**Unit IV**
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, Engineering applications.

**Textbooks**