Numerical solutions for second-order ODEs using Runge-Kutta and Milne’s methods. Special Functions : Series solutions for Bessel’s differential equation (leading to Legendre’s differential equation (leading to ), including properties like Rodrigue’s formula and orthogonality. Module III: Complex Variables Analytic functions, Cauchy-Riemann equations (Cartesian and Polar forms), and harmonic properties. Complex integration: Cauchy’s Theorem Cauchy’s Integral Formula , and Residue Calculus. Conformal transformations such as , and bilinear transformations. Module IV: Probability Distributions
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Understanding sampling, hypothesis testing, and stochastic processes essential for data-driven engineering. Special Functions: Cauchy-Riemann equations (Cartesian and Polar forms)