Periodic functions, Dirichlet’s condition. Fourier series expansion of functions with period and with arbitrary period: periodic rectangular wave, Half-wave rectifier, rectangular pulse, Saw tooth wave. Half-range Fourier series. Triangle and half range expansions, Practical harmonic analysis, variation of periodic current.(8 hours) (RBT Levels: L1, L2 and L3)

Infinite Fourier transforms, Fourier cosine and sine transforms, Inverse Fourier transforms, Inverse Fourier cosine and sine transforms, discrete Fourier transform (DFT), Fast Fourier transform (FFT). (8 hours) (RBT Levels: L1, L2 and L3)

Definition, Z-transforms of basic sequences and standard functions. Properties: Linearity, scaling, first and second shifting, multiplication by n. Initial and final value theorem. Inverse Z- transforms. Application to difference equations. (8 hours) (RBT Levels: L1, L2 and L3)

Higher-order linear ODEs with constant coefficients - Inverse differential operator, problems.Linear differential equations with variable Coefficients-Cauchy’s and Legendre’s differential equations–Problems. Application of linear differential equations to L-C circuit and L-C-R circuit.(8 hours) (RBT Levels: L1, L2 and L3)

Principles of least squares, Curve fitting by the method of least squares in the form , , and . Correlation, Coefficient of correlation, Lines of regression, Angle between regression lines, standard error of estimate, rank correlation. (RBT Levels: L1, L2 and L3)(8 hours)

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