Fourier series and practical harmonic analysis: Periodic functions, Dirichlet’s condition. Fourier series expansion of functions with period 2π 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.

Infinite Fourier Transforms: Infinite Fourier transforms, Fourier cosine and sine transforms, Inverse Fourier transforms, Inverse Fourier cosine and sine transforms, discrete Fourier transform (DFT), Fast Fourier transform.

Z Transforms: 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.

Ordinary Differential Equations of Higher Order: 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.

Curve fitting, Correlation, and Regressions: Principles of least squares, Curve fitting by the method of least squares in the form y = a + bx, y = a + bx + c * x ^ 2 and y = axb. Correlation, Coefficient of correlation, Lines of regression, Angle between regression lines, standard error of estimate, rank correlation.