Importance of higher-order ordinary differential equations in Electrical & Electronics Engineering applications.
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.
Applications: Application of linear differential equations to L-C circuit and L-C-R circuit.

Self-Study: Finding the solution by the method of undetermined coefficients and method of variation of parameters.

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, Co-efficient of correlation, Lines of regression, Angle between regression lines, standard error of estimate, rank correlation.

Self-study: Fitting of curves in the form y = a e^bx

Periodic functions, Dirchlet’s condition, conditions for a Fourier series expansion, Fourier series of functions with period 2π and with arbitrary period. Half rang Fourier series. Practical harmonic analysis.

Application to variation of periodic current:

Self-study: Typical waveforms, complex form of Fourier series

Infinite Fourier transforms: Definition, Fourier sine, and cosine transform. Inverse Fourier transforms Inverse Fourier cosine and sine transforms. Problems.

Z-transforms: Definition, Standard z-transforms, Damping, and shifting rules, Problems. Inverse z-transform and applications to solve difference equations

Self-study: Convolution theorems of Fourier and z-transforms

Review of basic probability theory, Random variables-discrete and continuous Probability distribution function, cumulative distribution function, Mathematical Expectation, mean and variance, Binomial, Poisson, Exponential and Normal distribution (without proofs for mean and SD) – Problems.

Sampling Theory: Introduction to sampling distributions, standard error, Type-I and Type-II errors. Student’s t-distribution, Chi-square distribution as a test of goodness of fit.

Self-study: Test of hypothesis for means, single proportions only.