Electrical Engineering – EE
Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals,Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives,Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Differential equations: First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.
Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’series, Residue theorem, solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation,Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.
Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.
Fourier transform, Laplace transform, Z-transform.
Electric Circuits and Fields: Network graph, KCL, KVL, node and mesh analysis, transient response of dc and ac networks; sinusoidal steady-state analysis, resonance, basic filter concepts; ideal current and voltage sources,Thevenin’s, Norton’s and Superposition and Maximum Power Transfer theorems, two-port networks, three phase
circuits; Gauss Theorem, electric field and potential due to point, line, plane and spherical charge distributions;Ampere’s and Biot-Savart’s laws; inductance; dielectrics; capacitance.
Signals and Systems:
Representation of continuous and discrete-time signals;...