SECTION I
Unit I: Linear Differential Equations (LDE)
Solution of nth order LDE with Constant Coefficients, Method of Variation of Parameters,
Cauchy’s & Legendre’s DE, Solution of Simultaneous & Symmetric Simultaneous DE, Modeling of
Electrical Circuits.
Unit II: Complex Variables
Functions of Complex Variables, Analytic Functions, C-R Equations, Conformal Mapping, Bilinear
Transformation, Cauchy’s Theorem, Cauchy’s Integral Formula, Laurent’s Series, Residue
Theorem.
Unit III: Transforms
Fourier Transform (FT): Complex Exponential Form of Fourier Series, Fourier Integral Theorem,
Sine & Cosine Integrals, Fourier Transform, Fourier Sine and Cosine Transform and their
Inverses, Application to Wave Equation. Introductory Z-Transform (ZT): Definition, Standard
Properties, ZT of Standard Sequences and their Inverses. Solution of Simple Difference
Equations
SECTION II
Unit IV: Statistics and Probability
Measures of Central Tendency, Standard Deviation, Coefficient of Variation, Moments,
Skewness and Kurtosis, Correlation and Regression, Reliability of Regression Estimates.
Theorems and Properties of Probability, Probability Density Function, Probability Distributions:
Binomial, Poisson, Normal and Hypergometric; Test of Hypothesis: Chi-Square test.
Unit V: Vector Differential Calculus
Physical Interpretation of Vector Differentiation, Vector Differential Operator, Gradient,
Divergence and Curl, Directional Derivative, Solenoidal, Irrotational and Conservative Fields,
Scalar Potential, Vector Identities.
Unit VI: Vector Integral Calculus
Line, Surface and Volume integrals, Work-done, Green’s Lemma, Gauss’s Divergence Theorem,
Stoke’s Theorem, Applications to Problems in Electro-Magnetic Fields.
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