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Pune University Secon Year Engg ENGINEERING MATHEMATICS – III
Unit I: Linear Differential Equations (LDE) General nth order LDE. Solution of nth order LDE with constant coefficients. PI by variation of parameters. Cauchy’s & Legendre’s DE. Solution of Simultaneous & Symmetric Simultaneous DE. Applications to Electrical circuits. (8 Hrs)
Unit II: Complex Variables Functions of complex variables, Analytic functions, C-R equations, Conformal mapping, Billinear transformation, Residue theorem, Cauchy’s Integral theorem & Cauchy’s Integral formula (without proofs). (8 Hrs)
Unit III: Transforms
Fourier Transform (FT): Fourier Integral theorem. Sine & Cosine Integrals. Fourier Transform, Fourier Cosine Transform, Fourier Sine Transforms and their inverses. Problems on Wave equation.
Introductory Z Transform (ZT): Definition, Std. Properties (without proof), ZT of std. Sequences & Inverse. Solution of simple difference equations. (10 Hrs)
Unit IV: Laplace Transform (LT) Definition of LT, Inverse LT. Properties & theorems. LT of standard functions. LT of some special functions viz. error, 1st order Bessel’s, Periodic, Unit Step, Unit Impulse and ramp. Problems on finding LT & inverse LT. Applications of LT for solving ordinary differential equations. (10 Hrs)
Unit V: Vector Calculus
Vector Differentiation & its physical interpretation. Vector differential operator. Gradient, Divergence & Curl. Directional derivative. Vector identities. (8 Hrs)
Unit VI: Vector Analysis Line, Surface & Volume integrals. Conservative, Irrotational & Solenoidal fields. Scalar potential. Gauss’s, Stoke’s & Green’s theorems (without proofs). Applications to problems in Electromagnetic Fields. (8 Hrs)
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