MA3452 VECTOR calculus AND complex function

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Important questions 
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UNIT -1
1.guass and strokes theorem ****
2.divergence and curl **
3. Greens rarely asked 

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UNIT-4
1.Convolution theorem (8)
2.f(t)=?(8)
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2.application to solution of solution of second order diff equation with ordinary 

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UNIT-2
1.Cartesian and Harmonic function**
2.Bilinear transformation**
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Unit 3
1.Cauchy's residue theorem 

2.Countour integration **
3.Laurent series 
UNIT-5
1.CMethod of variation of parameters**
2.Homogenous equation of Euler’s **and Legendre’s type
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 *These questions are expected for the exams This may or may not be asked for exams .

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Syllabus

I VECTOR CALCULUS

Gradient and directional derivative Divergence and curt Vector identities Irrotational and Solenoidal vector fields Line integral over a plane curve-Surface integral Area of a curved surface Volume integral Green's, Gauss divergence and Stoke's theorems - Verification and application in evaluating line, surface and volume integrals.

UNIT ANALYTIC FUNCTION

Analytic functions Necessary and sufficient conditions for analyticity in Cartesian and polar coordinates Properties Harmonic conjugates Construction of analytic function Conformal mapping-Mapping by functions wzic. az 1-Bilinear transformation.

UNITI COMPLEX INTEGRATION

Line integral-Cauchy's integral theorem Cauchy's integral formula-Taylor's and Laurent's series -Singularities-Residues-Residue theorem-Application of residue theorem for evaluation of real integrals-Use of circular contour and semicircular contour.

UNIT IV LAPLACE TRANSFORMS

Existence conditions Transforms of elementary functions Transform of unit step function and unit impulse function Basic properties-Shifting theorems Transforms of derivatives and integrals. -Initial and final value theorems-Inverse transforms-Convolution theorem-Transform of periodic functions-Application to solution of linear second order ordinary differential equations with constant coefficients.

UNIT V ORDINARY DIFFERENTIAL EQUATIONS

Higher onder linear differential equations with constant coefficients Method of variation of parameters-Homogenous equation of Euler's and Legendre's type-System of simultaneous linear differential equations with constant coefficients Method of undetermined coefficients.

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