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Anna Mathematics II Sem-II
No Units Titles Sub Titles Chapters
1 Unit 1 Differential Equations Method of variation of parameters - Method of undetermined coefficients - Homogenous equation of Euler's and Legendre's type - System of simultaneous linear differential equations with constant coefficients VIEW CHAPTERS
2 Unit 2 Vector Calculus Gradient and directional derivative - Divergence and Curl - Irrotational and Solenoidal vector fields - Line integral over a plane curve - Surface integral and volume integral - Green's, Gauss divergence and Stoke's theorems - Verification and application in evaluating line, surface and volume integrals VIEW CHAPTERS
3 Unit 3 Anaylytic Function Analytic functions - Necessary and sufficient conditions for analyticity - Properties - Harmonic conjugates - Construction of analytic function - Conformal mapping - Mapping by functions 2 1 - Bilinear transformation VIEW CHAPTERS
4 Unit 4 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 with no pole on real axis VIEW CHAPTERS
5 Unit 5 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 ordinary differential equations with constant coefficients VIEW CHAPTERS
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