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 |