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# MA8251 ENGINEERING MATHEMATICS – II Lecture Notes Download

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Department | Civil Engineering |

Year | 1st Year |

Semester | 2nd Semester |

University | Anna University |

Regulation | R2017 |

Subject Code | MA8251 |

Subject Name | ENGINEERING MATHEMATICS – II |

Download File | MA8251 ENGINEERING MATHEMATICS – II Lecture Notes, Books, Important 2 Marks Question and Answers, 16 Mark Question with Answers, Syllabus & Question Bank |

## MA8251 ENGINEERING MATHEMATICS – II Syllabus

UNIT I MATRICES

Eigenvalues and Eigenvectors of a real matrix – Characteristic equation – Properties of Eigenvalues and Eigenvectors – Cayley-Hamilton theorem – Diagonalization of matrices – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms.

UNIT II VECTOR CALCULUS

Gradient and directional derivative – Divergence and curl – 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 III ANALYTIC FUNCTIONS

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 2 1 z z czczw , ,, – Bilinear transformation.

UNIT IV 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 V 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.

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## Download (MA8251 ENGINEERING MATHEMATICS – II Lecture Notes, Books, Important 2 Marks Question and Answers, 16 Mark Question with Answers, Syllabus & Question Bank)

MA8251 ENGINEERING MATHEMATICS – II – Download (**MA8251 ENGINEERING MATHEMATICS – II Lecture Notes, Books, Important 2 Marks Question and Answers, 16 Mark Question with Answers, Syllabus & Question Bank)**

## MA8251 ENGINEERING MATHEMATICS – II Lecture Notes Collection

MA8251 ENGINEERING MATHEMATICS – II Notes ( UNIT 1 – UNIT 5) – Download

## MA8251 ENGINEERING MATHEMATICS – II Question Bank With Answers

MA8251 ENGINEERING MATHEMATICS – II Question Bank With Answers – Download

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## MA8251 ENGINEERING MATHEMATICS – II 2 Mark Question With Answers

MA8251 ENGINEERING MATHEMATICS – II 2 Mark Question With Answers – Download

## MA8251 ENGINEERING MATHEMATICS – II 16 Mark Question With Answers

MA8251 ENGINEERING MATHEMATICS – II 16 Mark Question With Answers – Download