# MA8251 Engineering Mathematics II Syllabus Notes Question Papers Anna University

## MA8251 Engineering Mathematics II Syllabus Notes Question Papers Question Bank with answers - Anna University 2nd Semester Study materials

**Download Regulation 2017 MA8251 Engineering Mathematics II**** ****Syllabus ****Notes ****Question bank Question papers- ****regulation 2017 2nd Semester**

MA8251 Engineering Mathematics II (M2) study materials for all 5 unit Syllabus Notes, question banks, 2 marks with answers (Part A), 15 marks questions (Part B & Part C), Previous year question papers, model question papers in pdf format have been provided.

Students can make use of the below table to access all study materials for MA8251 Engineering Mathematics II in PDF as well as in word format. Students can also download M2 related PPT's and PDF's which they can use it to prepare for their exams as well as for their taking up their seminar during college hours.

#### MA8251 Engineering Mathematics II Syllabus | MA8251 Syllabus

UNIT I MATRICES

Eigenvalues and Eigen Vectors of a real matrix - Characteristics equation - Properties of Eigenvalues and Eigen vectors - 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 Derivatives - Divergence and Curl - Vector Identities - Ir-rotational and Solenoidal Vector fields - Line Integral over a plane cure - 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 ANALYTICS FUNCTIONS

Analytic functions - Necessary and Sufficient Conditions for analyticity in Cartesian and Polar Co ordinates - Properties - Harmonic Conjugates - Construction of Analytic Function - Conformal mapping - -Mapping by functions W=Z+C, CZ, 1/Z, Z^2 - 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 TRANSFORM

Existence Conditions - Transforms of Elementary functions - Transform of Unit Step Function and Unit Impulse Function - Basic Properties - Shifting teorems - Transforms of Derivatives and Integrals - Initial and Final Value Theorems - Inverse Transforms - Convolution Theorem - Transforms of periodic functions - Application to solution of linear second order ordinary differential equations with constant coefficients.

Eigenvalues and Eigen Vectors of a real matrix - Characteristics equation - Properties of Eigenvalues and Eigen vectors - 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 Derivatives - Divergence and Curl - Vector Identities - Ir-rotational and Solenoidal Vector fields - Line Integral over a plane cure - 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 ANALYTICS FUNCTIONS

Analytic functions - Necessary and Sufficient Conditions for analyticity in Cartesian and Polar Co ordinates - Properties - Harmonic Conjugates - Construction of Analytic Function - Conformal mapping - -Mapping by functions W=Z+C, CZ, 1/Z, Z^2 - 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 TRANSFORM

Existence Conditions - Transforms of Elementary functions - Transform of Unit Step Function and Unit Impulse Function - Basic Properties - Shifting teorems - Transforms of Derivatives and Integrals - Initial and Final Value Theorems - Inverse Transforms - Convolution Theorem - Transforms of periodic functions - Application to solution of linear second order ordinary differential equations with constant coefficients.

**MA8251 Engineering Mathematics II Study Materials**

**Download MA8251 Engineering Mathematics II Syllabus Notes Question Papers Question bank**

MA8251 Study Materials | Download Link |
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MA8251 Syllabus | Click here to download Syllabus |

MA8251 Notes | Click here to download Unit wise Notes |

MA8251 Question Bank | Click here to download Question Bank |

MA8251 Question Papers | Click here to download Question paper |

MA8251 2 marks with Answers (Part A) | Click here to download 2 marks with answers |

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