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# ANNA UNIVERSITY CHENNAI MARINE SYLLABUS 2017 REGULATION FOR MA8201 MATHEMATICS FOR MARINE ENGINEERING – II ENGINEERING SYLLABUS 2017 REGULATION

MA8201 MATHEMATICS FOR MARINE ENGINEERING – II SYLLABUS 2017 REGULATION

Anna University MA8201 MATHEMATICS FOR MARINE ENGINEERING – II SYLLABUS 2017 Regulation has been revised for the Students who joined in the academic year 2017-2018. So revised syllabus for Anna University Chennai Electrical and electronics engineering syllabus 2017 Regulation is given below. you can download MA8201 MATHEMATICS FOR MARINE ENGINEERING – II Regulation 2017 2nd Semester eee Syllabus from the below link. Syllabus 2017 regulation for 1st 2nd 3rd 4th 5th 6th 7th 8th Semester will be updated shortly and same can be downloaded year as soon as University announces. Anna University 1st year Syllabus Regulation 2017 is given below. MA8201 Syllabus for Regulation 2017 Students can be downloaded here.

MA8201 MATHEMATICS FOR MARINE ENGINEERING – II                               L T P C
4 0 0 4

OBJECTIVES :

This course is designed to cover topics such as Ordinary Differential Equations, Vector Calculus,
Complex Analysis and Laplace Transform. Ordinary Differential Equations is one of the powerful tools
to handle practical problems arising in the field of engineering. Vector calculus can be widely used for
modeling the various laws of physics. The various methods of complex analysis and Laplace
transforms can be used for efficiently solving the problems that occur in various branches of engineering disciplines.

## UNIT I ORDINARY DIFFERENTIAL EQUATIONS – FIRST ORDER AND APPLICATIONS                            12

Definition – Order and degree – Formation of differential equation – Solution of first order, first degree equations in variable separable form, homogeneous equations, other substitutions – Equations reducible to homogeneous and exact differential equations – Equations reducible to exact Integration – Factor – Linear differential equation of first order first degree, reducible to linear – Applications to electrical circuits and orthogonal trajectories

## UNIT II ORDINARY DIFFERENTIAL EQUATIONS – HIGHER ORDER AND APPLICATIONS                        12

Higher (nth) order linear differential equations – Definition and complementary solution – Methods of obtaining particular integral – Method of variation of parameters – Method of undetermined coefficients – Cauchy‟s homogeneous linear differential equations and Legendre‟s equations – System of ordinary differential equations – Simultaneous equations in symmetrical form – Applications to deflection of beams, struts and columns – Applications to electrical circuits and coupled circuits

## UNIT III VECTOR CALCULUS                                       12

Gradient – Divergence and curl – Directional derivative – Irrotational and solenoidal vector fields – Vector integration – Green‟s theorem in a plane, Gauss divergence theorem and Stokes‟ theorem (excluding proofs) – Simple applications involving cubes and rectangular parallelopipeds.

## UNIT IV ANALYTIC FUNCTIONS                                   12

Functions of a complex variable – Analytic functions – Necessary conditions – Cauchy – Riemann equation and sufficient conditions (excluding proofs) – Harmonic and orthogonal properties of analytic function – Harmonic conjugate – Construction of analytic functions – Conformal mapping:W=Z+C,CZ,1/Z,and bilinear transformation.

## UNIT V LAPLACE TRANSFORM                                  12

Laplace transform – Conditions for existence – Transform of elementary functions – Basic properties – Transform of derivatives and integrals – Transform of unit step function and impulse functions – Transform of periodic functions – Definition of inverse Laplace transform as contour integral – Convolution theorem (excluding proof) – Initial and final value theorems – Solution of linear ODE of second order with constant coefficients using Laplace transformation techniques.

TOTAL : 60 PERIODS

OUTCOMES :
After successfully completing the course, the student will have a good understanding of the following
topics:

• Apply various techniques in solving differential equations.
• Gradient, divergence and curl of a vector point function and related identities.
• Evaluation of line, surface and volume integrals using Gauss, Stokes and Green‟s theorems and their verification.
• Analytic functions, conformal mapping and complex integration.
• Laplace transform and inverse transform of simple functions, properties, various related theorems and application to differential equations with constant coefficients.

TEXT BOOKS :
1. Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, 9th Edition, Laxmi Publications (p) Ltd., 2014.
2. Grewal. B.S, “Higher Engineering Mathematics”, 43rd Edition, Khanna Publications, Delhi, 2014.

REFERENCES :
1. Jain R.K and Iyengar S.R.K, “Advanced Engineering Mathematics”, 3rd Edition, Narosa Publishing House Pvt. Ltd., 2007.
2. James, G., “Advanced Engineering Mathematics”, 3rd Edition, Pearson Education, 2007.
3. Kreyszig Erwin, “Advanced Engineering Mathematics”, 10th Edition, John Wiley, India, 2016.
4. Ramana B.V, “Higher Engineering Mathematics”, McGraw Hill Education Pvt. Ltd., New Delhi, 2016.

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