## MA3201 - MATHEMATICS FOR MARINE ENGINEERING – II (Syllabus) 2021-regulation Anna University

MA3201 MATHEMATICS FOR MARINE ENGINEERING – II  LPTC
4004

COURSE OBJECTIVES:
• To provide the required skill to apply the concepts of ordinary differential equations.
• To provide the required skill to apply higher order differential equations in marine applications.
• To provide the required skill to apply vector calculus.
• To provide the required skill to apply complex variables.
• To provide the required skill to apply Laplace transformation in marine engineering problems.

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

COURSE OUTCOMES: Upon successful completion of the course, students should be able to:
• Apply the concepts of ordinary differential equations.
• Apply higher order differential equations in marine applications.
• Apply vector calculus.
• Apply complex variables.
• Apply Laplace transformation in marine engineering problems.
• The basic and fundamental knowledge gained by the students in the application of ordinary differential equations vector fields and transformations will be applied by them in the process field related to marine engineering.

TEXT BOOKS:
1. Grewal. B.S, “Higher Engineering Mathematics”, 44th Edition, Khanna Publications, New Delhi, 2018.th
2. Kreyszig E, “Advanced Engineering Mathematics”, 10 Edition, John Wiley, India, 2016.

REFERENCES:
1. Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, 10thEdition, Laxmi Publications (p) Ltd., 2015.
2. Jain R.K and Iyengar S.R.K, “Advanced Engineering Mathematics”, 5thEdition, Narosa Publishing House Pvt. Ltd., 2016.
3. James, G., “Advanced Engineering Mathematics”, 5thEdition, Pearson Education, 2016.
4. Ramana B.V, “Higher Engineering Mathematics”, McGraw Hill Education Pvt. Ltd., New Delhi, 2016.