## MA3101 Syllabus - Mathematics for Marine Engineering – I 2021 Regulation Anna University

MA3101

MATHEMATICS FOR MARINE ENGINEERING – I

LTPC

4004

COURSE OBJECTIVES:
• To provide the required knowledge on fundamentals of geometry integrals and integral calculus for engineering applications.
• To understand the basic concepts of differentiation.
• To apply the concept of partial differentiation for the functions of several variables.
• To understand the basic concepts of integration.
• To apply the integration concepts in double and triple integrations.

UNIT I

THREE DIMENSIONAL ANALYTICAL GEOMETRY

12

Equation of lines and planes in three dimensional space -Equation of a sphere – Plane section of a sphere – Tangent plane – Equation of a cone – Right circular cone – Equation of a cylinder – Right circular cylinder.

UNIT II

DIFFERENTIAL CALCULUS

12

Differentiation of algebraic, circular, exponential and logarithmic functions, products, quotient functions of a function and simple implicit functions - Successive differentiation : Introduction and notation - nth order derivatives of standard functions - nth order derivatives using (a) Trigonometric identities and standard functions (b) Partial fractions - Leibnitz's theorem - Maclaurin’s theorem - Taylor’s theorem - Indeterminate forms and L’Hospital’s rule - Maxima and Minima of one variable functions – Concavity - Curve tracing of cartesian curves.

UNIT III

FUNCTIONS OF SEVERAL VARIABLES

12

Limits and continuity - Partial derivatives – Definition - Geometrical interpretation and rules of partial differentiation - Higher order partial derivatives - Homogeneous functions - Euler’s theorem for homogenous functions – Total derivatives and chain rules - Differentiation of implicit functions and composite functions - Errors and approximations - Maxima and Minima - Method of Lagrangian multipliers.

UNIT IV

INTEGRAL CALCULUS

12

Integration of standard forms by substitution and by parts - Definite integral as the limit of a sum - Application of integration to area under curve - Volume of revolution - First moment of area and the position of a centroid of an area - Work done by variable forces - Mean values, Root mean square values of sin nx and cos nx. Rules of Guldinus -Theorems of parallel and perpendicular axes - Second moments of area and moments of inertia of a rectangular and circular laminas.

UNIT V

MULTIPLE INTEGRALS

12

Double and triple integrals – Cartesian coordinates - Region of integration and change of order of integration - Spherical polar and cylindrical coordinates - Theorems of parallel and perpendicular axes - Second moments of area and moments of inertia of a rectangular and circular laminas - Applications - Area, Volume, Mass of wire, Lamina and solid - Centre of Gravity of wire, lamina and solid - Moment of inertia using multiple integrals.

TOTAL : 60 PERIODS

COURSE OUTCOMES: Upon successful completion of the course, students should be able to:
• Understand the fundamentals of geometry integrals and integral calculus for engineering applications.
• Appreciate for having the basic concepts of differentiation.
• Understand to apply the concept of partial differentiation for the functions of several variables.
• BUnderstand the basic concepts of integration and how to apply the integration concepts in double and triple integrations.
• The basic concepts of analytical geometry and differential and integral calculus learnt by the Students will be applied to marine engineering.

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

REFERENCES:
1. Bali N. P and Manish Goyal, “A Text Book of Engineering Mathematics”, 9th Edition, Laxmi Publications Ltd., 2014.
2. Embleton, W. and Jackson, L., “Mathematics for Engineers”, Vol - I, 7th Edition, Reed’s Marine Engineering Series, Thomas Reed Publications, 1997.
3. Jain R.K and Iyengar S.R.K,” Advanced Engineering Mathematics”, 5thEdition, Narosa Publishing House Pvt. Ltd., 2016.
4. James, G., “Advanced Engineering Mathematics”, 7 th Edition, Pearson Education, 2007.
5. Ramana, B.V, “Higher Engineering Mathematics”, McGraw Hill Education Pvt. Ltd, New Delhi, 2016.