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.
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. 8
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. 8
Integration of standard forms by substitution and by parts. The 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 in sin x and Cos nx. The rules of Guldinus. Theorems of parallel and perpendicular axes. Second moments of area and moments of inertia of a rectangular and circular laminas
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
1. Ramana B.V, Higher Engineering Mathematics, Tata McGraw Hill Publishing Company, New Delhi, 2007. 2. Glyn James, Advanced Engineering Mathematics, 7 th Edition, Pearson Education, 2007. 3. Jain R.K and Iyengar S.R.K, Advanced Engineering Mathematics, 3 rd Edition, Narosa Publishing House Pvt. Ltd., 2007.
1. Bali N. P and Manish Goyal, Text book of Engineering Mathematics, Third edition, Laxmi Publications(p) Ltd.,2008. 2. Grewal. B.S, Higher Engineering Mathematics, 40 th Edition, Khanna Publications, Delhi, 2007. 3. William Embleton and Leslie Jackson, Mathematics for Engineers Vol- I, 7 th Edition, Reed?s Marine Engineering Serires, Thomas Reed Publications, 1997.