MA2111-MATHEMATICS – I |
MATRICES |
Characteristic equation – Eigen values and eigen vectors of a real matrix – Properties – Cayley-Hamilton theorem (excluding proof) – Orthogonal transformation of a symmetric matrix to diagonal form – Quadratic form – Reduction of quadratic form to canonical form by orthogonal transformation. |
THREE DIMENSIONAL ANALYTICAL GEOMETRY |
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. |
DIFFERENTIAL CALCULUS |
Curvature in Cartesian co-ordinates – Centre and radius of curvature – Circle of curvature – Evolutes – Envelopes – Evolute as envelope of normals. |
FUNCTIONS OF SEVERAL VARIABLES |
Partial derivatives – Euler’s theorem for homogenous functions – Total derivatives – Differentiation of implicit functions – Jacobians – Taylor’s expansion – Maxima and Minima – Method of Lagrangian multipliers. |
MULTIPLE INTEGRALS |
Double integration – Cartesian and polar coordinates – Change of order of integration – Change of variables between Cartesian and polar coordinates – Triple integration in Cartesian co-ordinates – Area as double integral – Volume as triple integral |
REFERENCE |
Text Books |
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). |
Reference Books |
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”,
3rd Edition, Narosa Publishing House Pvt. Ltd., (2007). |