MA2111-MATHEMATICS – I Anna Univesity First Year Syllabus ( common to all department)

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).