MA2111 MATHEMATICS – I ANNA UNIVERSITY QUESTION BANK
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.
UNIT II THREE DIMENSIONAL ANALYTICAL GEOMETRY 12
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 III DIFFERENTIAL CALCULUS 12t
Curvature in Cartesian co-ordinates – Centre and radius of curvature – Circle of
curvature – Evolutes – Envelopes – Evolute as envelope of normals.
UNIT IV FUNCTIONS OF SEVERAL VARIABLES 12
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.
UNIT V MULTIPLE INTEGRALS 12
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
TOTAL : 60 PERIODS
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
Publications, Delhi, (2007).
1. Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill Publishing Company, New Delhi, (2007).
2. Glyn James, “Advanced Engineering Mathematics”, 7th Edition, Pearson Education, (2007).
3. Jain R.K and Iyengar S.R.K,” Advanced Engineering Mathematics”,
3rd Edition, Narosa Publishing House Pvt. Ltd., (2007).