MA2111 MATHEMATICS – I L T P C
UNIT I MATRICES
12
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
12
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 integral
TOTAL: 60 PERIODS
TEXT BOOK:
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
Delhi, (2007).
REFERENCES:
1. Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill Publishing Company, New Delhi, (2007).2. Glyn James, “Advanced Engineering Mathematics”, 7
(2007).
Edition, Pearson Education,
3. Jain R.K and Iyengar S.R.K,” Advanced Engineering Mathematics”,
rd
3 Edition, Narosa Publishing House Pvt. Ltd., (2007).
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