# 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

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

th

Edition, Khanna

Publications, Delhi, (2007).

REFERENCES:

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).

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