**UNIT 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.

**UNIT II 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.

**UNIT III DIFFERENTIAL CALCULUS**

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**

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**

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”, 40th

Edition, Khanna Publications,Delhi, (2007).

REFERENCES:

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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