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You are here:Open notes-->Anna-University-->MA2111-Mathematics---I

**MA2111 Mathematics - I**

# How to study this subject

**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

th

Edition, Khanna Publications,

Delhi, (2007). 5

**REFERENCES:**

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”,

3

rd

Edition, Narosa Publishing House Pvt. Ltd., (2007).

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