MA2111 Mathematics I - SUBJECT CATALOG

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SYLLABUS:

MA2111                                       MATHEMATICS – I                                  3     1   0   4

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”,   40th edition

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”,

rd

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