MA6151 MATHEMATICS – I

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MA6151 MATHEMATICS – I

MA6151	MATHEMATICS – I	L T P	C
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OBJECTIVES:

·         To develop the use of matrix algebra techniques this is needed by engineers for practical applications.

·         To make the student knowledgeable in the area of infinite series and their convergence so that he/ she will be familiar with limitations of using infinite series approximations for solutions arising in mathematical modeling.

·         To familiarize the student with functions of several variables. This is needed in many branches of engineering.

·         To introduce the concepts of improper integrals, Gamma, Beta and Error functions which are needed in engineering applications.

·         To acquaint the student with mathematical tools needed in evaluating multiple integrals and their usage.

UNIT I          MATRICES                                                                                                                      9+3

Eigen values and Eigenvectors of a real matrix – Characteristic equation – Properties of eigenvalues and eigenvectors – Statement and applications of Cayley-Hamilton Theorem – Diagonalization of matrices – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms.

UNIT II          SEQUENCES AND SERIES                                                                                         9+3

Sequences: Definition and examples  – Series: Types and Convergence – Series of positive terms –

Tests of convergence: Comparison test, Integral test and D‟Alembert‟s ratio test		– Alternating series –
Leibnitz‟s test – Series of positive and negative terms – Absolute and conditional convergence.
UNIT III	APPLICATIONS OF DIFFERENTIAL CALCULUS	9+3

Curvature in Cartesian co-ordinates – Centre and radius of curvature – Circle of curvature – Evolutes

– Envelopes - Evolute as envelope of normals.

UNIT IV        DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES                                         9+3

Limits and Continuity – Partial derivatives – Total derivative – Differentiation of implicit functions – Jacobian and properties – Taylor‟s series for functions of two variables – Maxima and minima of functions of two variables – Lagrange‟s method of undetermined multipliers.

UNIT V         MULTIPLE INTEGRALS                                                                                               9+3

Double integrals in cartesian and polar coordinates – Change of order of integration – Area enclosed by plane curves – Change of variables in double integrals – Area of a curved surface - Triple integrals

– Volume of Solids.

TOTAL (L:45+T:15): 60 PERIODS

OUTCOMES:

·         This course equips students to have basic knowledge and understanding in one fields of materials, integral and differential calculus.

TEXT BOOKS:

^1.      Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, Eighth Edition, Laxmi

Publications Pvt Ltd., 2011.

^2.     Grewal. B.S, “Higher Engineering Mathematics”, 41^{st Edition, Khanna Publications, Delhi,} 2011.

REFERENCES:

1      Dass, H.K., and Er. Rajnish Verma,” Higher Engineering Mathematics”, S. Chand Private Ltd.,

2011.

2      Glyn James, “Advanced Modern Engineering Mathematics”, 3^rd Edition, Pearson Education, 2012.

3      Peter V. O‟Neil,” Advanced Engineering Mathematics”, 7^thEdition, Cengage learning, 2012.

4    Ramana   B.V,   “Higher   Engineering   Mathematics”,   Tata   McGraw   Hill   Publishing

Company, New Delhi, 2008.

5      Sivarama Krishna Das P. and Rukmangadachari E., “Engineering Mathematics”, Volume I,

Second Edition, PEARSON Publishing, 2011.

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