MA8151 MATHEMATICS Syllabus Anna University 1st Semester

MA8151                     MATHEMATICS – I                                                   L T P C
            (Common to all branches of B.E. / B.Tech. Programmes)            3 1 0 4

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
Eigenvalues and Eigenvectors of a real matrix – Characteristic equation – Properties of eigenvalues and eigenvectors – Cayley-Hamilton Theorem – Diagonalization of matrices – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms.
UNIT II INFINITE SERIES 9+3
Sequences – Convergence of series – General properties – Series of positive terms – Tests of convergence (Comparison test, Integral test, Comparison of ratios and D‟Alembert‟s ratio test) – Alternating series – Series of positive and negative terms – Absolute and conditional convergence – Power Series – Convergence of exponential, logarithmic and Binomial Series.
UNIT III FUNCTIONS OF SEVERAL VARIABLES 9+3
Limits and Continuity – Partial derivatives – Homogeneous functions and Euler‟s theorem – Total derivative – Differentiation of implicit functions – Change of variables –Jacobians – Partial differentiation of implicit functions – Taylor‟s series for functions of two variables – Errors and approximations – Maxima and minima of functions of two variables – Lagrange‟s method of undetermined multipliers.
UNIT IV IMPROPER INTEGRALS 9+3
Improper integrals of the first and second kind and their convergence – Evaluation of integrals involving a parameter by Leibnitz rule – Beta and Gamma functions – Properties – Evaluation of integrals using Beta and Gamma functions – Error functions.
UNIT V MULTIPLE INTEGRALS 9+3
Double integrals – Change of order of integration – Double integrals in polar coordinates – Area enclosed by plane curves – Triple integrals – Volume of Solids – Change of variables in double and triple integrals – Area of a curved surface.
TOTAL : 60 PERIODS
TEXT BOOKS:
1. Grewal B.S., “Higher Engineering Mathematics”, Khanna Publishers, New Delhi, 41st Edition, 2011.
2. Ramana B.V., “Higher Engineering Mathematics”, Tata McGraw Hill Co. Ltd., New Delhi, 11th Reprint, 2010.
REFERENCES:
1. Jain R.K. and Iyengar S.R.K., “Advanced Engineering Mathematics”, Narosa Publications, New Delhi, 3rd Edition, 2007.
2. Bali N., Goyal M. and Watkins C., “Advanced Engineering Mathematics”, Firewall Media (An imprint of Lakshmi Publications Pvt., Ltd.,), New Delhi, 7th Edition, 2009.
3. Greenberg M.D., “Advanced Engineering Mathematics”, Pearson Education, New Delhi, 2nd Edition, 5th Reprint, 2009.
4. Peter V.O‟Neil, “Advanced Engineering Mathematics”, Cengage Learning India Pvt., Ltd, New Delhi, 2007.

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