BE-MECH-Syllabus-MA6151-Mathematics I-Semester1-Anna University

MA6151                                                     MATHEMATICS – I                                                L  T  P C

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 – 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.

OUTCOMES:

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

·          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”,  41st   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”, 3rd  Edition, Pearson Education,

2012.

3.        Peter V. O’Neil,” Advanced Engineering Mathematics”, 7th Edition, 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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