### MA6151 Mathematics - I syllabus - Anna university reg-2013 1st semester syllabus

ANNA UNIVERSITY CHENNAI
MA6151 MATHEMATICS – I SYLLABUS
REGULATION - 2013
FIRST SEMESTER SYLLABUS
B.E. / B. Tech. (All Branches except Marine Engineering)

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
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
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
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
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
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: 60 PERIODS

TEXT BOOKS:
• Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, Eighth Edition, Laxmi
Publications Pvt Ltd., (2011).
• Grewal. B.S, “Higher Engineering Mathematics”, 41
st Edition, Khanna Publications, Delhi,
(2011).
REFERENCES:
• Dass, H.K., and Er. Rajnish Verma,” Higher Engineering Mathematics”, S. Chand Private Ltd.,
(2011).
• Glyn James, “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education,
(2012).
• Peter V. O’Neil,” Advanced Engineering Mathematics”, 7th Edition, Cengage learning, (2012).
• Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill Publishing
Company, New Delhi, (2008).
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