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
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”, 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”,
3
2012.
3 Peter V. O‟Neil,” Advanced Engineering Mathematics”, 7
Company, New Delhi, 2008.
rd
Edition, Pearson Education,
5 Sivarama Krishna Das P. and Rukmangadachari E., “Engineering Mathematics”, Volume I,
Second Edition, PEARSON Publishing, 2011.
th
Edition, Cengage learning, 2012.
4 Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill Publishing
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