## March 2, 2010

### MA1101 MATHEMATICS I SYLLABUS

ANNA UNIVERSITY TIRUCHIRAPPALLI -620 024
Regulations 2007 Curriculum SEMESTER I
Common to all B.E. / B.Tech. (Except B.E. Marine Engineering)
MA1101 MATHEMATICS I

UNIT I MATRICES 10
Characteristic equation – Eigen values and Eigen vectors of a real matrix – Properties of
Eigen values – Problem solving using Cayley-Hamilton theorem – Similarity
transformation – Orthogonal transformation of a symmetric matrix to diagonal form –
Quadratic form – Orthogonal reduction to its canonical form.

UNIT II THREE DIMENSIONAL GEOMETRY (9+2)
Angle between two lines – Coplanar lines – Shortest distance between skew lines –
Equation of a sphere – Plane section of a sphere – Tangent plane – Orthogonal Spheres.

UNIT– III DIFFERENTIAL CALCULUS (9+2)

Curvature – Cartesian and Parametric Co-ordinates – Centre and Radius of curvature –
Circle of curvature – Envelopes – Evolutes.

UNIT – IV FUNCTIONS OF SEVERAL VARIABLES (10+2)
Partial derivatives – Euler’s theorem for homogeneous functions – Total derivative –
Differentiation of implicit functions – Jacobians – Maxima / Minima for functions of two
variables – Method of Lagrange’s multipliers – Taylor’s expansion.

UNIT – V ORDINARY DIFFERENTIAL EQUATIONS (ODE) (10+3)

Solution of second and higher order linear ODE with constant coefficients –
Simultaneous first order linear equations with constant coefficients – Linear equations of
second order with variable coefficients – Cauchy’s and Legendre’s linear equations –
Method of variation of parameter.

L + T = 48 + 12 = 60

TEXT BOOK

Grewal, B.S., “Higher Engineering Mathematics”, Thirty eighth Edition, Khanna Publishers, New Delhi, 2005.

REFERENCES
1. Glyn James., “Advanced Modern Engineering Mathematics”, Third Edition, Pearson Education Ltd, New Delhi, 2004.
2. Venkataraman. M. K., “Engineering Mathematics”, Volume I and II Revised enlarged Fourth Edition, The National Publishing Company, Chennai, 2004.
3. Veerarajan. T., “Engineering Mathematics (for first year)”, Fourth Edition, Tata McGraw – Hill Publishing Company Limited, New Delhi, 2005.
4. V. Sundaram, R. Balasubramanian, K.A. Lakshminarayanan, “Engineering Mathematics”, Fifth Edition, Vikas Publishing house Pvt. Ltd., New Delhi, 2006.

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