MATHEMATICS – I SYLLABUS- ANNA UNIVERSITY MADURAI

 MATHEMATICS – I  SYLLABUS(10AMA01)

ANNA UNIVERSITY MADURAI

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UNIT I MATRICES


Characteristic equation – Eigen values and Eigen vectors of a real matrix – Properties ofEigen values – Problem solving using Cayley-Hamilton theorem (excluding proof) –Similarity transformation - Orthogonal transformation of a symmetric matrix to diagonalform – Quadratic form - Orthogonal reduction to its canonical form.



UNIT II THREE DIMENSIONAL GEOMETRY


Angle between two lines – Coplanar lines – Shortest distance between skew lines –Equation of a sphere – Plane section of a sphere – Tangent plane – Orthogonal spheres –Equation of a cone – Right circular cone – Equation of a cylinder – Right circular
cylinder


UNIT III DIFFERENTIAL CALCULUS


Curvature - Cartesian and Parametric Co-ordinates – Centre and radius of curvature –Circle of curvature – Envelopes - Evolutes – Evolute as envelop of normals.


UNIT IV FUNCTIONS OF SEVERAL VARIABLES


Partial derivatives – Euler’s theorem for homogeneous functions – Total derivatives –Differentiation of implicit functions – Jacobians –– Maxima / Minima for functions oftwo variables – Method of Lagrange’s multipliers - Taylor’s expansion


UNIT V ORDINARY DIFFERENTIAL EQUATIONS (ODE)


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


TEXT BOOKS:


1. “Higher Engineering Mathematics”, Grewal, B.S., Thirty Eighth Edition, KhannaPublishers, New Delhi, 2005.


2. “Engineering Mathematics”, Venkataraman.M.K., Volume I and II Revisedenlarged Fourth Edition, The National Publishing Company, Chennai, 2004.


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