MA6151 ENGINEERING MATHEMATICS – I  SYLLABUS (REGULATION 2013) AFFILIATED TO ANNA UNIVERSITY (SEMESTER 1)

UNIT I: MATRICES 

(MA6151) Eigen values and Eigen vectors of a real matrix – Characteristic equation – Properties of eigenvalues and eigen vectors. – 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.