Eigen values and Eigenvectors of real matrix-Properties of Eigen values and Eigenvectors- Cayley Hamilton Theorem (statement only) and its applications. Diagonalization of a real symmetric matrix- Quadratic forms - Reduction of quadratic form to canonical form by orthogonal transformation- Nature of the quadratic form.
Basics-Radius of Curvature in Cartesian co-ordinates – Centre and circle of curvature in Cartesian co- ordinates – Evolutes – Envelopes.
Partial derivatives –Total derivatives – Jacobians– Maxima and Minima of functions of two variables – Lagrange’s method of undetermined multipliers.
Homogeneous Linear ODEs with constant coefficients – Linear ODE with variable coefficients - Cauchy’s and Legendre’s Equations – Method of variation of parameters –- Applications: Modelling of Free Oscillations of a Mass-Spring system.
Double integration (Cartesian co-ordinates) – Change of order of integration – Applications of double integral (Area) – Triple Integration (Cartesian co-ordinates) – Applications: Volume as triple integrals and solids of revolution.
Reference Book:
1 Engineering Mathematics-I by G.Balaji 2 James, “Glyn Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education(2012). 3 Mathematics –I By Dr.Singaravelu
Text Book:
1 Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, Eighth Edition, Laxmi Publications PvtLtd.,(2011) 2 Grewal. B.S, “Higher Engineering Mathematics”, 41Edition, Khanna Publications, Delhi,(2011).