MATRICES AND EIGENVALUE PROBLEMS
Eigenvalues and Eigenvectors of real matrix-Properties of Eigenvalues 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.
APPLICATIONS OF DIFFERENTIAL CALCULUS
Curvature-Radius of Curvature in Cartesian co-ordinates – Centre and circle of curvature in Cartesian co- ordinates – Evolutes – Envelopes.
FUNCTIONS OF SEVERAL VARIABLES
Partial derivatives –Total derivatives – Jacobians – Taylor’s series of functions of two variables –Maxima and Minima of functions of two variables – Lagrange’s method of undetermined multipliers.
ORDINARY DIFFERENTIAL EQUATIONS OF HIGER ORDER
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 of solids.
Reference Book:
Bali N. P and Manish Goyal, “A Text book of Engineering Mathematicsâ€, Eighth Edition, Laxmi Publications Pvt Ltd.,
James Stewart, “Calculus: Early Transcendentals†,Cengage Learning , 8th Edition , New Delhi 2015
David C Lay, Linear Algebra and its applications, Pearson, 2018.
Text Book:
B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 44th Edition, 2018.
Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, John Wiley & Sons, 2016.
