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.
Curvature-Radius of Curvature in Cartesian co-ordinates – Centre and circle of curvature in Cartesian co- ordinates – Evolutes – Envelopes.
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.
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:
Text Book: 1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 44th Edition, 2018. 2. Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, John Wiley & Sons, 2016.
Text Book:
Reference Book: 1. Bali N. P and Manish Goyal, “A Text book of Engineering Mathematicsâ€, Eighth Edition, Laxmi Publications Pvt Ltd., (2011) 2. James Stewart, “Calculus: Early Transcendentals†,Cengage Learning , 8th Edition , New Delhi 2015 3. David C Lay, Linear Algebra and its applications, Pearson, 2018. 4. G.B.Thomas, Calculus, 12th Edition, Pearson Education India, 2015. 5. Ramana.B.V., “Higher Engineering Mathematics†, McGraw Hill Education Pvt Ltd, New Delhi , 2016 6. T. Veerarajan, Engineering Mathematics, 3rd Edition, Tata McGraw-Hill, New Delhi, 2011
