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 –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 of Triple integral (Volume).
Reference Book:
1. Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, 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
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.
