Linear Algebra continued: Inner products and Orthogonality; Determinants; Eigenvalues and Eigenvectors;
Diagonalisation of symmetric matrices. Multivariable calculus: Functions on R^n, partial and total derivatives;
Chain rule; Maxima, minima and saddles; Lagrange multipliers; Integration in R^n, change of variables,
Fubini’s theorem; Gradient, Divergence and Curl; Line and Surface integrals in R^2 and R^3; Stokes, Green’s
and Divergence theorems. Introduction to Ordinary Differential Equations; Linear ODEs and Canonical
forms for linear transformations.
Suggested books and references:
Apostol, T. M., Calculus, Volume II, 2nd edition
,Wiley, India, 2007.
Strang, G., Linear Algebra and its Applications, 4th Edition
Artin, M., Algebra
,Prentice Hall of India.
Hirsch, M., Smale, S. and Devaney, R. L., Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd edition
,Academic Press, 2004.