UM 102: Analysis and Linear Algebra II
Credits: 4:0
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, Brooks/Cole, 2006.
- 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.