### UM 102: Analysis and Linear Algebra II

#### Credits: 3:0

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:

1. Apostol, T. M., Calculus, Volume II, 2nd edition, Wiley, India, 2007.
2. Strang, G., Linear Algebra and its Applications, 4th Edition, Brooks/Cole, 2006.
3. Artin, M., Algebra, Prentice Hall of India.
4. Hirsch, M., Smale, S. and Devaney, R. L., Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd edition, Academic Press, 2004.

#### All Courses

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 04 Oct 2022