# UM 102: Analysis and Linear Algebra II

### Course Syllabus

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.

### Assignments

Assignments will be posted roughly once a week.

### Suggested books

1. T. M. Apostol, Calculus, Volume II, 2nd. Edition, Wiley Wiley India, 2007.
2. Kalyan Mukherjea, Differential Calculas in Normed Linear Spaces (Texts and Readings in Mathematics), Hindustan Book Agency, 2007.
3. G. Strang, Linear Algebra And Its Applications, 4th Edition, Brooks/Cole, 2006
4. M. Artin, Algebra, Prentice Hall of India, 1994.
5. M. Hirsch, S. Smale, R. L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd Edition, Academic Press, 2004.

### Course Details

#### Announcements

• Final Examination Syllabus

The syllabus for the finale examination will be the material covered in all the lectures on the course. The questions will be based on the topics after linear algebra, but...

• Midterm Syllabus

The syllabus for the midterm examination will be the material covered in lectures up to February 9, 2018 (including the lecture on this day). This roughly corresponds to the following...

• Tutorials

Tutorial sessions will begin on Monday, 8/01/2018.