# TEW - TEW for Mathematics Teachers of Engineering Colleges in and around Chennai

## Speakers and Syllabus

The Teacher Enrichment Workshop is a programme funded by the National Council for Mathematics (NCM) - the funding body for various instructional schools conducted at several levels in various places throughout the country. This Workshop is also part of the outreach activity `Enriching Collegiate Education' of the Institute of Mathematical Sciences (IMSc) Chennai, which co-sponsors the activity. The TEW is meant for college teachers to revisit and update their content-knowledge. The lectures in the Workshop covers specific topics which are relevant for the teachers' classroom instructions. An important component of this Workshop is the discussion hour during which the teachers will have opportunities to get their doubts cleared and work out routine to advanced exercises.

This Workshop is meant for mathematics teachers of Engineering colleges in and around Chennai. In view of infrastructural difficulties accommodation will NOT be provided for participants.

**Syllabus:**

**Applications of Linear Algebra :**

1. Vector spaces, Linear transformations and Matrices

2. Determinants, Diagonalizability and Nilpotence

3. Jordan form

4. Inner product spaces

5. Unitary, self-adjoint, normal, and hermitian operators

6. Spectral theorem

**Applications of Partial Differential Equations (PDE)** :

- First Order PDE, 2 lectures: Method of characteristics for linear, semilinear and nonlinear equations avoiding the complicated geometrical approach.
- Scalar Conservation Laws, 2 lectures:

1. Breakdown of smooth solution and need for conservative formulation of the equations.

2. Conservation law, weak solution and entropy condition.

3. Examples to highlight important properties of solutions of hyperbolic conservation laws. - Wave Equations, 2 lectures:

1. Examples of some wave equations and their solutions, wave equation in one-space dimension.

2. Wave equation in two and three space dimensions and properties of the solutions.

**Fourier Series and Fourier Transformations :**

1. What is a Fourier series?

2. Fourier coefficients in an interval of length 2Pi, symmetric with respect to origin and in a general interval.

3. Fourier Sine and Cosine series.

4. Parseval's identity and its applications.

5. Fourier transformations, both continuous and discrete.

6. Applications of Fourier series and Transformations.

Name of the Speaker with affiliation |
Number of Lectures |
Detailed Syllabus |

S. Viswanath (SV) IMSc Chennai |
6 | Linear Algebra |

Phoolan Prasad (PP) IISc, Bangalore |
6 | Partial Differential Equations |

T. N. Shanmugam (TNS) Anna University, Chennai |
6 | Fourier series and Fourier Transform |

## Time Table

DAY |
Date |
09.30-11.00 |
11:00-11:30 |
11:30-13:00 |
13:00-14:00 |
14:00-15:30 |
15:30-15:45 |
15:45-16:45 |
16:45 |

Mon | 26/11/2018 | PP | TEA | SV | Lunch | TNS | TEA | Discussion | Snacks |

Tue | 27/11/2018 | PP | SV | TNS | |||||

Wed | 28/11/2018 | PP | SV | TNS | |||||

Thu | 29/11/2018 | PP | SV | TNS | |||||

Fri | 30/11/2018 | PP | SV | TNS | |||||

Sat | 01/12/2018 | PP | SV | TNS |