Lecturer: K.S. Narain , ICTP

**Overview of the course **

**Guide to accessing online material for this course:**Video recordings of the lectures are linked under the respective lecture headings. The course had 35 lectures and in addition it included 14 tutorials.

The list below gives the names of topics in the lecture notes. The full text is taken from the book called Mathematics For Physicists (Philippe Dennery and Andre Krzywicki), Mathematics for Physicists (Text Book from Google e-books preview)

Written by

Philippe Dennery,Andre Krzywicki, Chapter 1, 2, 3 and 4 for the second part of the course(lectures 18-34)

to see more references please have a look at http://www.damtp.cam.ac.uk/user/fq201/ where you must see teaching part of that address and the notes on Differential Equations 2007 and Complex Methods 2007 are available , you can easily download them as they are really useful to actually have them in general.

However prof. Narain did not teach all the chapters either did not give several proves rather described how we can use several theorems to come over problems in physics , so the main topics are discussed as the following:

**Topics presented: **

1-Linear algebra (1^{st }chapter which includes 7or 8 lectures)

2-Complex analysis (2^{nd }chapter includes 8 lectures)

3-Function spaces and Fourier transform (8 lectures)

4-Differential equations (8 lectures)

Notes for individual chapters will not be linked so we link every video in its own lecture .

where you must see teaching part of that address and the notes on Differential Equations 2007 and Complex Methods 2007 are available , you can easily download them as they are really useful to actually have them and see the whole content.

o lecture 1

*The first notion is discussed as Vector Spaces *

- The definition of vector in 2 dimensions(with length and direction)
- is explained by x,y coordinates
- Adding two vectors mentioned. The rules of vectors in 2 and 3
- dims have been included.
- Rules of addition and multiplication by numbers and all properties of Null vector have been said.
- Bra-ket notation and negative operator and negative vector discussed.
- All properties beyond 2 dims mentioned as commutative rule,
- associative rule, multiplication rule ,associative law for multiplication.
- Distributive law for addition of numbers and distributive law for
- addition of vectors are involved.