Advanced Calculus and Methods of Mathematical Physics

Textbooks

There are variosu textbooks for differnt parts of the course. Here are is a list of some books that you can find useful. I will update the list if I come across new titles:

1) Walter Rudin, Principle of Mathematical Analysis, third edition, McGraw-Hill, 1976

This books is very densly written, but contains all the essnetial results of the course. Morever, it has many challenging exercises.

2) S. Kantorovitz, Several Real Variables, Springer Verlag 2016

This book covers almost all the multi-variable part of the course. A particular feature is that it avoids the differential forms formalism for integration and might be easier for less mathematically inclinded reader.

2) Michael Tayloer, Introduction to Analysis in several variable.

This text is a textbook covering multivariable calculus, Fourier analysis, and complex analysis. Moreover, it is a good source of exercises at various degrees of difficulty.

3) K.F. Riley, M.P. Hobson, S.J. Bence, Mathematical Methods for Physics and Engineering, 3rd edition, Cambridge University Press, 2006.

This books contains almost all the topics that will be discussed in the course. One advantage of the text is that it thoroughly discusses connection to physics.

Assessment

The grade in the course is entirely based on the final exam. By submitting homework you can improve this grade by up to 0.66 points. More detailes about hoemwork will be announced in class.