Good books on Mathematical methods

[Phy4life]

Hello, I'm a first year Physics student. I've decided to take on mathematical methods and be as thorough with it as I possibly can.
I am looking for books that cover vector calculus, Orthogonal transformations, tensors, curvilinear co-ordinates, index notations and the dirac-delta function in details.
I am currently using:
Mathematical Methods for Physicists by Boas,
Mathematical Methods for Physicists by Arfken and Weber (my favourite till now),
Vector Analysis by Spiegel

Are these enough to get me through? If you have other books in mind that may be helpful, please mention. Thank you.

 

[mak52810]

Mathematical Methods for Physicists by Boas, this book is a gem.

 

[ZapperZ]

I'm not being anal-retentive, but the proper title for Boas's text is "Mathematical Methods in the Physical Sciences". This book has been discussed, reviewed, and recommended (especially by me) several times in various threads.

Zz.

 

[Seydlitz]

I'm not being anal-retentive, but the proper title for Boas's text is "Mathematical Methods in the Physical Sciences". This book has been discussed, reviewed, and recommended (especially by me) several times in various threads.

Zz.

I also heartily recommend this book! The explanation in the book is very clear and instructive that even as a beginner I've rather few problem in doing the exercises and understanding the concept. If you are interested with the some theory of the mathematics this book also offer some of that, meaning you don't spend the entire books solving equations without knowing the important theorem behind it.

 

[NumericalFEA]

...curvilinear co-ordinates...

Here is one, devoted to curvilinear coordinates on surfaces, with applications related to mechanics of shells. Importantly, it contains a significant number of ready-to-use source codes in C/C++:

https://www.amazon.com/dp/0646594044/?tag=pfamazon01-20

 

[Leaph]

the dirac-delta function

I think that it is impossible to understand the dirac-delta without knowing the distribution's theory. So I recommend Schwatz's "mathematics for the physical sciences". It explain very clearly fourier's transform too.

 

[Konoha]

Mathematical Methods for Physicists by Boas is pure gold.