Math Books I Study(& love) These Days

As an undergrad student of physics, I have been studying mathematics rigorously from the first days of my freshman year. Here is a list of books that I have been studying lately to develop my mathematical background:

Vector Calculus by Susan Jane Colley

Vector calculus is a mathematical tool that a physicist uses on a daily basis. The branches of physics where vector calculus is used are a lot in number; classical mechanics, classical electromagnetism, fluid mechanics, classical field theory- to name a few. And it’s an prerequisite to learn differential geometry.

I have been studying vector calculus for some time. And Susan Jane Colley’s has been quite a nice guide to learning vector calculus. What I love about the book is that it’s emphasis on rigorous development of the subject while still not very dry to study. And it contains lots of nice problems to test one mathematical understanding; especially the miscellaneous problems at the end of the chapter amalgamates concepts of all the sections inside it.

I am also studying Murray R. Speigel’s Vector Analysis together with Hobson’s and Arfken’s Mathematical physics books as supplementary books on this topic.

Principles of Mathematical Analysis by Walter Rudin

As I mentioned in the previous blog post, learning analysis with rigor is a necessity for a wanna be theoretical physicist. And what other book could I study except this classic text on analysis. This book has a traditional statement-proof based approach. While it may seem like too congested, this book is spot on rigor. The problems at the end of the each chapter will test one’s ability to proof statements.

Though I have only studied 3 chapters of the book, I wish to study all the chapters in the near future.

AFirst Course in Differential Equations with Modeling Applications by Dennis G. Zill

Though the time span of my journey in physics is very short, one tool I have used countless times to this day is the craft of solving differential equations. Whatever area of physics you may be studying you will obviously find yourself solving ODEs or PDEs. Though I haven't still encountered the problems where solving PDEs is a must, my journey with classical mechanics, classical electrodynamics, fluid dynamics has demanded a good proficiency over ODEs.

Zill's book is particularly entertaining in its friendly approach. A lot of people in my country study Ross's book for learning ODEs, but this book seems to me particulary dry. Besides, the problems at the end of the each chapter in Zill's book, has been classified into few categories to address different needs of the reader. But, the most important thing that puts this book ahead of Ross's one is its emphasis on modeling physical phenomena and numerical ODE solving.

A nice book, indeed.

A First Course in Probability by Sheldon Ross

I have just started studying this book, so can't tell much about it. But, nonetheless this book seems to me a good one after studying a few pages. It has lots off nice problems too.

Mathematical Statistics with Applications by Scheaffer et al.

Let's be honest; all the students of physical sciences need to learn statistical methods. But I prefer to learn everything rigorously. For this reason, I was a little disappointed when the freshman Statistics course at my university followed a surveyor's style, rather than focusing on the mathematical basis of statistics. So, I wanted a book with emphasis on mathematical rigor than blindly applying statistical methods. 

Scheffer et al's book is really suitable on this regard. Lots of proofs, lots of challenging problems to test one's skill. Yeah, this book is a bliss.

A First Course in Complex Analysis by Dennis G. Zill

I started this book some 7/8 months earlier. As an introductory book this book is particulary well written. The text is not that heavy, but explains the concepts really well.

With this book, I am also studying Tristan Needham's Visual Complex Analysis to develop intuition in this field of mathematics. Actually, Needham's book is a real gem, a book with real uncommon approach, but spot on realizing its goal to give satisfying picture of the complex number field.

Integral Transforms and Their Applications by Debnath et al.

I was searching for a mathematically oriented text on integral transforms, as I didn't like the 'physicist' approach towards the subject. So, did a little research on internet, and Voila! found this grand creation. This book covers Fourier, Laplace and Legendre (and few others) transforms rigorously with many examples of application in physics.

This book is particularly encyclopedic, may not be suitable as an introductory text if you read it thoroughly page after page. This book needs a more discontinuous approach for studying it which you will understand if you go through the contents of the book.

So, what do you think about this books? Let me know.