Richard Feynman (Nobel price winner with exceptional educational skills):

The Theory of Fundamental Processes (1961)

The Feynman Lectures on Physics (1963-65; drie delen)

The Character of Physical Law (1965)

Photon-Hadron Interactions (1972)

QED: The Strange Theory of Light and Matter (1985)

Surely You're Joking, Mr. Feynman! (1985)

Elementary Particles and the Laws of Physics (1987, met Steven Weinberg)

What Do You Care What Other People Think? (1988)

Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher (1994, postuum)

Six Not So Easy Pieces: Einstein's Relativity, Symmetry and Space-Time (1997, postuum)

The Meaning of It All: Thoughts of a Citizen Scientist (1998, postuum)

The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman (1999, postuum)

Selected papers of Richard Feynman (2000, postuum)

Perfectly Reasonable Deviations from the Beaten Track (2005, postuum)

Don't You Have Time to Think? (2005, postuum

Ravinder, it's Erwin Kreyszig: Advanced Engineering Mathematics. (latest ed: 10th), available online, btw, just search for it. Great book.

I agree with previous answers.  Kreyzig's book "Advanced Engineering Mathematics" is a fantastic book for better and proper understanding of mathematics and its applications.

Frankly speaking, I was not aware that my simple question will ignite a good discussion here. But I am loving it. Trying to find both sides of the question, Physics and Maths. Both are my favorite subject, though I major in Physics.

Thanks a lot to everyone here.

Since we are talking about science with the help of “ mathematical functions” (this vague description is close to be considered humorous because it entails from y=k to δ(x) ) we can not resort to only “one good book” (like the Bible).Even if we consider as common layman a high school graduate still there is no one source only to look in. Searching in the google one by one topic and reading credible websites- like AMS, and Mathworld for math, Nature, even the science sections of serious news papers for physics- under the guidance of an inspiring teacher that knows well the history of science and who assigns regularly small précis with a variety of these topics, you can have the task achieved satisfactorily enough. If there is someone that knows such a book let me now so that I can buy it myself!

It is difficult to find such books because mathematics is like river and their physical meaning are like branches of river. I would be happy if I will get such books. But  I would suggest that one should refer good books on engineering branches  for the physical meaning in their context.  

Try to consider the site http://www.msri.org/attachments/TUM-manuscript-030612.pdf (Critical Issues in Mathematics Education Series, Volume 5

May 2009 Workshop Report

Prepared by Yvonne Lai

Teaching

Undergraduates

Mathematics),

http://www.physics.ohio-state.edu/~lbao/archive/papers/Probv_pre.pdf,

the site http://nrich.maths.org/6864/index?nomenu=1

and the literature there.

You can also see Mathematical Analyis I/II. by Vladimir A. Zorich.

The book is  accessible to English-speaking readers. This textbook consists of two parts. It is aimed primarily at university students and teachers specializing in mathematics and natural sciences, and at all those who wish to see both the rigorous mathematical theory and examples of its effective use in the solution of real problems of natural science.

I can also   recommend

Mathematical Physics: A Modern Introduction to Its Foundations by Hassani,

Mathematical Methods In the Physical Sciences by Boas, which is a standard text for junior-level mathematical method courses.

Reference https://www.physicsforums.com/threads/good-math-methods-in-physics-book.379895/

At the most introductory level there is Basic Training in Mathematics: A Fitness Program for Science Students by R. Shankar,

http://www.amazon.com/Basic-Training-Mathematics-Fitness-Students/dp/0306450356/ref=ntt_at_ep_dpi_2.

Arfken and Weber is a standard text for grad-level (or possibly senior-level) mathematical methods courses.

Dear Vijay:

You may read the following:L

The Feynman Lectures on Physics, boxed set: The New Millennium Edition:

Hardcover: 1552 pages

Publisher: Basic Books;

Language: English

ISBN-10: 0465023827

ISBN-13: 978-0465023820

For me this is one of the best books that marry mathematics with a very deep physical explanation.

Regards,

Gamal

Thank you all for your inputs. Currently I am reading few books recommended above. Thanks again.

I was pondering too regarding this.But I came across a fundamental book "Mathematical methods for Mathematician Physical Scientists and Engineer" by J.Dunning - Davies.Hope this will explain. As per to my concern I have seen the topics included are illustrious .

Regards

Emmanuel