Whelan - A first course in mathematical physics

1. Halliday, D., Resnick, R., Walker, J.
2. Principles of Physics, Ninth Edition, Volume 1 (-20) International Student Version
3. 9th Edition
4. 2011
5. Print ISBN: 978-0-470-56837-8

1. Boas, M.L.
2. Mathematical Methods 3E
3. 3rd Edition
4. 2010
5. Print ISBN: 978-0-470-94796-8

1. Kusse, B., Westwig, E.A.
2. Mathematical Physics
3. Applied Mathematics for Scientists and Engineers
4. 1998
5. Print ISBN: 978-0-471-15431-0

1. Courant, R., Hilbert, D.
2. Methods of Mathematical Physics
3. Volume 2
4. 1989
5. Print ISBN: 978-0-471-50439-9
6. ISBN: 978-3-527-61723-4
7. Adobe PDF ISBN: 978-3-527-61724-1

1. Fanchi, J.R.
2. Math Refresher for Scientists and Engineers, Third Edition
3. 3rd Edition
4. 2006
5. Print ISBN: 978-0-471-75715-3
6. Mobi-lite ISBN: 978-0-470-32623-7
7. Adobe PDF ISBN: 978-0-471-79154-6
8. ISBN: 978-0-471-79155-3

1. Understanding Physics
2. 1998
3. Print ISBN: 978-0-471-97553-3

1. Vaughn, M.T.
2. Introduction to Mathematical Physics
3. 2007
4. Print ISBN: 978-3-527-40627-2
5. ISBN: 978-3-527-61885-9
6. Adobe PDF ISBN: 978-3-527-61886-6

1. Fujita, S., Godoy, S.V.
2. Mathematical Physics
3. 2009
4. Print ISBN: 978-3-527-40808-5

1. Masujima, M.
2. Applied Mathematical Methods in Theoretical Physics
3. 2nd Edition
4. 2009
5. Print ISBN: 978-3-527-40936-5
6. ISBN: 978-3-527-62774-5
7. Adobe PDF ISBN: 978-3-527-62775-2

1. Nonequilibrium Statistical Physics
2. 2013
3. Print ISBN: 978-3-527-41092-7
4. Adobe PDF ISBN: 978-3-527-67057-4
5. ISBN: 978-3-527-67139-7

1. Toral, R., Colet, P.
2. Stochastic Numerical Methods
3. An Introduction for Students and Scientists
4. 2014
5. Print ISBN: 978-3-527-41149-8
6. MobiPocket ISBN: 978-3-527-68311-6
7. ePub ISBN: 978-3-527-68312-3
8. Adobe PDF ISBN: 978-3-527-68313-0
9. WOL obook PDF ISBN: 978-3-527-68314-7

1. Martin, B.R., Shaw, G.
2. Mathematics for Physicists
3. 2015
4. Print ISBN: 978-0-470-66022-5
5. ePub ISBN: 978-1-118-67661-5
6. Adobe PDF ISBN: 978-1-118-67663-9

Author

Professor Colm T. Whelan

Old Dominion University

Department of Physics

4600 Elkhorn Avenue

VA

United States

Cover

math formula: fotolia_ shotsstudio; sepia-Motive: fotolia_ agsandrew

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Print ISBN: 978-3-527-41333-1

ePDF ISBN: 978-3-527-68713-8

ePub ISBN: 978-3-527-68715-2

Mobi ISBN: 978-3-527-68714-5

Cover Design Adam-Design, Weinheim, Germany

For Agnieszka, of course

This book is an elementary introduction to the mathematics needed for students taking undergraduate classes in the physical sciences. My ambition is to present in a simple and easily intelligible way the core material they will need for their courses and help them to uncover the character of the physical laws, which can sometimes, unfortunately, be obscured by a lack of understanding of and sympathy with the precise mathematical language in which, perforce, they have to be expressed. I have emphasized the direct connection between the conceptual basis of the physics the students are about to learn and the mathematics they are studying. The first part of the book introduces the core mathematics and while I have included numerous applications in this section I felt that a fuller understanding could only be achieved if the physical context was given a more complete introduction. In the second part of the book, I have given a series of brief overviews of some of the more beautiful and conceptually stimulating areas of physics.

The material in this book is designed for a one- or two-semester course to be ideally taken at the start of the sophomore year. I assume the readers have no previous knowledge. The first two chapters give a brief overview of some of the more elementary mathematics one might hope that students bring with them from high school and their first year. The choice of material included in the course involved some painful pruning. I am all too aware of the numerous shortcuts I have taken, the many important interesting and beautiful diversions I have ignored, and the rigor I have forsaken all with one principle object in view to equip the students with a basic mathematical toolkit that will allow them to enjoy and profit from their higher level physics courses. I rather hope that the student will be sufficiently intrigued by the exposure to the interesting topics covered in this text to seek out some other more formal and rigorous specialist mathematics courses. A large number of problems have been included, for none of which is the use of a calculator needed. These form an integral part of the book and students are strongly encouraged to attempt all of them.

C T W
Norfolk, May, 28, 2015

It is often said that most mathematical errors, which get published, follow the word clearly and involve the improper interchange of two limits. In simple terms, a limit is the number that a function or sequence approaches as the input or index approaches some value. For example, we will say that the sequence approaches the limit 0 as moves to infinity Or, in other words, we can make arbitrarily small by choosing big enough. We often write this as

We can also take the limit of a function, for example, if