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Examples of elementary textbooks
- G.B. Thomas and R.L. Finney Calculus and Analytc Geometry, Addison-Wesley
Basic calculus book. All of the material in this book will be used
in this course and little will be repeated.
- B. Kolman and D.R. Hill Elementary Linear Algebra, Prentice Hall 2000.
Rudimentary knowledge of chapters 1-6 is required. Almost
everything in these chapters will be covered in PHYS607, however, it
will be hard to follow without previous background.
- W.E. Boyce and R.C. DiPrima Elementary Differential Equations
and Boundary Value Problems, Wiley 1997.
Rudimentary knowledge of chapters 1-4 and 7 is required.
We will go again only over some elements of chapter 3. We will
cover chapters 5, 6, 10, and 11 in PHYS608.
- M.L. Boas Mathematical Methods in the Physical Sciences, Wiley 1983.
This is the best book filling the gap between basic calculus
and our course. It is an undergraduate level text but it does cover many
subjects which we will discuss (but some are just not there).
- P. Dennery and A. Krzywicki Mathematics for Physicists, Harper 1967
(available from Dover).
One of the best books on mathematical analysis parts. Written
from mathematicians viewpoint but physicist emphasis on selection of
material. Although it does not relate to physics by any examples,
it uses intuitive ``physical" reasoning.
- J. Mathews and R.L. Walker Mathematical Methods of Physics, Benjamin,
Very understandable text based on Richard Feynman lectures.
Has little coverage of Arfken-Weber chapters 1-3, but for later chapters
the overlap becomes better. Good concise chapter on group theory.
- H. Cohen Mathematics for Scientists and Engineers, Prentice-Hall 1992.
Includes a lot of examples from simple to quite difficult
that will certainly be helpful to you.
Goes far enough in some subjects but not in other. Contains serious errors.
- M.D. Greenberg (UD Professor) Advanced Engineering Mathematics,
2nd edition, Prentice-Hall 1998.
Another very good book with range of subjects similar to Boas' text.
- E.B. Saff and A.D. Snider Fundamentals of Complex Analysis
for Mathematics, Science, and Engineering, Prentice Hall 1993.
This book does not have more material than Chapters 6 and
7 in Arfken-Weber, but it explains it all in every detail
on 450 pages. A huge number of examples.
- S. Hassani Foundations of Mathematical Physics, Allyn and Bacon, 1991.
More mathematical point of view and more rigour than other texts.
- M. Hamermesh Group Theory and its Applications to Physical Problems,
Probably the most popular of group theory books for physicists
which tells it must be good. It is both rigorous and physically
oriented. However, it is 600 pages long.
- J.F. Cornwell Group Theory in Physics, Academic 1984.
I looked at it briefly only but it seems like an excellent book.
Gives proofs (harder in appendices which makes reading of the main text
- I.G. Kaplan Symmetry of Many-Electron Systems, Academic 1975.
One of the best sources. Gives minimum of general group theory
(omits harder proofs)
needed to get to physical applications. Unfortunately, it is out of print.
- C.M. Bender and S. Orszag Advanced Mathematical Methods for Scientists
and Engineers, McGraw-Hill, 1978.
- P.M. Morse and H. Feschbach Methods of Theoretical Physics,
Classic text which has all of it but is rather hard to read.
- F.W. Byron and R.F. Fuller Mathematics of Classical and Quantum Physics,
Addison-Wesley, 1972 (available from Dover).
Classic text lightly written. Some subjects at a quite advanced
level while other are rather elementary and not very rigorous.
- M. Reed and B. Simon Methods of Modern Mathematical Physics,
Rigorous text written by top notch mathematical physicists.
Covers subjects relevent for quantum mechanics and field theory.
- J.P. Serre Linear Representations of Finite Groups, Springer Verlag
Very compact and somewhat formal mathematical approach.
- M.I. Petrashen and E.D. Trifonov Applications of Group Theory
in Quantum Theory, MIT Press, Cambridge, 1969.
- A. Messiah Quantum Mechanics, North-Holland 1961.
This classic quantum mechanics book contains a very good appendix on
- J. A. Gallian Contemporary Abstract Algebra, Heath 1990.
This text doesn't care about physics, however, it is an admirable
book. Very lightly written and simultanously rigorous. Interesting
- E. A. Coddington An Introduction to Ordinary Differential Equations,
This is an undergraduate text on the subject but in contrast to many
other texts it does contain proofs of more advanced theorems such as Fuchs'
theorem (including convergence).
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