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Tensors and Dierential Forms. Vector Spaces. Eigenvalue Problems. Ordinary Dierential Equations. Sturm-Liouville Theory. Partial Dierential Equations. Greens Functions. Complex Variable Theory. Further Topics in Analysis. Gamma Function. Bessel Functions. Legendre Functions. Angular Momentum. Group Theory. More Special Functions. Fourier Series. Integral Transforms. Integral Equations. Calculus of Variations.
Probability and Statistics. The changes extend not only to the topics and their presentation, but also to the exercises that are an important part of the student experience. The new edition contains exercises that were not in previous editions, and there has been a wide-spread reorganization of the previously existing exercises to optimize their placement relative to the material in the text. Since many instructors who have used previous editions of this text have favorite problems they wish to continue to use, we are providing detailed tables showing where the old problems can be found in the new edition, and conversely, where the problems in the new edition came from.
We have included the full text of every problem from the sixth edition that was not used in the new seventh edition. Many of these unused exercises are excellent but had to be left out to keep the book within its size limit. Some may be useful as test questions or additional study material. Complete methods of solution have been provided for all the problems that are new to this seventh edition.
This feature is useful to teachers who want to determine, at a glance, features of the various exercises that may not be com- pletely apparent from the problem statement.
While many of the problems from the earlier editions had full solutions, some did not, and we were unfortunately not able to undertake the gargantuan task of generating full solutions to nearly problems. Not part of this Instructors Manual but available from Elseviers on-line web site are three chapters that were not included in the printed text but which may be important to some instructors.
These include A new chapter designated 31 on Periodic Systems, dealing with mathe- matical topics associated with lattice summations and band theory, A chapter 32 on Mathieu functions, built using material from two chap- ters in the sixth edition, but expanded into a single coherent presentation, and 1 CHAPTER 1. In addition, also on-line but external to this Manual, is a chapter designated 1 on Innite Series that was built by collection of suitable topics from various places in the seventh edition text.
This alternate Chapter 1 contains no material not already in the seventh edition but its subject matter has been packaged into a separate unit to meet the demands of instructors who wish to begin their course with a detailed study of Innite Series in place of the new Mathematical Preliminaries chapter.
Because this Instructors Manual exists only on-line, there is an opportunity for its continuing updating and improvement, and for communication, through it, of errors in the text that will surely come to light as the book is used. The authors invite users of the text to call attention to errors or ambiguities, and it is intended that corrections be listed in the chapter of this Manual entitled Errata and Revision Status. Errata and comments may be directed to the au- thors at harrisat qtp.
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It is our hope that this Instructors Manual will have value to those who teach from Mathematical Methods for Physicists and thereby to their students.
Page Figure Page Exercise The answer is then correct. Page Eq. Page After Eq. Consistency with the duplication formula then determines C 2. The text assumes it to be kr. Disregard it. Page Table The column of references should, in its entirety, read: Corrections and Additions to Exercise Solutions None as of now. Chapter 3 Exercise Solutions 1.
Mathematical Preliminaries 1. This is valid because a multiplicative constant does not aect the conver- gence or divergence of a series. This expression approaches 1 in the limit of large n. Divergent for a 1 b 1 1. The solution is given in the text. Applying Gauss test, this indicates divergence.
Let s n be the absolute value of the nth term of the series. Therefore this series converges. Because the s n are larger than corre- sponding terms of the harmonic series, this series is not absolutely con- vergent. With all signs positive, this series is the harmonic series, so it is not aboslutely convergent. We therefore see that the terms of the new series are decreasing, with limit zero, so the original series converges.
With all signs positive, the original series becomes the harmonic series, and is therefore not absolutely convergent. Form the nth term of 2 c 1. Make the observation that. Summing now over p, we get. The solutions are given in the text.
The upper limit x does not have to be small, but unless it is small the convergence will be slow and the expansion relatively useless. The two series have dierent, nonoverlapping convergence intervals. Start by obtaining the rst few terms of the power-series expansion of the expression within the square brackets.
Expanding the logarithm,. The series for 2 is obtained. The integrated terms vanish, and the new integral is the negative of that already treated in part a.
Use mathematical induction. First, dierentiate the Leibniz formula for n 1, getting the two terms n1. The terms then combine to yield n. One way to verify the binomial coecient sum is to recognize that it is the number of ways j of n objects can be chosen: either j 1 choices are made from the rst n 1 objects, with the nth object the jth choice, or all j choices are made from the rst n 1 objects, with the nth object remaining unchosen.
The proof is now completed by noticing that the Leibniz formula gives a correct expression for the rst derivative. Thus, we want to see if we can simplify 1 p! The formula for u n p follows directly by inserting the partial fraction decomposition. If this formula is summed for n from 1 to innity, all terms cancel except that containing u 1 , giving the result. The proof is then completed by inserting the value of u 1 p 1.
After inserting Eq. Using now Eq. Insertion of this expression leads to the recovery of Eq. Applying Eq.
ISBN 13: 9780120598274
Through four editions, Arfken and Weber's best-selling Mathematical Methods for Physicists has provided upper-level undergraduate and graduate students with the paramount coverage of the mathematics necessary for advanced study in physics and engineering. It provides the essential mathematical methods that aspiring physicists are likely to encounter as students or beginning researchers. Appropriate for a physics service course, as well as for more advanced coursework, this is the book of choice in the field. An essential addition to the bookshelf of any serious student of physics or research professional in the field.