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Student Solutions Manual for Mathematical Methods for Physics and Engineering
The second edition of Mathematical Methods for Physics and Engineering carried
more than twice as many exercises, based on its various chapters, as did the first.
In the Preface we discussed the general question of how such exercises should
be treated but, in the end, decided to provide hints and outline answers to all
problems, as in the first edition. This decision was an uneasy one as, on the one
hand, it did not allow the exercises to be set as totally unaided homework that
could be used for assessment purposes, but, on the other, it did not give a full
explanation of how to tackle a problem when a student needed explicit guidance
or a model answer.
In order to allow both of these educationally desirable goals to be achieved, we
have, in the third edition, completely changed the way this matter is handled.
All of the exercises from the second edition, plus a number of additional ones
testing the newly added material, have been included in penultimate subsections
of the appropriate, sometimes reorganised, chapters. Hints and outline answers
are given, as previously, in the final subsections, but only to the odd-numbered
exercises. This leaves all even-numbered exercises free to be set as unaided
homework, as described below.
For the four hundred plus odd-numbered exercises, complete solutions are available,
to both students and their teachers, in the form of this manual; these are in
addition to the hints and outline answers given in the main text. For each exercise,
the original question is reproduced and then followed by a fully worked solution.
For those original exercises that make internal reference to the text or to other
(even-numbered) exercises not included in this solutions manual, the questions
have been reworded, usually by including additional information, so that the
questions can stand alone. Some further minor rewording has been included to
improve the page layout.
In many cases the solution given is even fuller than one that might be expected
of a good student who has understood the material. This is because we have
aimed to make the solutions instructional as well as utilitarian. To this end, we
have included comments that are intended to show how the plan for the solution
is formulated and have provided the justifications for particular intermediate
steps (something not always done, even by the best of students). We have also
tried to write each individual substituted formula in the form that best indicates
how it was obtained, before simplifying it at the next or a subsequent stage.
Where several lines of algebraic manipulation or calculus are needed to obtain a
final result, they are normally included in full; this should enable the student to
determine whether an incorrect answer is due to a misunderstanding of principles
or to a technical error.
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