Mathematical Methods: For Students of Physics and Related Fields

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Springer Science & Business Media, Jun 15, 2000 - Mathematics - 659 pages

Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material.

Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics.

This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.

Some praise for the previous edition:

"The book has many strengths. For example: Each chapter starts with a preamble that puts the chapters in context. Often, the author uses physical examples to motivate definitions, illustrate relationships, or culminate the development of particular mathematical strands. The use of Maxwell's equations to cap the presentation of vector calculus, a discussion that includes some tidbits about what led Maxwell to the displacement current, is a particularly enjoyable example. Historical touches like this are not isolated cases; the book includes a large number of notes on people and ideas, subtly reminding the student that science and mathematics are continuing and fascinating human activities."

--Physics Today

 

"Very well written (i.e., extremely readable), very well targeted (mainly to an average student of physics at a point of just leaving his/her sophomore level) and very well concentrated (to an author's apparently beloved subject of PDE's with applications and with all their necessary pedagogically-mathematical background)...The main merits of the text are its clarity (achieved via returns and innovations of the context), balance (building the subject step by step) and originality (recollect: the existence of the complex numbers is only admitted far in the second half of the text!). Last but not least, the student reader is impressed by the graphical quality of the text (figures first of all, but also boxes with the essentials, summarizing comments in the left column etc.)...Summarizing: Well done."

--Zentralblatt MATH

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Contents

III
1
IV
10
V
15
VI
32
VII
38
VIII
45
IX
46
X
49
LII
334
LIII
339
LIV
344
LV
357
LVI
362
LVII
370
LVIII
376
LIX
381

XI
62
XII
71
XIII
77
XV
81
XVI
92
XVII
99
XVIII
115
XIX
123
XX
130
XXI
139
XXII
140
XXIII
160
XXIV
171
XXV
176
XXVI
180
XXVII
193
XXVIII
197
XXIX
201
XXX
205
XXXII
208
XXXIII
213
XXXIV
221
XXXV
227
XXXVI
243
XXXVII
249
XXXVIII
252
XXXIX
256
XL
264
XLII
275
XLIII
285
XLIV
289
XLVI
302
XLVII
308
XLVIII
315
XLIX
320
L
321
LI
328
LX
386
LXI
399
LXII
405
LXIII
413
LXV
418
LXVI
425
LXVII
428
LXVIII
432
LXIX
448
LXX
452
LXXI
456
LXXII
467
LXXIII
474
LXXIV
475
LXXV
483
LXXVI
494
LXXVII
502
LXXVIII
514
LXXIX
519
LXXX
520
LXXXI
522
LXXXII
532
LXXXIII
562
LXXXIV
580
LXXXV
587
LXXXVI
592
LXXXVII
607
LXXXVIII
615
LXXXIX
618
XC
619
XCI
628
XCII
639
XCIII
644
XCIV
647
XCV
649
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