Partial Differential Equations

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Springer Science & Business Media, 1991 - Mathematics - 263 pages
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This book is based on a course I have given five times at the University of Michigan, beginning in 1973. The aim is to present an introduction to a sampling of ideas, phenomena, and methods from the subject of partial differential equations that can be presented in one semester and requires no previous knowledge of differential equations. The problems, with hints and discussion, form an important and integral part of the course. In our department, students with a variety of specialties-notably differen tial geometry, numerical analysis, mathematical physics, complex analysis, physics, and partial differential equations-have a need for such a course. The goal of a one-term course forces the omission of many topics. Everyone, including me, can find fault with the selections that I have made. One of the things that makes partial differential equations difficult to learn is that it uses a wide variety of tools. In a short course, there is no time for the leisurely development of background material. Consequently, I suppose that the reader is trained in advanced calculus, real analysis, the rudiments of complex analysis, and the language offunctional analysis. Such a background is not unusual for the students mentioned above. Students missing one of the "essentials" can usually catch up simultaneously. A more difficult problem is what to do about the Theory of Distributions.
 

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Contents

II
1
III
7
IV
11
V
17
VI
22
VII
25
VIII
33
IX
41
XXVII
133
XXVIII
137
XXIX
140
XXX
147
XXXI
151
XXXII
152
XXXIII
158
XXXIV
163

X
52
XI
61
XII
64
XIII
70
XIV
74
XV
83
XVI
87
XVII
95
XVIII
96
XIX
99
XX
103
XXI
108
XXII
112
XXIII
117
XXIV
121
XXV
123
XXVI
126
XXXV
167
XXXVI
172
XXXVII
177
XXXVIII
181
XXXIX
188
XL
197
XLI
200
XLII
207
XLIII
214
XLIV
225
XLV
234
XLVI
239
XLVII
247
XLVIII
259
XLIX
261
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