Partial Differential Equations
Springer, 1982 - 249 páginas
This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy 's example of a linear equation without solutions.
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If a surface S : z = u ( x , y ) is a union of characteristic curves , then S is an integral surface . For then through any point P of S there passes a ...
Equation ( 7.1 ) can be viewed as a relation between the coordinates ( x , y , z ) of a point on an integral surface and the direction of the normal of the ...
A surface z = u ( x , y ) referred to parameters set can be thought of as consisting ... by the points of the surface and the corresponding tangent planes .
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