Lecture notes in applied differential equations of mathematical physics

340 Pages·2008·1.69 MB·English

by  Luiz C. L. Botelho

Lecture Notes in
Applied Differential
Equations of
Mathematical Physics
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Lecture Notes in
Applied Differential
Equations of
Mathematical Physics
Luiz C L Botelho

Federal University, Brazil
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
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Published by
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
LECTURE NOTES IN APPLIED DIFFERENTIAL EQUATIONS OF
MATHEMATICAL PHYSICS
Copyright © 2008 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
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ISBN-13 978-981-281-457-9
ISBN-10 981-281-457-4
Printed in Singapore.
ZhangJi - Lec Notes in Applied.pmd 1 12/10/2008, 7:41 PM
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For all those who do not think that doing research
and writing is just to sign and be “co-author”
in other’s papers.
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Foreword
“...Both Mathematics and Physics are in a state of crisis in present days,
from intellectual and social sides simultaneously. Both have much to con-
tribute to each other’s disciplines, and I believe that a renewal of their
traditional liaison would go far to cure at least the intellectual side of the
malaise felt by workersin both disciplines...” — Robert Hermann in Lec-
tures in Mathematical Physics — Vol. I & Vol. II.
My aim in this set of informal lecture notes on applied mathematical
analysis is to present mathematical author’s original research material
(Chaps.3–9andappendixes)revisedandamplifiedofourtwopreviouswork
on path-integrals in statistical and quantum physics and strongly focused
at a pure and applied mathematical audience of readers.
We have a strong believe that mathematics students can find a source
ofinspirationtostimulatemutualinteractionoftheirdisciplineandphysics
and thus, undertaking the reading of physics books, talking with physi-
cists and try to read our previous two monographs in classical and
quantum physics. The special emphasis in this supplementary volume 3
is on advanced mathematical analysis methods with its applications to
solve partial differential equations in finite and infinite dimensions arising
in applied settings. Another objective behind writing this set of author’s
mostly original results in the form of lectures is the hope it could serve
to show that the “aridity” and “sterility” that one finds in much modern
“estimate mathematical analysis” can be conterweighted side by side by
mathematical analysis formulae exactly used in the modern applications.
Awordonthe“methodology”inoursetoflecturenotesasasetofcom-
plementary notes we feel that the students should read the chapter with a
pencil and paper at hand, after which they should make additional studies
in the specific topic in the literature and thus present their studies in sem-
inars to others students with all lectures mathematical details workedout.
Luiz C.L. Botelho
Professor
vii
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