Distribution Theory And Applications
Abdellah El-kinani Β· Mohamed Oudadess
Π°ΠΏΡ. 2010β―Π³. Β· Series On Concrete And Applicable Mathematics ΠΠ½ΠΈΠ³Π°Β 9 Β· World Scientific Publishing Company
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π°Ρ ΠΊΠ½ΠΈΠ³Π°
220
ΠΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΡΡΡΠ°Π½ΠΈΡ
family_home
ΠΠΎΠΆΠ½ΠΎ Π΄ΠΎΠ±Π°Π²ΠΈΡΡ
info
reportΠΡΠ΅Π½ΠΊΠΈ ΠΈ ΠΎΡΠ·ΡΠ²Ρ Π½Π΅ ΠΏΡΠΎΠ²Π΅ΡΠ΅Π½Ρ. ΠΠΎΠ΄ΡΠΎΠ±Π½Π΅Π΅β¦
ΠΠ± ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ ΠΊΠ½ΠΈΠ³Π΅
This book is an introductory course to the very important theory of distributions, as well as its applications in the resolution of partial differential equations (PDEs). It begins with a chapter of general interest, on the fundamental spaces (or test function spaces). The book advances and concludes with a chapter on Sobolev spaces, which are known to be very important in the resolution of PDEs.The very basic properties of distributions are examined in detail. Several formal methods have been first used, without rigorous justifications (Dirac function, principal value of Cauchy, finite parts of Hadamard). They find their natural frame in distribution theory. It is the same for Laplace transformation which is a fundamental tool in symbolic calculations.A detailed treatment is given to the convolution product for it is a central theme in distribution theory. Another very important instrument, covered in several chapters, is the Fourier transformation which is among the most fundamental tools in different mathematical disciplines, and also in physics. Convolution algebras, which are sufficient for the treatment of classical PDEs, are used in various applications.The general frame for the resolution of PDEs is the theory of kernels β the first elements of which are sufficient to show the practicality of distribution theory in applications.Comments are provided to clarify the settings and sustain calculations. This book may be used by mathematicians, physicists, engineers and graduate students.
ΠΠ± Π°Π²ΡΠΎΡΠ΅
Abdellah El Kinani (Ecole Normale SupΓΒ©rieure de Takaddoum, Morocco);Mohamed Oudadess (Ecole Normale SupΓΒ©rieure de Takaddoum, Morocco)
ΠΡΠ΅Π½ΠΈΡΠ΅ ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΡΡ ΠΊΠ½ΠΈΠ³Ρ
ΠΠΎΠ΄Π΅Π»ΠΈΡΠ΅ΡΡ Ρ Π½Π°ΠΌΠΈ ΡΠ²ΠΎΠΈΠΌ ΠΌΠ½Π΅Π½ΠΈΠ΅ΠΌ.
ΠΠ΄Π΅ ΡΠΈΡΠ°ΡΡ ΠΊΠ½ΠΈΠ³ΠΈ
Π‘ΠΌΠ°ΡΡΡΠΎΠ½Ρ ΠΈ ΠΏΠ»Π°Π½ΡΠ΅ΡΡ
Π£ΡΡΠ°Π½ΠΎΠ²ΠΈΡΠ΅ ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ Google Play ΠΠ½ΠΈΠ³ΠΈ Π΄Π»Ρ Android ΠΈΠ»ΠΈ iPad/iPhone. ΠΠ½ΠΎ ΡΠΈΠ½Ρ
ΡΠΎΠ½ΠΈΠ·ΠΈΡΡΠ΅ΡΡΡ Ρ Π²Π°ΡΠΈΠΌ Π°ΠΊΠΊΠ°ΡΠ½ΡΠΎΠΌ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈ, ΠΈ Π²Ρ ΡΠΌΠΎΠΆΠ΅ΡΠ΅ ΡΠΈΡΠ°ΡΡ Π»ΡΠ±ΠΈΠΌΡΠ΅ ΠΊΠ½ΠΈΠ³ΠΈ ΠΎΠ½Π»Π°ΠΉΠ½ ΠΈ ΠΎΡΠ»Π°ΠΉΠ½ Π³Π΄Π΅ ΡΠ³ΠΎΠ΄Π½ΠΎ.
ΠΠΎΡΡΠ±ΡΠΊΠΈ ΠΈ Π½Π°ΡΡΠΎΠ»ΡΠ½ΡΠ΅ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΡ
Π‘Π»ΡΡΠ°ΠΉΡΠ΅ Π°ΡΠ΄ΠΈΠΎΠΊΠ½ΠΈΠ³ΠΈ ΠΈΠ· Google Play Π² Π²Π΅Π±-Π±ΡΠ°ΡΠ·Π΅ΡΠ΅ Π½Π° ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ΅.
Π£ΡΡΡΠΎΠΉΡΡΠ²Π° Π΄Π»Ρ ΡΡΠ΅Π½ΠΈΡ ΠΊΠ½ΠΈΠ³
Π§ΡΠΎΠ±Ρ ΠΎΡΠΊΡΡΡΡ ΠΊΠ½ΠΈΠ³Ρ Π½Π° ΡΠ°ΠΊΠΎΠΌ ΡΡΡΡΠΎΠΉΡΡΠ²Π΅ Π΄Π»Ρ ΡΡΠ΅Π½ΠΈΡ, ΠΊΠ°ΠΊ Kobo, ΡΠΊΠ°ΡΠ°ΠΉΡΠ΅ ΡΠ°ΠΉΠ» ΠΈ Π΄ΠΎΠ±Π°Π²ΡΡΠ΅ Π΅Π³ΠΎ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²ΠΎ. ΠΠΎΠ΄ΡΠΎΠ±Π½ΡΠ΅ ΠΈΠ½ΡΡΡΡΠΊΡΠΈΠΈ ΠΌΠΎΠΆΠ½ΠΎ Π½Π°ΠΉΡΠΈ Π² Π‘ΠΏΡΠ°Π²ΠΎΡΠ½ΠΎΠΌ ΡΠ΅Π½ΡΡΠ΅.
