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SIF5088 PARTIELLE DIFFERENSIALLIGNINGER (PARTIAL DIFFERENTIAL EQUATIONS)
HØSTEN 2002

  A partial differential equation is an equation involving a function of several variables, and its partial derivatives. Many natural laws come in the form of partial differential equations. Thus these are important in science, in particular in physics, astronomy, and mathematiacal modelling. Partial differential equations also occur in pure mathematics. The course aims at giving the student a good understanding of the basic methods and fundamental theories of this interesting field of mathematical analysis.
Om kurset Kurset foreleses med to dobbelt-timer i uken. Foreläsningarna hålles på svenska.
Foreleser  Professor Peter Lindqvist
Institutt for matematiske fag
Rom 1152 SBII
Tlf. 73 59 35 29
lqvist@math.ntnu.no
Lærebok Utvalgte deler av R. McOwen: "Partial Differential Equations (Methods and Applications), Prentice Hall 1996. Prøv å få den utgaven som er slik at på siden som står motsatt "Preface" står det "1098765432", og det stoppes med "2" og ikke inkluderer "1". Alle bøker trykt 1998 eller senere duger bra ("Second Edition") Se http://www.math.neu.edu/~mcowen/PDE_errata.html for rettelser
Forelesninger Mandag 12 - 14 og onsdag 8 - 10 i rom F3.
Begynner 19. august.
Øvinger Fredag 14 - 15 i rom F3
Begynner 30. august.

  
  Øving 30.8.
§ 1.1 Exs. 4, 5b, 6a
§ 1.2 Ex. 2
 Øving 6.9.
§ 1.2 Ex. 5
§ 1.4 Ex. 1
§ 2.1 Exs.1, 4
§ 2.2 Ex. 4
§ 2.3 Ex. 10a
 Øving 13.9.
§ 2.1 Ex. 7
§ 3.1 Ex. 1
§ 3.2 Exs. 1, 2, 5
Øving 20.9.
§ 3.3 Ex. 6
§ 3.4 Ex. 1
§ 4.1 Ex. 6
 Øving 27.9.
§ 4.1 Ex. 7
§ 4.2 Exs. 10, 11
§ 4.3 Exs. 1, 2		 Øving 4.10.
§ 4.1 Ex. 5
§ 4.3 Exs. 3, 4
§ 4.4 Exs. 2, 8
  Øving 11.10.
§ 5.1 Ex. 7
§ 5.2 Exs. 1b, 1c, 4, 11
 Øving 18.10.
§ 5.1 Ex. 1
§ 5.2 Exs 2, 5, 7, 8
§ 5.3 Ex. 3
 Øving 25.10.
§ 6.1 Exs. 2, 3, 5a
§ 6.2 Exs. 2
  Øving 1.11.
§ 6.1 Exs. 5c, 6
§ 6.2 Ex. 1
§ 6.5 Ex. 2
 Øving 8.11.
Selected examples		 Øving 22.11.
Selected examples
Pensum
Chapter 1: § 1.1 a-d, § 1.2, § 1.4
Chapter 2: § 2.1, § 2.2 a, § 2.3 a, c, d
Chapter 3: § 3.1, § 3.2 c (Kirchhoff's formula), e, § 3.3, § 3.4
Chapter 4  
Chapter 5  
Chapter 6: § 6.1a (The LP-norm, Hölder's inequality, Minkowski's inequality, strong and weak convergence), § 6.1b (Definition of weak derivatives and of the Sobolev spaces H1,P, W1,P, and H01,P), § 6.2a (Poincaré's inequality in Theorem 1), § 6.4 (Sobolev's inequality), § 6.5 (H=W and Kondrachov's theorem, both without proof).
It is also required to find the Euler-Lagrange equation of a variational integral.
All the exercises.



Eksamen 29. november 2002.
Lovlig hjelpemiddel er ett A4 ark der man kan skrive hva man vil. Bare offisielle ark er godkjent. Disse fås på inst. ktr. i 4. etasje Sentralbygg II.
  Følgende bøker kan dessutom anbefalas:

L. Evans: Partial Differential Equations, AMS 1998 - More advanced than McOwen, but all details are clearly exposed. Reliable!

J. Jost: Partielle Differentialgleichungen, Springer 1998. - A good one!

J. Logan: An Introduction to Nonlinear Partial Differential Equations, John Wiley & Sons 1994.- Informative, interesting, and easy to read.

F. John: Partial Differential Equations, Springer 1986.
A rather advanced account of the classical theory.

A. Tveito & R. Winther: Introduction to Partial Differential Equations (A Computational Approach), Springer 1988. - An excellent elementary account!
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Oppdatert: 2002-09-30

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