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## TMA4305 PARTIELLE DIFFERENSIALLIGNINGER (PARTIAL DIFFERENTIAL EQUATIONS)VÅREN 2005

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 in this interesting field of mathematical analysis.

Om kurset Kurset foreleses med to dobbelt-timer i uken. The lectures are in English.
Foreleser
Professor Peter Lindqvist
Institutt for matematiske fag
Rom 1152 SBII
Tlf. 73 59 35 29
lqvist@math.ntnu.no
Lærebok Utvalgte deler av L.C. Evans: "Partial Differential Equations , AMS 1998.
Forelesninger Tirsdag 10 - 12 rom F4 (gamle fysikk)
Fredag 12 - 14 rom F4 (gamle fysikk).
Begynner 11. januar.
Øvinger Mandag 16:15-17:00 R21 (Realfagb. A, U2)
Exercise 24.1. § 2.5 ex. 1, 2, 3, 4. ( 18-19 i F4 )
Exercise 31.1. § 2.5 ex. 4, 5, 6 (16-17 i R21)
Exercise 7.2 § 2.5, ex. 9, 10, 11, 12
Exercise 14.2 § 2.5 ex. 14 b, 14 c, 15 a, 15 b.
Exercise 21.2 § 2.5 ex. 16, 17, 18
Exercise 28.2 § 3.5 ex. 13, 14
Exercise 14.3 § 3.5 ex. 2, 3
Exercise 4.3 § 6.4 ex. 5, 6, 7
Exercise 11.3 §5.10 ex. 6,8, 13
Pensum Utvalgte deler av Chapt. 1,2,3,4,5,6,8.
 Chapter 1 . Chapter 2 . Chapter 3 Sections 3.2.1, 3.2.2, 3.4.1. Chapter 4 Section 4.4.1. Chapter 5 Sections 5.1, 5.2, 5.3.2, 5.6.1, 5.7 Chapter 6 Section 6.4 Chapter 8 Section 8.1.2 Alle øvingsoppgaver.
Eksamen 9. juni. Tillatt hjelpemiddel er et A4-ark der man kan skrive hva man vil. Bare offisielle ark er godkjent. Disse fås på instituttkontoret i 4. etasje, Sentralbygg II.

Følgende bøker kan dessuten anbefales:

R. McOwen: Partial Differential Equations (Methods and Applications), Prentice Hall.

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

J. Jost: Partial Differential Equations, Springer 2002 (In particular, Chapter 8 is a comprehensible account of Sobolev's space.)

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!

H.Holden & N. Risebro: Front Tracking for Hyperbolic Conservation Laws, Springer 2002. - Chapter 1 is an excellent introduction.

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