Einführung in die mathematischen Methoden der Theoretischen Physik
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Einführung in die mathematischen Methoden der Theoretischen Physik

Einführung in die mathematischen Methoden der Theoretischen Physik

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About the Book

Table of Contents:
1. Mathematische Grundlagen.- 1.1. Der Begriff des Feldes und des Gradienten.- 1.2. Integration der Feldgrößen.- 1.3. Tensoren.- 1.4. Koordinatentransformationen.- 1.5. Einfachste Differentialoperatoren.- 1.6. Übungsbeispiele zu Kap. 1.- 2. Partielle Differentialgleichungen der Physik.- 2.1. Die Poissonsche Differentialgleichung.- 2.2. Die partielle Differentialgleichung von Schwingungsvorgängen.- 2.3. Die Differentialgleichungen der Diffusion und Wärmeleitung.- 2.4. Einfachste Differentialgleichungen der Quantenmechanik.- 2.5. Übungsbeispiele zu Kap. 2.- 3. Lösungsansätze für partielle Differentialgleichungen.- 3.1. Trennung der Variablen.- 3.2. Die Laplacegleichung.- 3.3. Die schwingende Saite.- 3.4. Übungsbeispiele zu Kap. 3.- 4. Rand und Eigenwertaufgaben.- 4.1. Problemstellung.- 4.2. Sturm-Liouville-Differentialoperatoren.- 4.3. Der Entwicklungssatz.- 4.4. Die Lösung der Anfangsrandwertaufgabe.- 4.5. Die inhomogene Randwertaufgabe.- 4.6. Nadelartige Funktionen.- 4.7. Ergänzungen und Bemerkungen.- 4.8. Übungsbeispiele zu Kap. 4.- 5. Singuläre Differentialgleichungen.- 5.1. Der Begriff der singulären Differentialgleichung. Differentialgleichungen der Fuchsschen Klasse.- 5.2. Die hypergeometrische Differentialgleichung.- 5.3. Die konfluente hypergeometrische Differentialgleichung.- 5.4. Übungsbeispiele zu Kap. 5.- 6. Spezielle Funktionen.- 6.1. Kugelfunktionen.- 6.2. Zylinderfunktionen.- 6.3. Hermitesche und Laguerresche Polynome.- 6.4. Übungsbeispiele zu Kap. 6.- 7. Verallgemeinerte Funktionen.- 7.1. Problemstellung.- 7.2. Testfunktionen.- 7.3. Verallgemeinerte Funktionen.- 7.4. Die Diracsche Deltafunktion.- 7.5. Die Derivierte einer verallgemeinerten Funktion.- 7.6. Produkte von verallgemeinerten Funktionen. Das Funktional ?(g(x)).- 7.7. Dieuneigentliche Funktion ?(1/r).- 7.8. Ergänzungen und Bemerkungen.- 7.9. Übungsbeispiele zu Kap. 7.- 8. Die Methode der Greenschen Funktionen für partielle Differentialgleichungen.- 8.1. Die klassische Lösung der Poissongleichung.- 8.2. Greensche Funktionen und die Deltafunktion.- 8.3. Die Greensche Funktion der Poissongleichung.- 8.4. Die Greensche Funktion der Wärmeleitung (Diffusion).- 8.5. Die Greenschen Funktionen der Wellengleichung und ihrer Verallgemeinerungen.- 8.6. Übungsbeispiele zu Kap. 8.- A. Funktionentheorie.- B. Die Gammafunktion.- Literatur.- Sachwortverzeichnis.


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Product Details
  • ISBN-13: 9783528033194
  • Publisher: Springer Fachmedien Wiesbaden
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Width: 170 mm
  • ISBN-10: 3528033193
  • Publisher Date: 01 Jan 1976
  • Height: 244 mm
  • No of Pages: 212
  • Returnable: Y


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Einführung in die mathematischen Methoden der Theoretischen Physik
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