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Computational Physics: Numerische Methoden und computergestützte Verfahren mit Python

Computational Physics: Numerische Methoden und computergestützte Verfahren mit Python

          
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About the Book

Das Lehrbuch "Computational Physics" bietet Studierenden einen praxisorientierten Einstieg in die computergestützte Physik

Table of Contents:
1 Fehler und Zahlen 1.1 Vorüberlegungen 1.2 Rundungsfehler 1.3 Stabilität iterativer Algorithmen 2 Lösung linearer Gleichungssysteme, Singulärwertzerlegung 2.1 Fall I: lineare Gleichungssysteme mit eindeutiger Lösung 2.2 Fälle I-III: die Singulärwertzerlegung 3 Eigenwerte und Eigenvektoren 3.1 Mathematische Wiederholung 3.2 Jacobi-Rotation 3.3 Diagonalisierung mit Hilfe des Householder-Algorithmus 3.4 Matrixdiagonalisierung in der Quantenmechanik 3.5 Die Potenzmethode und der Lanczos-Algorithmus 4 Differentiation und Integration 4.1 Differentiation 4.2 Einfache eindimensionale Integrale 4.3 Problematische eindimensionale Integrale 4.4 Hauptwertintegrale 4.5 Mehrdimensionale Integrale 4.6 Fourier-Transformationen 5 Numerische Minimierung 5.1 Funktionen von einer Variablen 5.2 Minimierung im Rn: Liniensuchmethoden 5.3 Newton- und Quasi-Newton-Verfahren 5.4 Minimierung unter Nebenbedingungen 6 Lösung nicht-linearer Gleichungssysteme 6.1 N = 1: Gleichungen einer Variablen 6.2 N > 1: Gleichungssysteme mit mehreren Variablen 6.3 Mathematischer Ausflug: Banachscher Fixpunktsatz 7 Systeme gewöhnlicher Differentialgleichungen 7.1 Problemstellung, Euler-Verfahren 7.2 Runge-Kutta-Verfahren 7.3 Mehr-Schritt-Verfahren 7.4 Steife Differentialgleichungen 8 Partielle Differentialgleichungen 8.1 Einleitung 8.2 Die Poisson-Gleichung 8.3 Anfangswertprobleme 9 Zufallszahlen, Random walks 9.1 Zufallszahlen 9.2 Anwendung: Random walks 10 Klassische Molekulardynamik 10.1 Einleitung 10.2 Messung von Observablen 10.3 Kanonische Molekulardynamik-Simulationen 11 Klassische Monte-Carlo Verfahren 11.1 Integrale, importance sampling 11.2 Das Ising-Modell 11.3 Monte-Carlo Simulationen kontinuierlicher Systeme 11.4 Lösung der Boltzmann-Gleichung 11.5 Optimierung: Das Problem des Handlungsreisenden 12 Gleichgewichts-Mean-Field-Näherungen 12.1 Das Bogoliubov-Variationsprinzip 12.2 Zum Heisenbergmodell mit Spin 1 13 Zeitentwicklung quantenmechanischer Systeme 13.1 Exakte Zeitentwicklung 13.2 Die Magnus-Entwicklung 13.3 Zeitabhängige Variationsnäherung 13.4 Zeitabhängige Hartree-Fock Näherung für Fermionen 14 Grundlagen des Machine Learning


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Product Details
  • ISBN-13: 9783527414284
  • Publisher: Wiley-VCH Verlag GmbH
  • Binding: Paperback
  • Language: German
  • Sub Title: Numerische Methoden und computergestützte Verfahren mit Python
  • ISBN-10: 3527414282
  • Publisher Date: 25 Sep 2024
  • Height: 244 mm
  • No of Pages: 350
  • Width: 170 mm


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