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 Mathematik in Physik und Technik: Eine Einführung mit 572 Aufgaben und Lösungen(Springer-Lehrbuch)

Mathematik in Physik und Technik: Eine Einführung mit 572 Aufgaben und Lösungen(Springer-Lehrbuch)

          
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About the Book

Mathematik in Physik und Technik ist ein Lehrbuch für Studenten der Physik und der Ingenieurwissenschaften, die an sich schon mit den Grundlagen der Mathematik vertraut sind, allerdings noch Schwierigkeiten haben, dieses mathematische Wissen auf konkrete Fragestellungen der Physik zu übertragen. Die vorliegende Aufgabensammlung frischt daher nicht nur latent Vorhandenes auf, sondern versucht, mathematische Methoden in Anlehnung an die Physik anschaulich darzustellen und einzuüben. Welche Rolle spielen Dimensionen, was darf vernachlässigt werden, wie kommt man zu sinnvollen mathematischen Modellen physikalischer Vorgänge? Eine wahre Fundgrube für jeden, der nicht nur Wissen sammeln, sondern auch tatsächlich lernen will, es umzusetzen.

Table of Contents:
1. Rechnen mit physikalischen Größen.- 1.1 Dimensionen.- 1.2 Bilder von Funktionen.- 1.3 Skizzieren von Kurven.- 1.4 Anwendung von Differentialen.- 1.5 Berechnen von Extremen.- 1.6 Approximieren durch Polynome.- 1.7 Anwendung von Integralen.- 2. Fourier-Analyse.- 2.1 Beschreibung von Sinusschwingungen.- 2.2 Fourier-Reihen.- 2.3 Fourier-Integrale.- 3. Vektorrechnung.- 3.1 Vektoralgebra.- 3.2 Vektorfelder.- 3.3 Der Gradient.- 3.4 Die Divergenz.- 3.5 Die Rotation.- 3.6 Ableitung eines Vektors in vorgegebener Richtung.- 3.7 Ableitungen von Produkten und zweite Ableitungen.- 3.8 Die Maxwellschen Gleichungen.- 3.9 Der Satz von Helmholtz.- 3.10 Tensoralgebra.- 3.11 Eigenwerte von symmetrischen Tensoren.- 3.12 Die Tensordivergenz.- 3.13 Der Deformationstensor.- 3.14 Das Hookesche Gesetz.- 4. Gewöhnliche Differentialgleichungen.- 4.1 Geschwindigkeitsfelder.- 4.2 Analytische Lösungsmethoden.- 4.3 Beispiele von Gleichungen erster Ordnung.- 4.4 Eindimensionale stationäre Felder.- 4.5 Das Newtonsche Gesetz.- 4.6 Harmonische Pendel.- 4.7 Gekoppelte Pendel.- 4.8 Anharmonische Pendel.- 5. Partielle Differentialgleichungen.- 5.1 Gleichungen erster Ordnung.- 5.2 Klassifizierung partieller Differentialgleichungen.- 5.3 Die Diffusionsgleichung.- 5.4 Die Schrödingergleichung.- 5.5 Schwingende Saite und Membran.- 5.6 Die Telegrafengleichung.- 5.7 Elastischer Stab.- 5.8 Strömungen.- 5.9 Schallwellen.- 5.10 Elektromagnetische Wellen.- 6. Randbedingungen.- 6.1 Randbedingungen bei der Diffusionsgleichung.- 6.2 Randbedingungen bei der Wellengleichung.- 6.3 Randbedingungen in der Hydrodynamik.- 6.4 Randbedingungen für das elektromagnetische Feld.- 7. Besondere Lösungen linearer Probleme.- 7.1 Lineare Operatoren.- 7.2 Eigenwerte und Eigenfunktionen.- 7.3 Erzwungene Schwingungen.- 7.4Anfangswertprobleme.- 7.5 Greensche Funktionen.- 7.6 Spiegelungen.- 8. Lineare Wellen.- 8.1 Einleitung.- 8.2 Stehende Wellen.- 8.3 Fortschreitende Wellen.- 8.4 Komplexe Wellenzahlen.- 8.5 Multipole.- 9. Integralgleichungen.- 9.1 Beispiele.- 9.2 Lösungsmethoden.- 9.3 Die Boltzmanngleichung.- 10. Analytische Approximationen.- 10.1 Variationsrechnung.- 10.2 Variationsprinzip statt Funktionalgleichung.- 10.3 Direktes Lösen von Variationsproblemen.- 10.4 Störungsrechnung.- 10.5 Quasiklassische Approximation.- 11. Wahrscheinlichkeitsrechnung.- 11.1 Diskrete und kontinuierliche Verteilungen.- 11.2 Wahrscheinlichkeitsverteilungen.- 11.3 Bedingte Wahrscheinlichkeiten.- 11.4 Drei besondere Wahrscheinlichkeitsverteilungen.- 11.5 Mittelwerte.- 11.6 Die binomiale Verteilung.- 11.7 Summen stochastisch unabhängiger Variablen.- 11.8 Statistik.- 11.9 Markovsche Prozesse.- 11.10 Stationäre stochastische Prozesse.- A. Formeln und Tabellen.- B. Glossar oft gebrauchter Zeichen.- C. Allgemeine Literatur.- D. Lösungen der Aufgaben.


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Product Details
  • ISBN-13: 9783540567387
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 455
  • Series Title: Springer-Lehrbuch
  • Sub Title: Eine Einführung mit 572 Aufgaben und Lösungen
  • Width: 155 mm
  • ISBN-10: 3540567380
  • Publisher Date: 09 Sep 1993
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 24 mm
  • Weight: 648 gr


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