Numerische Methoden in der Technik
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Numerische Methoden in der Technik: Ein Lehrbuch mit MATLAB-Routinen

Numerische Methoden in der Technik: Ein Lehrbuch mit MATLAB-Routinen


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About the Book

Iterationsverfahren zur Losung nichtlinearer Gleichungen - Lineare Gleichungssysteme - Lineare Optimierung - Interpolation und Approximation - Numerische Integration - Differentialgleichungen - Aufgaben - Losungen

Table of Contents:
1 Einführung.- 2 Iterationsverfahren zur Lösung nichtlinearer Gleichungen.- 2.1 Fixpunktsatz.- 2.2 Fehlerschranken.- 2.3 Newtonverfahren.- 2.4 Regula falsi.- 2.5 Konvergenzordnung.- 2.6 Übertragung auf mehrdimensionale Probleme.- 2.7 Realisierung mit MATLAB.- 3 Lineare Gleichungssysteme.- 3.1 Gauß-Algorithmus.- 3.2 Pivotelementsuche.- 3.3 Nachiteration.- 3.4 Iterative Lösung von linearen Gleichungssystemen.- 3.5 Überbestimmtes lineares Gleichungssystem.- 3.6 Nichtlineare Ausgleichsprobleme.- 4 Lineare Optimierung.- 4.1 Austauschverfahren.- 4.2 Graphische Lösung des linearen Optimierungsproblems.- 4.3 Simplex-Verfahren.- 5 Interpolation und Approximation.- 5.1 Polynominterpolation.- 5.2 Ausgleichspolynome.- 5.3 Kubische Splines.- 5.4 Bezier Splines.- 5.5 Approximation durch trigonometrische Polynome.- 5.6 Fast Fourier Transformation.- 6 Numerische Integration.- 6.1 Trapezformel.- 6.2 Simpsonformel.- 6.3 Rombergverfahren.- 7 Differentialgleichungen.- 7.1 Eulerverfahren.- 7.2 Weitere Einschrittverfahren.- 7.3 MATLAB-Routinen.- 7.4 Wasserrakete — Beispiel für ein Differentialgleichungssystem.- 7.5 Implizite Verfahren.- 7.6 Stabilität.- 7.7 Mehrschrittverfahren.- 7.8 Randwertaufgaben.- 7.9 Partielle Differentialgleichungen.- 8 Aufgaben.- 8.1 Aufgaben zu Gleitpunktarithmetik.- 8.2 Aufgaben zu Iterationsverfahren.- 8.3 Aufgaben zu linearen Gleichungssystemen.- 8.4 Aufgaben zur linearen Optimierung.- 8.5 Aufgaben zu Interpolation und Approximation.- 8.6 Aufgaben zu Integration und Differentialgleichungen.- 8.7 Aufgaben zu MATLAB.- 9 Lösungen.- 9.1 Aufgaben zu Gleitpunktarithmetik.- 9.2 Aufgaben zu Iterationsverfahren.- 9.3 Aufgaben zu linearen Gleichungssystemen.- 9.4 Aufgaben zur linearen Optimierung.- 9.5 Aufgaben zu Interpolation und Approximation.- 9.6 Aufgabenzu Integration und Differentialgleichungen.- 9.7 Aufgaben zu MATLAB.- A Einführung in MATLAB.- A.1 Allgemeines.- A.2 Fundamentals.- A.2.1 Eingabe von Matrizen.- A.2.2 Matrixelemente.- A.2.3 Variable.- A.2.4 Information über Variable.- A.2.5 Zahlen und Arithmetik.- A.2.6 Komplexe Zahlen.- A.2.7 Ausgabeformat.- A.2.8 Help-Funktion.- A.2.9 Sichern.- A.3 Matrizen, Vektoren.- A.3.1 Rechenoperationen.- A.3.2 Matrizenfunktionen.- A.3.3 Elementeweise Rechenoperationen.- A.3.4 Vektor- und Matrixmanipulationen.- A.4 Analysis.- A.4.1 Differentiation.- A.4.2 Integration.- A.4.3 Polynome.- A.4.4 Interpolation.- A.4.5 Nichtlineare Gleichungen und Optimierung.- A.4.6 Differentialgleichungen.- A.5 Graphik.- A.5.1 Zweidimensionale Graphik.- A.5.2 Dreidimensionale Graphik.- A.5.3 Graphikbildschirm.- A.6 Programmsteuerung.- A.6.1 for-Schleifen.- A.6.2 while-Schleifen.- A.6.3 if/else Ausdrücke.- A.6.4 Vergleichsoperatoren, logische Operatoren.- A.6.5 Eingabe.- A.7 m-Files.- A.7.1 Programm-Files.- A.7.2 function-Files.- B Verzeichnis der m-Files.- C Orthogonalitätsbeziehungen.- E Drei-Körper-Problem.- Sachwortverzeichnis.

About the Author :
Prof. Dr. Richard Mohr lehrt und forscht im Fachbereich Grundlagen der Fachhochschule für Technik in Esslingen.


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Product Details
  • ISBN-13: 9783528069889
  • Publisher: Springer Fachmedien Wiesbaden
  • Publisher Imprint: Vieweg+Teubner Verlag
  • Height: 244 mm
  • No of Pages: 250
  • Returnable: N
  • Width: 170 mm
  • ISBN-10: 3528069880
  • Publisher Date: 11 Sep 1998
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Sub Title: Ein Lehrbuch mit MATLAB-Routinen


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Numerische Methoden in der Technik: Ein Lehrbuch mit MATLAB-Routinen
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