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Der mathematische Werkzeugkasten

Anwendungen in Natur und Technik

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Author: Glaeser, Georg

Year: 2006

Publisher: Heidelberg, Elsevier Spektrum Akademischer Verl.

Media group: Ausleihbestand

available

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Branch	Locations	Status	Reservations	Due date	Barcode	Floor plan	Lending note
Branch: Hauptstelle	Locations: MA-10 77	Status: available	Reservations: 0	Due date:	Barcode: 00178276	Floor plans: Floor plan	Lending note:

Content

Einleitung

1. Gleichungen, Gleichungssysteme

1.1 Elementares über Zahlen und Gleichungen

1.2 Lineare Gleichungen

1.3 Lineare Gleichungssysteme

1.4 Quadratische Gleichungen

1.5 Algebraische Gleichungen höheren Grades

1.6 Weitere Anwendungen

2. Proportionen, ähnliche Objekte

2.1 Ähnlichkeit ebener Figuren

2.2 Ähnlichkeit räumlicher Objekte

2.3 Wie im Kleinen, so nicht im Großen!

2.4 Fliehkraft und Gravitation

2.5 Weitere Anwendungen

3. Winkel und Winkelfunktionen

3.1 Die Satzgruppe des Pythagoras

3.2 Bogenmaß

3.3 Sinus, Kosinus, Tangens

3.4 Das schiefwinklige Dreieck

3.5 Weitere Anwendungen

4. Vektorrechnung

4.1 Elementare Vektor-Operationen

4.2 Skalarprodukt und Vektorprodukt

4.3 Schnitt von Geraden und Ebenen

4.4 Abstände, Winkel, Flächen und Volumina

4.5 Spiegelung

4.6 Weitere Anwendungen

5. Funktionen und ihre Ableitungen

5.1 Reelle Funktion und Umkehrfunktion

5.2 Potenz-, Exponential- und Logarithmusfunktion

5.3 Ableitungsfunktion einer reellen Funktion

5.4 Differentiationsregeln

5.5 Differenzieren mit dem Computer

5.6 Lösen von Gleichungen der Form f(x) = 0

5.7 Weitere Anwendungen

6. Kurven und Flächen

6.1 Kongruenz-Bewegungen

6.2 Matrizenrechnung und einige Anwendungen

6.3 Parameterisierung von Kurven

6.4 Hüllkurven

6.5 Flächen

6.6 Weitere Anwendungen

7. Infinitesimalrechnung

7.1 Rechnen mit unendlich kleinen Größen

7.2 Kurvendiskussion

7.3 Extremwertaufgaben

7.4 Reihenentwicklung

7.5 Integrieren als Umkehrvorgang des Differenzierens

7.6 Interpretationen des bestimmten Integrals

7.7 Näherungsweises Integrieren

7.8 Weitere Anwendungen

A. Zahlen

A.1 Zahlenmagie

A.2 Rationale und irrationale Zahlen

A.3 Berühmte irrationale Zahlen

A.4 Die Fibonacci-Zahlen

A.5 Imaginäre und komplexe Zahlen

B. Musik und Mathematik

B.1 Denkansatz, naturwissenschaftliche Grundlagen

B.2 Systembildung

B.3 Stimmung von Instrumenten - Intonation

B.4 Zahlensymbolik

B.5 Zeitgestalt - Rhythmus

B.6 Harmonik (Harmonikale Grundlagenforschung)

B.7 Rechenbeispiele

Index

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Details

Author: Glaeser, Georg

Statement of Responsibility: Georg Glaeser

Year: 2006

Publisher: Heidelberg, Elsevier Spektrum Akademischer Verl.

Classification: MA-10, FO-80

Subject type: Lehrbücher

ISBN: 3827416183

ISBN (2nd): 9783827416186

Description: 2. Auflage, XIV, 402 S. : Ill., graph. Darst.

Tags: Mathematik allgemein; Mathematik; Forschung, Organisation, Recht; Fortbildung

Media group: Ausleihbestand

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