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book: Mathematik für die ersten Semester
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Mathematik für die ersten Semester

  • Wolfgang Mückenheim
Language: German
Published/Copyright: 2015
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De Gruyter Studium
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De Gruyter Studium

About this book

This book teaches what is known as higher mathematics – in other words, mathematics that extends beyond simple calculation, which is generally taught in the last years of high school and extended and learned in greater depth in the first semester of college study. It begins with an introduction to the language of mathematics and then covers the themes of arithmetic, algebra, geometry, and infinitesimal calculus.

  • Mathematics for the start of study
  • Clear, compact, and marvelously descriptive
  • For students majoring in technology and the natural sciences

Author / Editor information

Wolfgang Mückenheim, Hochschule Augsburg.

Topics

  • Publicly Available

    Frontmatter

    I
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    Vorwort

    V
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    Über Mathematik und Wirklichkeit und dieses Buch

    VII
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  • Publicly Available

    Inhalt

    XI
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  • Teil I: Grundlagen
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    1. Logik

    3
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    2. Mengen

    8
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    3. Relationen

    15
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  • Teil II: Arithmetik
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    4. Die natürlichen Zahlen

    25
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    5. Erweiterungen der Zahlenmenge

    31
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  • Teil III: Elementare Geometrie
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    6. Ebene Geometrie

    45
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    7. Trigonometrie

    51
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    8. Vektoren

    55
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    9. Geometrie des ℝ3

    68
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  • Teil IV: Lineare Algebra
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    10. Lineare Gleichungssysteme

    81
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    11. Matrizen

    90
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    12. Determinanten

    99
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    13. Transformationen mit Matrizen

    114
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    14. Iterative Lösung von linearen Gleichungssystemen

    127
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  • Teil V: Algebra und Geometrie
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    15. Polynome

    133
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    16. Zweidimensionale quadratische Formen

    144
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    17. Die Kegelschnitte

    152
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    18. Sphärische Geometrie

    175
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  • Teil VI: Infinitesimalrechnung
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    19. Folgen

    183
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    20. Reihen

    191
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    21. Stetige Funktionen

    197
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    22. Funktionenfolgen und Funktionenreihen

    200
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  • Teil VII: Differentialrechnung
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    23. Der Differentialquotient

    207
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    24. Die Exponentialfunktion

    214
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    25. Die Winkelfunktionen

    224
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    26. Kurvendiskussion

    230
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    27. Approximation von Funktionen

    234
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    28. Funktionen mehrerer Variablen

    245
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  • Teil VIII: Integralrechnung
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    29. Das Integral

    253
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    30. Integrationsmethoden

    257
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    31. Kurvenlänge und Kurvenkrümmung

    268
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    32. Mehrfachintegrale

    270
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    33. Integraltransformationen

    274
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  • Teil IX: Vektoranalysis
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    34. Differentiation von Feldern

    289
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    35. Integralsätze

    299
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  • Teil X: Differentialgleichungen
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    36. Gewöhnliche Differentialgleichungen

    307
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    Literatur

    313
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    Stichwortverzeichnis

    315
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
May 19, 2015
eBook ISBN:
9783110377347
Paperback published on:
April 24, 2015
Paperback ISBN:
9783110377330
Edition:
4. Aufl.
Pages and Images/Illustrations in book
Front matter:
16
Main content:
325
https://doi.org/10.1515/9783110377347
eBook ISBN: 9783110377347
Paperback ISBN: 9783110377330
Keywords for this book
Mathematik; Einführung; Algebra
Audience(s) for this book
Students of technology and science including at universities of technology
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