Analytische Geometrie Für Studierende Der Technik Und Zum Selbststudium
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I. Graphische Darstellungen.- 1. Das rechtwinklige Koordinatensystem.- 2. Graphische Darstellungen.- 3. Beispiele und Übungen.- II. Punkte und Strecken.- 4. Entfernung zweier Punkte.- 5. Steigung. Richtungswinkel eines Vektors.- 6. Beispiele.- 7. Teilungsverhältnis.- 8. Inhalt eines Vielecks.- III. Die gerade Linie.- 9. Die Hauptgleichung der Geraden.- 10. Beispiele.- 11. Andere Gleichungsformen der Geraden.- 12. Beispiele.- 13. Überführung der allgemeinen Gleichung in die Normalform.- 14. Abstand eines Punktes von einer Geraden.- 15. Die Gleichungen der Winkelhalbierenden.- 16. Strahlenbüschel.- 17. Verschiedene Längeneinheiten auf den Koordinatenachsen.- IV. Allgemeines über Kurvengleichungen.- 18. Tangente als Grenzlage einer Sekante.- 19. Parallelverschiebung und Drehung des Koordinatensystems.- 20. Polarkoordinaten.- 21. Parameterdarstellung.- V. Der Kreis..- 22. Die Kreisgleichung.- 23. Beispiele.- 24. Kreistangente.- 25. Kreisbüschel.- 26. Polargleichung des Kreises.- VI. Die Parabel.- 27. Definition. Scheitelgleichung.- 28. Eine einfache Konstruktion der Parabel.- 29. Parallele Sehnen.- .30. Gleichung der Tangente. Tangent?neigenschaften.- 31. Normale und Subnormale.- 32. Krümmungskreis im Scheitel der Parabel.- 33. Fläche eines Parabelsegments.- 34. Beispiele.- 35. Die Parabel als Bild der ganzen Funktion.- 36. Gleichung der Tangente in einem Punkte der Parabel.- 37. Beispiele.- VII. Die Ellipse.- 38. Affine Kurven.- 39. Die Ellipse als affine Figur des Kreises.- 40. Konstruktion der Ellipse aus den Scheitelkreisen.- 41. Konstruktion und Gleichung der Tangente.- 42. Der Ellipsenzirkel.- 43. Parametergleichung.- 44.Scheitelgleichung der Ellipse.- 45. Krümmungskreise in den Scheiteln der Ellipse.- 46. Die Diagonalpunkte mit ihren Tangenten.- 47. Beispiele.- 48. Die Ellipse als Kreisprojektion. Fläche.der Ellipse.- 49. Konjugierte Durchmesser.- 50. Brennpunkte der Ellipse.- VIII. Die Hyperbel.- 51. Flächengleiche Parallelogramme. Achsengleichung.- 52. Asymptoten. Scheitel. Achsen.- 53. Zwei Hyperbelkonstruktionen.- 54. Konstruktion und Gleichung einer Tangente.- 55. Eine Parameterdarstellung.- 56. Beispiele.- 57. Die Asymptoten oder Parallele dazu als Koordinatenachsen.- 58. Beispiele.- 59. Brennpunkte einer Hyperbel.- 60. Beispiele.- IX. Allgemeine Gleichungen der Kegelschnitte.- 61. Kegelschnitte.- 62. Die allgemeine Gleichung 2. Grades mit zwei Variablen.- 63. Beispiele.- 64. Umformung der Parabelgleichung.- 65. Beispiele.- 66. Besondere Fälle.- Ergebnisse.
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