Math 3AC: Analytic Geometry and Calculus I

by Kenn Huber

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A new take on the classic mathematical approach of learning Precalculus and Calculus separately, this book merges the two topics together. Using calculus notation to inspire the precalculus examples helps students of either a Precalculus or Calculus with support course.

Description from LibreTexts.

Publisher
Irvine Valley College
Subjects
Mathematics
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Basic Algebra Review
  7. 1.1: Solving Linear Equations
  8. 1.2: Plotting in the Cartesian Plane
  9. 1.3: Slopes and 3 Forms for Lines
  10. 1.4: Solving Linear Inequalities
  11. 1.5: Functions
  12. 1.6: Solving Non-Linear Equations
  13. 1.7: Graph Transformations
  14. 1.8: Parabolas
  15. 1.9: Quadratic Equations
  16. 2: Limits
  17. 2.1: Definition of Limit
  18. 2.2: Limit Laws
  19. 2.3: Polynomial Functions
  20. 2.4: Polynomial Inequalities
  21. 3: Rational Functions
  22. 3.1: Domains of Functions
  23. 3.2: Rational Functions
  24. 3.3: Using Rational Functions
  25. 3.4: Limits and Rational Functions
  26. 3.5: Asymptotes
  27. 4: Basic Trigonometry
  28. 4.1: Circles and Triangles
  29. 4.2: Functions of the Circle
  30. 4.3: Ratios in Triangles
  31. 4.4: Graphing Other Trigonometric Functions
  32. 4.5: Trigonometric Identities
  33. 5: Continuity
  34. 5.1: Continuous Functions
  35. 5.2: Piecewise Functions
  36. 5.3: Absolute Value Functions
  37. 5.4: The Intermediate Value Theorem
  38. 6: Function Algebra
  39. 6.1: Basic Function Algebra
  40. 6.2: Inverses
  41. 6.3: Radical Functions
  42. 7: Derivatives
  43. 7.1: Tangent Lines and the Derivative
  44. 7.2: An Alternate Definition of Derivative
  45. 7.3: Derivative as a Function
  46. 7.4: Differentiability
  47. 7.5: Derivatives and Graphs
  48. 8: More Derivatives
  49. 8.1: Derivative Shortcuts
  50. 8.2: Trig Derivatives
  51. 8.3: Exponential Functions
  52. 8.4: Derivatives of Exponential Functions
  53. 8.5: Derivative Examples
  54. 9: Chain Rule and Inverse Trig Functions
  55. 9.1: Chain Rule
  56. 9.2: Inverse Functions and Derivatives
  57. 9.3: The Inverse Trigonometric Functions
  58. 9.4: Applications of Inverse Trig Functions
  59. 9.5: Derivatives of Inverse Trig Functions
  60. 10: Logarithms
  61. 10.1: Logarithms
  62. 10.2: Exponential Growth and Decay
  63. 10.3: Derivatives of Logarithms
  64. 10.4: Logarithmic Differentiation
  65. 11: Applications of Derivatives
  66. 11.1: Theorems of Calculus
  67. 11.2: Linearization
  68. 11.3: Extreme Values
  69. 11.4: Implicit differentiation
  70. 11.5: L’Hopital’s Rule
  71. 11.6: Curve Sketching
  72. 12: Word Problems with Derivatives
  73. 12.1: Linearization
  74. 12.2: Related Rates
  75. 12.3: Optimization
  76. 12.4: Solving Trigonometric Equations
  77. 12.5: Trigonometric Applications
  78. 12.6: Hyperbolic Trigonometric Functions
  79. 12.7: Inverse Hyperbolic Trigonometric Functions
  80. 13: Integrals
  81. 13.1: Areas and Distances
  82. 13.2: Definite Integrals
  83. 13.3: The Fundamental Theorem of Calculus
  84. 13.4: Anti-Derivatives and the Indefinite Integral
  85. 13.5: More Definite Integrals
  86. 13.6: Anti-derivative Applications
  87. Back Matter
  88. Index
  89. Glossary
  90. Detailed Licensing
  91. Detailed Licensing