FHC_Interactive_Calculus_1A

by Jennifer Sinclair

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Introduction to differential calculus, including limits, derivatives and their applications to curve-sketching, families of functions, and optimization. Includes polar and parametric equations.

Description from LibreTexts.

Publisher
Foothill 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

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Functions and Graphs
  7. 1.0: Prelude to Functions and Graphs
  8. 1.1: Review of Functions
  9. 1.1E: Exercises for Section 1.1
  10. 1.2: Basic Classes of Functions
  11. 1.2E: Exercises for Section 1.2
  12. 1.3: Trigonometric Functions
  13. 1.3E: Exercises for Section 1.3
  14. 1.4: Inverse Functions
  15. 1.4E: Exercises for Section 1.4
  16. 1.5: Exponential and Logarithmic Functions
  17. 1.5E: Exercises for Section 1.5
  18. 1.6: Chapter 1 Review Exercises
  19. 2: Limits
  20. 2.0: Prelude to Limits
  21. 2.1: A Preview of Calculus
  22. 2.1E: Exercises for Section 2.1
  23. 2.2: The Limit of a Function
  24. 2.2E: Exercises for Section 2.2
  25. 2.3: The Limit Laws
  26. 2.3E: Exercises for Section 2.3
  27. 2.4: Continuity
  28. 2.4E: Exercises for Section 2.4
  29. 2.5: Chapter 2 Review Exercises
  30. 3: Derivatives
  31. 3.0: Prelude to Derivatives
  32. 3.1: Defining the Derivative
  33. 3.1E: Exercises for Section 3.1
  34. 3.2: The Derivative as a Function
  35. 3.2E: Exercises for Section 3.2
  36. 3.3: Differentiation Rules
  37. 3.3E: Exercises for Section 3.3
  38. 3.4: Derivatives as Rates of Change
  39. 3.4E: Exercises for Section 3.4
  40. 3.5: Derivatives of Trigonometric Functions
  41. 3.5E: Exercises for Section 3.5
  42. 3.6: The Chain Rule
  43. 3.6E: Exercises for Section 3.6
  44. 3.7: Derivatives of Inverse Functions
  45. 3.7E: Exercises for Section 3.7
  46. 3.8: Implicit Differentiation
  47. 3.8E: Exercises for Section 3.8
  48. 3.9: Derivatives of Exponential and Logarithmic Functions
  49. 3.9E: Exercises for Section 3.9
  50. 3.10: Chapter 3 Review Exercises
  51. 4: Applications of Derivatives
  52. 4.0: Prelude to Applications of Derivatives
  53. 4.1: Related Rates
  54. 4.1E: Exercises for Section 4.1
  55. 4.2: Linear Approximations and Differentials
  56. 4.2E: Exercises for Section 4.2
  57. 4.3: Maxima and Minima
  58. 4.3E: Exercises for Section 4.3
  59. 4.4: The Mean Value Theorem
  60. 4.4E: Exercises for Section 4.4
  61. 4.5: Derivatives and the Shape of a Graph
  62. 4.5E: Exercises for Section 4.5
  63. 4.6: Limits at Infinity and Asymptotes
  64. 4.6E: Exercises for Section 4.6
  65. 4.7: Applied Optimization Problems
  66. 4.7E: Exercises for Section 4.7
  67. 4.8: L’Hôpital’s Rule
  68. 4.8E: Exercises for Section 4.8
  69. 4.9: Antiderivatives
  70. 4.9E: Exercises for Section 4.9
  71. 4.10: Chapter 4 Review Exercises
  72. 5: Parametric Equations and Polar Coordinates
  73. 5.0: Prelude to Parametric Equations and Polar Coordinates
  74. 5.1: Parametric Equations
  75. 5.1E: Exercises for Section 5.1
  76. 5.2: Slopes and Tangent Lines of Parametric Curves
  77. 5.2E: Exercises for Section 5.2
  78. 5.3: Polar Coordinates
  79. 5.3E: Exercises for Section 5.3
  80. 5.4: Chapter 5 Review Exercises
  81. 6: Appendices
  82. 6.0: A- Table of Derivatives
  83. 6.1: The Precise Definition of a Limit
  84. 6.1E: Exercises for Section 2.5
  85. 6.2: Newton’s Method
  86. 6.2E: Exercises for Section 4.9
  87. 6.3: Conic Sections
  88. 6.3E: Exercises for Section 3.6
  89. Back Matter
  90. Index
  91. Glossary
  92. Detailed Licensing