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FHC_Interactive_Calculus_1A

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FHC_Interactive_Calculus_1A

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

Mathematics
Author
Jennifer Sinclair
Publisher
Foothill College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 83 sections
  1. 01: Functions and Graphs
  2. 1.00: Prelude to Functions and Graphs
  3. 1.01: Review of Functions
  4. 1.1E: Exercises for Section 1.1
  5. 1.02: Basic Classes of Functions
  6. 1.2E: Exercises for Section 1.2
  7. 1.03: Trigonometric Functions
  8. 1.3E: Exercises for Section 1.3
  9. 1.04: Inverse Functions
  10. 1.4E: Exercises for Section 1.4
  11. 1.05: Exponential and Logarithmic Functions
  12. 1.5E: Exercises for Section 1.5
  13. 1.06: Chapter 1 Review Exercises
  14. 02: Limits
  15. 2.00: Prelude to Limits
  16. 2.01: A Preview of Calculus
  17. 2.1E: Exercises for Section 2.1
  18. 2.02: The Limit of a Function
  19. 2.2E: Exercises for Section 2.2
  20. 2.03: The Limit Laws
  21. 2.3E: Exercises for Section 2.3
  22. 2.04: Continuity
  23. 2.4E: Exercises for Section 2.4
  24. 2.05: Chapter 2 Review Exercises
  25. 03: Derivatives
  26. 3.00: Prelude to Derivatives
  27. 3.01: Defining the Derivative
  28. 3.1E: Exercises for Section 3.1
  29. 3.02: The Derivative as a Function
  30. 3.2E: Exercises for Section 3.2
  31. 3.03: Differentiation Rules
  32. 3.3E: Exercises for Section 3.3
  33. 3.04: Derivatives as Rates of Change
  34. 3.4E: Exercises for Section 3.4
  35. 3.05: Derivatives of Trigonometric Functions
  36. 3.5E: Exercises for Section 3.5
  37. 3.06: The Chain Rule
  38. 3.6E: Exercises for Section 3.6
  39. 3.07: Derivatives of Inverse Functions
  40. 3.7E: Exercises for Section 3.7
  41. 3.08: Implicit Differentiation
  42. 3.8E: Exercises for Section 3.8
  43. 3.09: Derivatives of Exponential and Logarithmic Functions
  44. 3.9E: Exercises for Section 3.9
  45. 3.10: Chapter 3 Review Exercises
  46. 04: Applications of Derivatives
  47. 4.00: Prelude to Applications of Derivatives
  48. 4.01: Related Rates
  49. 4.1E: Exercises for Section 4.1
  50. 4.02: Linear Approximations and Differentials
  51. 4.2E: Exercises for Section 4.2
  52. 4.03: Maxima and Minima
  53. 4.3E: Exercises for Section 4.3
  54. 4.04: The Mean Value Theorem
  55. 4.4E: Exercises for Section 4.4
  56. 4.05: Derivatives and the Shape of a Graph
  57. 4.5E: Exercises for Section 4.5
  58. 4.06: Limits at Infinity and Asymptotes
  59. 4.6E: Exercises for Section 4.6
  60. 4.07: Applied Optimization Problems
  61. 4.7E: Exercises for Section 4.7
  62. 4.08: LHopitals Rule
  63. 4.8E: Exercises for Section 4.8
  64. 4.09: Antiderivatives
  65. 4.9E: Exercises for Section 4.9
  66. 4.10: Chapter 4 Review Exercises
  67. 05: Parametric Equations and Polar Coordinates
  68. 5.00: Prelude to Parametric Equations and Polar Coordinates
  69. 5.01: Parametric Equations
  70. 5.1E: Exercises for Section 5.1
  71. 5.02: Slopes and Tangent Lines of Parametric Curves
  72. 5.2E: Exercises for Section 5.2
  73. 5.03: Polar Coordinates
  74. 5.3E: Exercises for Section 5.3
  75. 5.04: Chapter 5 Review Exercises
  76. 06: Appendices
  77. 6.00: A- Table of Derivatives
  78. 6.01: The Precise Definition of a Limit
  79. 6.1E: Exercises for Section 2.5
  80. 6.02: Newtons Method
  81. 6.2E: Exercises for Section 4.9
  82. 6.03: Conic Sections
  83. 6.3E: Exercises for Section 3.6