Analytic Geometry and Calculus I (IVC Math 3A OER)

by Leonard Lamp, Kenn Huber & Mohamad Youssef

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This course covers basic concepts of analytic geometry, limits and continuity; and differentiation and integration of algebraic, trigonometric, exponential, logarithmic and hyperbolic functions. Applications include related rates and optimization problems. L'hospital's rule is studied. Credit may be earned in MATH 3A or 3AH, but not both. C-ID: MATH 210

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

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Functions and Graphs
  7. 1.1: Prelude to Functions and Graphs
  8. 1.2: Review of Functions
  9. 1.2E: Exercises for Section 1.2
  10. 1.3: Basic Classes of Functions
  11. 1.3E: Exercises for Section 1.3
  12. 1.4: Trigonometric Functions
  13. 1.4E: Exercises for Section 1.4
  14. 1.5: Inverse Functions
  15. 1.5E: Exercises for Section 1.5
  16. 1.6: Exponential and Logarithmic Functions
  17. 1.6E: Exercises for Section 1.6
  18. 2: Limits and Derivatives
  19. 2.1: The Tangent and Velocity Problems
  20. 2.1E: Exercises for Section 2.1
  21. 2.2: The Limit of a Function
  22. 2.2E: Exercises for Section 2.2
  23. 2.3: Calculating Limits Using the Limit Laws
  24. 2.3E: Exercises for Section 2.3
  25. 2.4: The Precise Definition of a Limit
  26. 2.4E: Exercises for Section 2.4
  27. 2.5: Continuity
  28. 2.5E: Exercises for Section 2.5
  29. 2.6: Limits at Infinity; Horizontal Asymptotes
  30. 2.6E: Exercises for Section 2.6
  31. 2.7: Derivatives and Rates of Change
  32. 2.7E: Exercises for Section 2.7
  33. 2.8: The Derivative as a Function
  34. 2.8E: Exercises for Section 2.8
  35. 3: Differentiation Rules
  36. 3.1: Basic Differentiation Rules
  37. 3.1E: Exercises for Section 3.1
  38. 3.2: The Product and Quotient Rules
  39. 3.2E: Exercises for Section 3.2
  40. 3.3: Derivatives of Trigonometric Functions
  41. 3.3E: Exercises for Section 3.3
  42. 3.4: The Chain Rule
  43. 3.4E: Exercises for Section 3.4
  44. 3.5: Implicit Differentiation
  45. 3.5E: Exercises for Section 3.5
  46. 3.6: Derivatives of Inverse Trigonometric and Logarithmic Functions
  47. 3.6E: Exercises for Section 3.6
  48. 3.7: Rates of Change in the Natural and Social Sciences
  49. 3.7E: Exercises for Section 3.7
  50. 3.8: Exponential Growth and Decay
  51. 3.8.1: Exercises for Section 3.8
  52. 3.9: Related Rates
  53. 3.9E: Exercises for Section 3.9
  54. 3.10: Linear Approximations and Differentials
  55. 3.10E: Exercises for Section 3.10
  56. 3.11: Hyperbolic Functions
  57. 3.11E: Exercises for Section 3.11
  58. 4: Applications of Differentiation
  59. 4.1: Maximum and Minimum Values
  60. 4.1E: Exercises for Section 4.1
  61. 4.2: The Mean Value Theorem
  62. 4.2E: Exercises for Section 4.2
  63. 4.3: Indeterminate Forms and l'Hospital's Rule
  64. 4.3E: Exercises for Section 4.3
  65. 4.4: How Derivatives Affect the Shape of a Graph
  66. 4.4E: Exercises for Section 4.4
  67. 4.5: Limits at Infinity and Asymptotes
  68. 4.5E: Exercises for Section 4.5
  69. 4.6: Optimization Problems
  70. 4.6E: Exercises for Section 4.6
  71. 4.7: Newton’s Method
  72. 4.7E: Exercises for Section 4.7
  73. 5: Integrals
  74. 5.1: Antiderivatives
  75. 5.1E: Exercises for Section 5.1
  76. 5.2: Areas and Distances
  77. 5.2E: Exercises for Section 5.2
  78. 5.3: The Definite Integral
  79. 5.3E: Exercises for Section 5.3
  80. 5.4: The Fundamental Theorem of Calculus
  81. 5.4E: Exercises for Section 5.4
  82. 5.5: Indefinite Integrals and the Net Change Theorem
  83. 5.5E: Exercises for Section 5.5
  84. 5.6: Substitution
  85. 5.6E: Exercises for Section 5.6
  86. Back Matter
  87. Index
  88. Glossary
  89. Detailed Licensing
  90. Detailed Licensing