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

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

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

Mathematics
Author
Leonard Lamp, Kenn Huber & Mohamad Youssef
Publisher
Irvine Valley College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 80 sections
  1. 01: Functions and Graphs
  2. 1.01: Prelude to Functions and Graphs
  3. 1.02: Review of Functions
  4. 1.2E: Exercises for Section 1.2
  5. 1.03: Basic Classes of Functions
  6. 1.3E: Exercises for Section 1.3
  7. 1.04: Trigonometric Functions
  8. 1.4E: Exercises for Section 1.4
  9. 1.05: Inverse Functions
  10. 1.5E: Exercises for Section 1.5
  11. 1.06: Exponential and Logarithmic Functions
  12. 1.6E: Exercises for Section 1.6
  13. 02: Limits and Derivatives
  14. 2.01: The Tangent and Velocity Problems
  15. 2.1E: Exercises for Section 2.1
  16. 2.02: The Limit of a Function
  17. 2.2E: Exercises for Section 2.2
  18. 2.03: Calculating Limits Using the Limit Laws
  19. 2.3E: Exercises for Section 2.3
  20. 2.04: The Precise Definition of a Limit
  21. 2.4E: Exercises for Section 2.4
  22. 2.05: Continuity
  23. 2.5E: Exercises for Section 2.5
  24. 2.06: Limits at Infinity Horizontal Asymptotes
  25. 2.6E: Exercises for Section 2.6
  26. 2.07: Derivatives and Rates of Change
  27. 2.7E: Exercises for Section 2.7
  28. 2.08: The Derivative as a Function
  29. 2.8E: Exercises for Section 2.8
  30. 03: Differentiation Rules
  31. 3.01: Basic Differentiation Rules
  32. 3.1E: Exercises for Section 3.1
  33. 3.02: The Product and Quotient Rules
  34. 3.2E: Exercises for Section 3.2
  35. 3.03: Derivatives of Trigonometric Functions
  36. 3.3E: Exercises for Section 3.3
  37. 3.04: The Chain Rule
  38. 3.4E: Exercises for Section 3.4
  39. 3.05: Implicit Differentiation
  40. 3.5E: Exercises for Section 3.5
  41. 3.06: Derivatives of Inverse Trigonometric and Logarithmic Functions
  42. 3.6E: Exercises for Section 3.6
  43. 3.07: Rates of Change in the Natural and Social Sciences
  44. 3.7E: Exercises for Section 3.7
  45. 3.08: Exponential Growth and Decay
  46. 3.8.01: Exercises for Section 3.8
  47. 3.09: Related Rates
  48. 3.9E: Exercises for Section 3.9
  49. 3.10: Linear Approximations and Differentials
  50. 3.10E: Exercises for Section 3.10
  51. 3.11: Hyperbolic Functions
  52. 3.11E: Exercises for Section 3.11
  53. 04: Applications of Differentiation
  54. 4.01: Maximum and Minimum Values
  55. 4.1E: Exercises for Section 4.1
  56. 4.02: The Mean Value Theorem
  57. 4.2E: Exercises for Section 4.2
  58. 4.03: Indeterminate Forms and l'Hospital's Rule
  59. 4.3E: Exercises for Section 4.3
  60. 4.04: How Derivatives Affect the Shape of a Graph
  61. 4.4E: Exercises for Section 4.4
  62. 4.05: Limits at Infinity and Asymptotes
  63. 4.5E: Exercises for Section 4.5
  64. 4.06: Optimization Problems
  65. 4.6E: Exercises for Section 4.6
  66. 4.07: Newtons Method
  67. 4.7E: Exercises for Section 4.7
  68. 05: Integrals
  69. 5.01: Antiderivatives
  70. 5.1E: Exercises for Section 5.1
  71. 5.02: Areas and Distances
  72. 5.2E: Exercises for Section 5.2
  73. 5.03: The Definite Integral
  74. 5.3E: Exercises for Section 5.3
  75. 5.04: The Fundamental Theorem of Calculus
  76. 5.4E: Exercises for Section 5.4
  77. 5.05: Indefinite Integrals and the Net Change Theorem
  78. 5.5E: Exercises for Section 5.5
  79. 5.06: Substitution
  80. 5.6E: Exercises for Section 5.6