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Math C180: Calculus I

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Math C180: Calculus I

This is the first course in the calculus sequence. It satisfies the requirement for majors in mathematics, science, or engineering. Topics include limits, derivatives of algebraic and transcendental functions, applications of derivatives, indefinite integrals, definite integrals, the Fundamental Theorem of Calculus, and applications of integration.

Mathematics
Author
Michael Everett
Publisher
Coastline College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 95 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 1.1
  5. 1.03: Basic Classes of Functions
  6. 1.3E: Exercises for Section 1.2
  7. 1.04: Trigonometric Functions
  8. 1.4E: Exercises for Section 1.3
  9. 1.05: Inverse Functions
  10. 1.5E: Exercises for Section 1.4
  11. 1.06: Exponential and Logarithmic Functions
  12. 1.6E: Exercises for Section 1.5
  13. 1.07: Review Exercises for Chapter 1
  14. 02: Limits
  15. 2.01: Prelude to Limits
  16. 2.02: A Preview of Calculus
  17. 2.2E: Exercises for Section 2.1
  18. 2.03: The Limit of a Function
  19. 2.3E: Exercises for Section 2.2
  20. 2.04: Infinite Limits
  21. 2.4E: Exercises for Section 2.3
  22. 2.05: The Limit Laws
  23. 2.5E: Exercises for Section 2.4
  24. 2.06: Limits at Infinity
  25. 2.6E: Exercises for Section 2.5
  26. 2.07: Continuity
  27. 2.7E: Exercises for Section 2.6
  28. 2.08: The Precise Definition of a Limit
  29. 2.8E: Exercises for Section 2.7
  30. 2.09: Chapter Review Exercises
  31. 03: Derivatives
  32. 3.01: Prelude to Derivatives
  33. 3.02: Defining the Derivative
  34. 3.2E: Exercises for Section 3.1
  35. 3.03: The Derivative as a Function
  36. 3.3E: Exercises for Section 3.2
  37. 3.04: Differentiation Rules
  38. 3.4E: Exercises for Section 3.3
  39. 3.05: Derivatives of Trigonometric Functions
  40. 3.5E: Exercises for Section 3.4
  41. 3.06: Derivatives as Rates of Change
  42. 3.6E: Exercises for Section 3.5
  43. 3.07: The Chain Rule
  44. 3.7E: Exercises for Section 3.6
  45. 3.08: Implicit Differentiation
  46. 3.8E: Exercises for Section 3.7
  47. 3.09: Derivatives of Exponential and Logarithmic Functions
  48. 3.9E: Exercises for Section 3.8
  49. 3.10: Derivatives of the Inverse Trigonometric Functions
  50. 3.11: Chapter 3 Review Exercises
  51. 04: Applications of Derivatives
  52. 4.01: Prelude to Applications of Derivatives
  53. 4.02: Related Rates
  54. 4.2E: Exercises for Section 4.1
  55. 4.03: Maxima and Minima
  56. 4.3E: Exercises for Section 4.2
  57. 4.04: The Mean Value Theorem
  58. 4.4E: Exercises for Section 4.3
  59. 4.05: Derivatives and the Shape of a Graph
  60. 4.5E: Exercises for Section 4.4
  61. 4.06: Limits at Infinity and Asymptotes
  62. 4.07: Applied Optimization Problems
  63. 4.7E: Exercises for Section 4.6
  64. 4.08: Parametric Equations
  65. 4.8E: Exercises for Section 4.7
  66. 4.09: Derivatives of Parametric Equations
  67. 4.9E: Exercises for Section 4.8
  68. 4.10: Newtons Method
  69. 4.10E: Exercises for Section 4.9
  70. 4.11: Linear Approximations and Differentials
  71. 4.11E: Exercises for Section 4.10
  72. 4.12: Antiderivatives
  73. 4.12E: Exercises for Section 4.11
  74. 4.13: Chapter 4 Review Exercises
  75. 05: Integration
  76. 5.01: Approximating Areas
  77. 5.1E: Exercises for Section 5.1
  78. 5.02: The Definite Integral
  79. 5.2E: Exercises for Section 5.2
  80. 5.03: The Fundamental Theorem of Calculus
  81. 5.3E: Exercises for Section 5.3
  82. 5.04: Integration Formulas and the Net Change Theorem
  83. 5.4E: Exercises for Section 5.4
  84. 5.05: Substitution
  85. 5.5E: Exercises for Section 5.5
  86. 5.06: Integrals Involving Exponential and Logarithmic Functions
  87. 5.6E: Exercises for Section 5.6
  88. 5.07: Integrals Resulting in Inverse Trigonometric Functions
  89. 5.7E: Exercises for Section 5.7
  90. 5.08: Chapter 5 Review Exercises
  91. 06: Appendices
  92. 6.01: Trigonometric Identities
  93. 6.02: Review of Derivative Rules
  94. 6.03: Table of Derivatives
  95. 6.04: Table of Integrals