Math C180: Calculus I

by Michael Everett

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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.

Description from LibreTexts.

Publisher
Coastline 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. Licensing
  3. TitlePage
  4. InfoPage
  5. Table of Contents
  6. Licensing
  7. 1: Functions and Graphs
  8. 1.1: Prelude to Functions and Graphs
  9. 1.2: Review of Functions
  10. 1.2E: Exercises for Section 1.1
  11. 1.3: Basic Classes of Functions
  12. 1.3E: Exercises for Section 1.2
  13. 1.4: Trigonometric Functions
  14. 1.4E: Exercises for Section 1.3
  15. 1.5: Inverse Functions
  16. 1.5E: Exercises for Section 1.4
  17. 1.6: Exponential and Logarithmic Functions
  18. 1.6E: Exercises for Section 1.5
  19. 1.7: Review Exercises for Chapter 1
  20. 2: Limits
  21. 2.1: Prelude to Limits
  22. 2.2: A Preview of Calculus
  23. 2.2E: Exercises for Section 2.1
  24. 2.3: The Limit of a Function
  25. 2.3E: Exercises for Section 2.2
  26. 2.4: Infinite Limits
  27. 2.4E: Exercises for Section 2.3
  28. 2.5: The Limit Laws
  29. 2.5E: Exercises for Section 2.4
  30. 2.6: Limits at Infinity
  31. 2.6E: Exercises for Section 2.5
  32. 2.7: Continuity
  33. 2.7E: Exercises for Section 2.6
  34. 2.8: The Precise Definition of a Limit
  35. 2.8E: Exercises for Section 2.7
  36. 2.9: Chapter Review Exercises
  37. 3: Derivatives
  38. 3.1: Prelude to Derivatives
  39. 3.2: Defining the Derivative
  40. 3.2E: Exercises for Section 3.1
  41. 3.3: The Derivative as a Function
  42. 3.3E: Exercises for Section 3.2
  43. 3.4: Differentiation Rules
  44. 3.4E: Exercises for Section 3.3
  45. 3.5: Derivatives of Trigonometric Functions
  46. 3.5E: Exercises for Section 3.4
  47. 3.6: Derivatives as Rates of Change
  48. 3.6E: Exercises for Section 3.5
  49. 3.7: The Chain Rule
  50. 3.7E: Exercises for Section 3.6
  51. 3.8: Implicit Differentiation
  52. 3.8E: Exercises for Section 3.7
  53. 3.9: Derivatives of Exponential and Logarithmic Functions
  54. 3.9E: Exercises for Section 3.8
  55. 3.10: Derivatives of the Inverse Trigonometric Functions
  56. 3.11: Chapter 3 Review Exercises
  57. 4: Applications of Derivatives
  58. 4.1: Prelude to Applications of Derivatives
  59. 4.2: Related Rates
  60. 4.2E: Exercises for Section 4.1
  61. 4.3: Maxima and Minima
  62. 4.3E: Exercises for Section 4.2
  63. 4.4: The Mean Value Theorem
  64. 4.4E: Exercises for Section 4.3
  65. 4.5: Derivatives and the Shape of a Graph
  66. 4.5E: Exercises for Section 4.4
  67. 4.6: Limits at Infinity and Asymptotes
  68. 4.7: Applied Optimization Problems
  69. 4.7E: Exercises for Section 4.6
  70. 4.8: Parametric Equations
  71. 4.8E: Exercises for Section 4.7
  72. 4.9: Derivatives of Parametric Equations
  73. 4.9E: Exercises for Section 4.8
  74. 4.10: Newton’s Method
  75. 4.10E: Exercises for Section 4.9
  76. 4.11: Linear Approximations and Differentials
  77. 4.11E: Exercises for Section 4.10
  78. 4.12: Antiderivatives
  79. 4.12E: Exercises for Section 4.11
  80. 4.13: Chapter 4 Review Exercises
  81. 5: Integration
  82. 5.1: Approximating Areas
  83. 5.1E: Exercises for Section 5.1
  84. 5.2: The Definite Integral
  85. 5.2E: Exercises for Section 5.2
  86. 5.3: The Fundamental Theorem of Calculus
  87. 5.3E: Exercises for Section 5.3
  88. 5.4: Integration Formulas and the Net Change Theorem
  89. 5.4E: Exercises for Section 5.4
  90. 5.5: Substitution
  91. 5.5E: Exercises for Section 5.5
  92. 5.6: Integrals Involving Exponential and Logarithmic Functions
  93. 5.6E: Exercises for Section 5.6
  94. 5.7: Integrals Resulting in Inverse Trigonometric Functions
  95. 5.7E: Exercises for Section 5.7
  96. 5.8: Chapter 5 Review Exercises
  97. 6: Appendices
  98. 6.1: Trigonometric Identities
  99. 6.2: Review of Derivative Rules
  100. 6.3: Table of Derivatives
  101. 6.4: Table of Integrals
  102. Back Matter
  103. Detailed Licensing
  104. Detailed Licensing
  105. Index
  106. Glossary
  107. Detailed Licensing