Math C180: Calculus I

by Chau D Tran

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