MTH 1 - Calculus I

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This course is the first in the three-course calculus sequence intended for majors in math, engineering, and physical sciences. The course covers elements of analytic geometry, derivatives, limits and continuity, differentiation of algebraic and trigonometric functions, and the definite integral.

Description from LibreTexts.

Publisher
Chabot College
Subjects
Mathematics
Licence
CC BY-NC-SA, 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: Applied Optimization Problems
  19. 1.7E: Exercises for Section 4.7
  20. 1.8: Chapter 1 Review Exercises
  21. 2: Limits
  22. 2.1: The Idea of Limits
  23. 2.1E: Exercises for Section 2.1
  24. 2.2: Definitions of Limits
  25. 2.2E: Exercises for Section 2.2
  26. 2.3: Techniques for Computing Limits
  27. 2.3E: Exercises for Section 2.3
  28. 2.4: Infinite Limits
  29. 2.4E: Exercises for Section 2.4
  30. 2.5: Limits at Infinity
  31. 2.5E: Exercises for Section 2.5
  32. 2.6: Continuity
  33. 2.6E: Exercises for Section 2.6
  34. 2.7: Precise Definition of a Limit
  35. 2.7E: Exercises for Section 2.7
  36. 2.8: Chapter 2 Review Exercises
  37. 3: Derivatives
  38. 3.1: Introducing the Derivative
  39. 3.1E: Exercises for Section 3.1
  40. 3.2: Differentiation Rules
  41. 3.2E: Exercises for Section 3.2
  42. 3.3: The Product and Quotient Rules
  43. 3.3E: Exercises for Section 3.3
  44. 3.4: Derivatives of Trigonometric Functions
  45. 3.4E: Exercises for Section 3.4
  46. 3.5: Derivatives as Rates of Change
  47. 3.5E: Exercises for Section 3.5
  48. 3.6: The Chain Rule
  49. 3.6E: Exercises for Section 3.6
  50. 3.7: Implicit Differentiation
  51. 3.7E: Exercises for Section 3.7
  52. 3.8: Related Rates
  53. 3.8E: Exercises for Section 3.8
  54. 3.9: Derivatives of Inverse Functions
  55. 3.9E: Exercises for Section 3.9
  56. 3.10: Derivatives of Exponential and Logarithmic Functions
  57. 3.10E: Exercises for Section 3.10
  58. 3.11: Chapter 3 Review Exercises
  59. 4: Applications of Derivatives
  60. 4.1: Maxima and Minima
  61. 4.1E: Exercises for Section 4.1
  62. 4.2: What Derivatives Tell Us
  63. 4.2E: Exercises for Section 4.2
  64. 4.3: Graphing Functions
  65. 4.3E: Exercises for Section 4.3
  66. 4.4: Optimization Problems
  67. 4.4E: Exercises for Section 4.4
  68. 4.5: Linear Approximations and Differentials
  69. 4.5E: Exercises for Section 4.5
  70. 4.6: The Mean Value Theorem
  71. 4.6E: Exercises for Section 4.6
  72. 4.7: L’Hôpital’s Rule
  73. 4.7E: Exercises for Section 4.7
  74. 4.8: Newton’s Method
  75. 4.8E: Exercises for Section 4.8
  76. 4.9: Antiderivatives
  77. 4.9E: Exercises for Section 4.9
  78. 4.10: Chapter 4 Review Exercises
  79. 5: Integration
  80. 5.1: Approximating Areas
  81. 5.1E: Exercises for Section 5.1
  82. 5.2: The Definite Integral
  83. 5.2E: Exercises for Section 5.2
  84. 5.3: The Fundamental Theorem of Calculus
  85. 5.3E: Exercises for Section 5.3
  86. 5.4: Working with Integrals
  87. 5.4.1: Exercises for Section 5.4
  88. 5.5: Substitution
  89. 5.5E: Exercises for Section 5.5
  90. 5.6: Integrals Involving Exponential and Logarithmic Functions
  91. 5.6E: Exercises for Section 5.6
  92. 5.7: Integrals Resulting in Inverse Trigonometric Functions
  93. 5.7E: Exercises for Section 5.7
  94. 5.8: Chapter 5 Review Exercises
  95. 6: Applications of Integration
  96. 6.1: Numerical Integration
  97. 6.1E: Exercises for Section 6.1
  98. 6.2: Areas Between Curves
  99. 6.2E: Exercises for Section 6.2
  100. 6.3: Determining Volumes by Slicing
  101. 6.3E: Exercises for Section 6.3
  102. 6.4: Volumes of Revolution - Cylindrical Shells
  103. 6.4E: Exercises for Section 6.4
  104. 6.5: Arc Length of a Curve and Surface Area
  105. 6.5E: Exercises for Section 6.5
  106. 6.6: Physical Applications of Integration
  107. 6.6E: Exercises for Section 6.6
  108. 6.7: Moments and Centers of Mass
  109. 6.7E: Exercises for Section 6.8
  110. 6.8: Integrals, Exponential Functions, and Logarithms
  111. 6.8E: Exercises for Section 6.9
  112. 6.9: Exponential Growth and Decay
  113. 6.9E: Exercises for Section 6.10
  114. 6.10: Calculus of the Hyperbolic Functions
  115. 6.10E: Exercises for Section 6.11
  116. 6.11: Chapter 6 Review Exercises
  117. 7: Appendices
  118. 7.1: A- Table of Derivatives
  119. 7.2: B- Table of Integrals
  120. Back Matter
  121. Index
  122. Glossary
  123. Detailed Licensing