Calculus 1

by Lana Anishchenko

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This is the first course in the calculus sequence for American River College.

Description from LibreTexts.

Publisher
American River College
Subjects
Mathematics
Licence
CC BY-SA 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Functions and Graphs
  7. 1.1: Review of Functions
  8. 1.1E: Exercises for Section 1.1
  9. 1.2: Basic Classes of Functions
  10. 1.2E: Exercises for Section 1.2
  11. 1.3: Trigonometric Functions
  12. 1.3E: Exercises for Section 1.3
  13. 1.4: Inverse Functions
  14. 1.4E: Exercises for Section 1.4
  15. 1.5: Exponential and Logarithmic Functions
  16. 1.5E: Exercises for Section 1.5
  17. 1.R: Chapter 1 Review Exercises
  18. 2: Limits
  19. 2.1: The Limit of a Function
  20. 2.1E: Exercises for Section 2.1
  21. 2.2: The Limit Laws
  22. 2.2E: Exercises for Section 2.2
  23. 2.3: Limits at Infinity and Asymptotes
  24. 2.3E: Exercises for Section 2.3
  25. 2.4: Continuity
  26. 2.4E: Exercises for Section 2.4
  27. 2.5: The Precise Definition of a Limit
  28. 2.5E: Exercises for Section 2.5
  29. 2.R: Chapter 2 Review Exercises
  30. 3: Derivatives
  31. 3.1: Defining the Derivative
  32. 3.1E: Exercises for Section 3.1
  33. 3.2: The Derivative as a Function
  34. 3.2E: Exercises for Section 3.2
  35. 3.3: Differentiation Rules
  36. 3.3E: Exercises for Section 3.3
  37. 3.4: Derivatives of Trigonometric Functions
  38. 3.4E: Exercises for Section 3.4
  39. 3.5: The Chain Rule
  40. 3.5E: Exercises for Section 3.5
  41. 3.6: Derivatives of Inverse Functions
  42. 3.6E: Exercises for Section 3.6
  43. 3.7: Implicit Differentiation
  44. 3.7E: Exercises for Section 3.7
  45. 3.8: Derivatives of Exponential and Logarithmic Functions and Logarithmic Differentiation
  46. 3.8E: Exercises for Section 3.8
  47. 3.9: Derivatives of the Hyperbolic Functions
  48. 3.9E: Exercises for Section 3.9
  49. 3.10: Derivatives as Rates of Change
  50. 3.10E: Exercises for Section 3.9
  51. 3.R: Chapter 3 Review Exercises
  52. 4: Applications of Derivatives
  53. 4.1: Related Rates
  54. 4.1E: Exercises for Section 4.1
  55. 4.2: Maxima and Minima
  56. 4.2E: Exercises for Section 4.2
  57. 4.3: The Mean Value Theorem
  58. 4.3E: Exercises for Section 4.3
  59. 4.4: Derivatives and the Shape of a Graph
  60. 4.4E: Exercises for Section 4.4
  61. 4.5: Applied Optimization Problems
  62. 4.5E: Exercises for Section 4.5
  63. 4.6: L’Hôpital’s Rule
  64. 4.6E: Exercises for Section 4.6
  65. 4.7: Linear Approximations and Differentials
  66. 4.7E: Exercises for Section 4.7
  67. 4.8: Newton’s Method
  68. 4.8E: Exercises for Section 4.8
  69. 4.R: Chapter 4 Review Exercises
  70. 5: Integration
  71. 5.1: Antiderivatives and Indefinite Integrals
  72. 5.1.1: Exercises for Section 5.1
  73. 5.2: Rectangular Approximations and the Definite Integral
  74. 5.2E: Exercises for Section 5.2
  75. 5.3: Graphical Interpretation and Properties of the Definite Integral
  76. 5.3E: Exercises for Section 5.3
  77. 5.4: The Fundamental Theorem of Calculus
  78. 5.4E: Exercises for Section 5.4
  79. 5.5: Substitution
  80. 5.5E: Exercises for Section 5.5
  81. 5.6: The Net Change Theorem
  82. 5.6E: Exercises for Section 5.6
  83. 5.R: Chapter 5 Review Exercises
  84. 6: Appendices
  85. 6.1: Appendix A- Table of Derivatives
  86. 6.2: Appendix B- Table of Integrals
  87. Back Matter
  88. Index
  89. Glossary
  90. Detailed Licensing
  91. Detailed Licensing