Contemporary Calculus

by Jeff Eldridge

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An OER textbook for differential, integral and vector calculus.

Description from LibreTexts.

Publisher
Edmonds 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

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. 0: Welcome to Calculus
  7. 0.1: A Preview of Calculus
  8. 0.2: Lines in the Plane
  9. 0.3: Functions and Their Graphs
  10. 0.4: Combinations of Functions
  11. 0.5: Mathematical Language
  12. 0.A: Answers
  13. 1: Limits and Continuity
  14. 1.0: Tangent Lines, Velocities and Graphs
  15. 1.1: The Limit of a Function
  16. 1.2: Properties of Limits
  17. 1.3: Continuous Functions
  18. 1.4: Definition of Limit
  19. 1.A: Answers
  20. 2: The Derivative
  21. 2.0: Introduction to Derivatives
  22. 2.1: The Definition of Derivative
  23. 2.2: Derivatives: Properties and Formulas
  24. 2.3: More Differentiation Patterns
  25. 2.4: The Chain Rule
  26. 2.5: Applications of the Chain Rule
  27. 2.6: Related Rates
  28. 2.7: Newton’s Method
  29. 2.8: Linear Approximation and Differentials
  30. 2.9: Implicit and Logarithmic Differentiation
  31. 2.A: Answers
  32. 3: Derivatives and Graphs
  33. 3.1: Finding Maximums and Minimums
  34. 3.2: Mean Value Theorem
  35. 3.3: The First Derivative and the Shape of f
  36. 3.4: The Second Derivative and the Shape of f
  37. 3.5: Applied Maximum and Minimum Problems
  38. 3.6: Asymptotic Behavior of Functions
  39. 3.7: L’Hôpital’s Rule
  40. 3.A: Answers
  41. 4: The Integral
  42. 4.0: Area
  43. 4.1: Sigma Notation and Riemann Sums
  44. 4.2: The Definite Integral
  45. 4.3: Properties of the Definite Integral
  46. 4.4: Areas, Integrals and Antiderivatives
  47. 4.5: The Fundamental Theorem of Calculus
  48. 4.6: Finding Antiderivatives
  49. 4.7: First Applications of Definite Integrals
  50. 4.8: Using Tables [and Technology] to Find Antiderivatives
  51. 4.9: Approximating Definite Integrals
  52. 4.A: Answers
  53. 5: Applications of Definite Integrals
  54. 5.1: Volumes by Slicing
  55. 5.2: Disks and Washers
  56. 5.3: Arclength and Surface Area
  57. 5.4: More Work
  58. 5.5: Volumes: Tubes
  59. 5.6: Moments and Centers of Mass
  60. 5.7: Improper Integrals
  61. 5.8: Additional Applications
  62. 5.A: Answers
  63. 6: Differential Equations
  64. 6.1: Introduction to Differential Equations
  65. 6.2: The Differential Equation y = f'(x)
  66. 6.3: Separable Equations
  67. 6.4: Exponential Growth and Decay
  68. 6.5: Heating, Cooling and Mixing
  69. 6.A: Answers
  70. 7: Transcendental Functions
  71. 7.1: One-to-One Functions
  72. 7.2: Inverse Functions
  73. 7.3: Inverse Trigonometric Functions
  74. 7.4: Derivatives of Inverse Trigonometric Functions
  75. 7.5: Integrals Involving Inverse Trigonometric Functions
  76. 7.A: Answers
  77. Back Matter
  78. Index
  79. Glossary
  80. Detailed Licensing
  81. Appendix D: Derivative Facts
  82. Appendix I: Integral Table