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Contemporary Calculus

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Contemporary Calculus

An OER textbook for differential, integral and vector calculus.

Mathematics
Author
Jeff Eldridge
Publisher
Edmonds College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 75 sections
  1. 0 Welcome to Calculus
  2. 0.1 A Preview of Calculus
  3. 0.2 Lines in the Plane
  4. 0.3 Functions and Their Graphs
  5. 0.4 Combinations of Functions
  6. 0.5 Mathematical Language
  7. 0.A Answers
  8. 1 Limits and Continuity
  9. 1.0 Tangent Lines Velocities and Graphs
  10. 1.1 The Limit of a Function
  11. 1.2 Properties of Limits
  12. 1.3 Continuous Functions
  13. 1.4 Definition of Limit
  14. 1.A Answers
  15. 2 The Derivative
  16. 2.0 Introduction to Derivatives
  17. 2.1 The Definition of Derivative
  18. 2.2 Derivatives Properties and Formulas
  19. 2.3 More Differentiation Patterns
  20. 2.4 The Chain Rule
  21. 2.5 Applications of the Chain Rule
  22. 2.6 Related Rates
  23. 2.7 Newtons Method
  24. 2.8 Linear Approximation and Differentials
  25. 2.9 Implicit and Logarithmic Differentiation
  26. 2.A Answers
  27. 3 Derivatives and Graphs
  28. 3.1 Finding Maximums and Minimums
  29. 3.2 Mean Value Theorem
  30. 3.3 The First Derivative and the Shape of f
  31. 3.4 The Second Derivative and the Shape of f
  32. 3.5 Applied Maximum and Minimum Problems
  33. 3.6 Asymptotic Behavior of Functions
  34. 3.7 L Hopital s Rule
  35. 3.A Answers
  36. 4 The Integral
  37. 4.0 Area
  38. 4.1 Sigma Notation and Riemann Sums
  39. 4.2 The Definite Integral
  40. 4.3 Properties of the Definite Integral
  41. 4.4 Areas Integrals and Antiderivatives
  42. 4.5 The Fundamental Theorem of Calculus
  43. 4.6 Finding Antiderivatives
  44. 4.7 First Applications of Definite Integrals
  45. 4.8 Using Tables and Technology to Find Antiderivatives
  46. 4.9 Approximating Definite Integrals
  47. 4.A Answers
  48. 5 Applications of Definite Integrals
  49. 5.1 Volumes by Slicing
  50. 5.2 Disks and Washers
  51. 5.3 Arclength and Surface Area
  52. 5.4 More Work
  53. 5.5 Volumes Tubes
  54. 5.6 Moments and Centers of Mass
  55. 5.7 Improper Integrals
  56. 5.8 Additional Applications
  57. 5.A Answers
  58. 06 Differential Equations
  59. 6.1 Introduction to Differential Equations
  60. 6.2 The Differential Equation y f'(x)
  61. 6.3 Separable Equations
  62. 6.4 Exponential Growth and Decay
  63. 6.5 Heating Cooling and Mixing
  64. 6.A Answers
  65. 07 Transcendental Functions
  66. 7.1 One-to-One Functions
  67. 7.2 Inverse Functions
  68. 7.3 Inverse Trigonometric Functions
  69. 7.4 Derivatives of Inverse Trigonometric Functions
  70. 7.5 Integrals Involving Inverse Trigonometric Functions
  71. 7.A Answers
  72. 8.1 Finding Antiderivatives A Review
  73. 8.2 Integration by Parts
  74. 8.3 Partial Fraction Decomposition
  75. 8.4 Trigonometric Substitution