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Calculus

The text guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them.

Mathematics
Author
Gilbert Strang & Edwin Herman
Publisher
MIT & University of Wisconsin-Stevens Point
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 117 sections
  1. : Appendices
  2. A: Table of Derivatives
  3. B: Table of Integrals
  4. : Table of Contents
  5. : InfoPage
  6. : Licensing
  7. : Table of Contents
  8. : TitlePage
  9. 4.04: Licensing
  10. 05: Integration
  11. 5.00: Prelude to Integration
  12. 5.01: Approximating Areas
  13. 5.1E: Exercises for Section 5.1
  14. 5.02: The Definite Integral
  15. 5.2E: Exercises for Section 5.2
  16. 5.03: The Fundamental Theorem of Calculus
  17. 5.3E: Exercises for Section 5.3
  18. 5.04: Integration Formulas and the Net Change Theorem
  19. 5.4E: Exercises for Section 5.4
  20. 5.05: Substitution
  21. 5.5E: Exercises for Section 5.5
  22. 5.06: Integrals Involving Exponential and Logarithmic Functions
  23. 5.6E: Exercises for Section 5.6
  24. 5.07: Integrals Resulting in Inverse Trigonometric Functions
  25. 5.7E: Exercises for Section 5.7
  26. 5.08: Calculus of the Hyperbolic Functions
  27. 5.8E: Exercises for Section 5.8
  28. 5.09: Chapter 5 Review Exercises
  29. 06: Introduction to Differential Equations
  30. 6.00: Prelude to Differential Equations
  31. 6.01: Basics of Differential Equations
  32. 6.1E: Exercises for Section 6.1
  33. 6.02: Direction Fields and Numerical Methods
  34. 6.2E: Exercises for Section 6.2
  35. 6.03: Separable Equations
  36. 6.3E: Exercises for Section 6.3
  37. 6.04: The Logistic Equation
  38. 6.4E: Exercises for Section 6.4
  39. 6.05: First-order Linear Equations
  40. 6.5E: Exercises for Section 6.5
  41. 6.06: Chapter 6 Review Exercises
  42. 07: Applications of Integration
  43. 7.00: Prelude to Applications of Integration
  44. 7.01: Areas between Curves
  45. 7.1E: Exercises for Section 7.1
  46. 7.02: Determining Volumes by Slicing
  47. 7.2E: Exercises for Section 7.2
  48. 7.03: Volumes of Revolution - Cylindrical Shells
  49. 7.3E: Exercises for Section 7.3
  50. 7.04: Arc Length of a Curve and Surface Area
  51. 7.4E: Exercises for Section 7.4
  52. 7.05: Physical Applications of Integration
  53. 7.5E: Exercises for Section 7.5
  54. 7.06: Moments and Centers of Mass
  55. 7.6E: Exercises for Section 7.6
  56. 7.07: Integrals Exponential Functions and Logarithms
  57. 7.7E: Exercises for Section 7.7
  58. 7.08: Exponential Growth and Decay
  59. 7.8E: Exercises for Section 7.8
  60. 7.09: Chapter 6 Review Exercises
  61. 08: Techniques of Integration
  62. 8.00: Prelude to Techniques of Integration
  63. 8.01: Integration by Parts
  64. 8.1E: Exercises for Section 8.1
  65. 8.02: Trigonometric Integrals
  66. 8.2E: Exercises for Section 8.2
  67. 8.03: Trigonometric Substitution
  68. 8.3E: Exercises for Section 8.3
  69. 8.04: Partial Fractions
  70. 8.4E: Exercises for Section 8.4
  71. 8.05: Other Strategies for Integration
  72. 8.5E: Exercises for Section 8.5
  73. 8.06: Numerical Integration
  74. 8.6E: Exercises for Section 8.6
  75. 8.07: Improper Integrals
  76. 8.7E: Exercises for Section 8.7
  77. 8.08: Chapter 8 Review Exercises
  78. 09: Sequences and Series
  79. 9.00: Prelude to Sequence and Series
  80. 9.01: Sequences
  81. 9.1E: Exercises for Section 9.1
  82. 9.02: Infinite Series
  83. 9.2E: Exercises for Section 9.2
  84. 9.03: The Divergence and Integral Tests
  85. 9.3E: Exercises for Section 9.3
  86. 9.04: Comparison Tests
  87. 9.4E: Exercises for Section 9.4
  88. 9.05: Alternating Series
  89. 9.5E: Exercises for Section 9.5
  90. 9.06: Ratio and Root Tests
  91. 9.6E: Exercises for Section 9.6
  92. 9.07: Chapter 9 Review Exercises
  93. 9.08: Power Series
  94. 10: Power Series
  95. 10.00: Prelude to Power Series
  96. 10.01: Power Series and Functions
  97. 10.1E: Exercises for Section 10.1
  98. 10.02: Properties of Power Series
  99. 10.2E: Exercises for Section 10.2
  100. 10.03: Taylor and Maclaurin Series
  101. 10.3E: Exercises for Section 10.3
  102. 10.04: Working with Taylor Series
  103. 10.4E: Exercises for Section 10.4
  104. 10.05: Chapter 10 Review Exercises
  105. 11: Parametric Equations and Polar Coordinates
  106. 11.00: Prelude to Parametric Equations and Polar Coordinates
  107. 11.01: Conic Sections
  108. 11.1E: Exercises for Section 11.1
  109. 11.02: Parametric Equations
  110. 11.2E: Exercises for Section 11.2
  111. 11.03: Calculus of Parametric Curves
  112. 11.3E: Exercises for Section 11.3
  113. 11.04: Polar Coordinates
  114. 11.4E: Exercises for Section 11.4
  115. 11.05: Area and Arc Length in Polar Coordinates
  116. 11.5E: Exercises for Section 11.5
  117. 11.06: Chapter 11 Review Exercises