Calculus

by Gregory Hartman et al.

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Publisher
Virginia Military Institute
Subjects
Mathematics, Calculus
Licence
CC BY-NC 3.0, 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: Limits
  7. 1.1: An Introduction to Limits
  8. 1.2: Epsilon-Delta Definition of a Limit
  9. 1.3: Finding Limits Analytically
  10. 1.4: One Sided Limits
  11. 1.5: Continuity
  12. 1.6: Limits Involving Infinity
  13. 1.E: Applications of Limits (Exercises)
  14. 2: Derivatives
  15. 2.1: Instantaneous Rates of Change- The Derivative
  16. 2.2: Interpretations of the Derivative
  17. 2.3: Basic Differentiation Rules
  18. 2.4: The Product and Quotient Rules
  19. 2.5: The Chain Rule
  20. 2.6: Implicit Differentiation
  21. 2.7: Derivatives of Inverse Functions
  22. 2.E: Applications of Derivatives(Exercises)
  23. 3: The Graphical Behavior of Functions
  24. 3.1: Extreme Values
  25. 3.2: The Mean Value Theorem
  26. 3.3: Increasing and Decreasing Functions
  27. 3.4: Concavity and the Second Derivative
  28. 3.5: Curve Sketching
  29. 3.E: Applications of the Graphical Behavior of Functions(Exercises)
  30. 4: Applications of the Derivative
  31. 4.1: Newton's Method
  32. 4.2: Related Rates
  33. 4.3: Optimization
  34. 4.4: Differentials
  35. 4.E: Applications of Derivatives (Exercises)
  36. 5: Integration
  37. 5.1: Antiderivatives and Indefinite Integration
  38. 5.2: The Definite Integral
  39. 5.3: Riemann Sums
  40. 5.4: The Fundamental Theorem of Calculus
  41. 5.5: Numerical Integration
  42. 5.E: Applications of Integration (Exercises)
  43. 6: Techniques of Integration
  44. Front Matter
  45. TitlePage
  46. InfoPage
  47. 6.1: Substitution
  48. 6.2: Integration by Parts
  49. 6.3: Trigonometric Integrals
  50. 6.4: Trigonometric Substitution
  51. 6.5: Partial Fraction Decomposition
  52. 6.6: Hyperbolic Functions
  53. 6.7: L'Hopital's Rule
  54. 6.8: Improper Integration
  55. 6.E: Applications of Antidifferentiation (Exercises)
  56. Back Matter
  57. Index
  58. 7: Applications of Integration
  59. 7.1: Area Between Curves
  60. 7.2: Volume by Cross-Sectional Area- Disk and Washer Methods
  61. 7.3: The Shell Method
  62. 7.4: Arc Length and Surface Area
  63. 7.5: Work
  64. 7.6: Fluid Forces
  65. 7.E: Applications of Integration (Exercises)
  66. 8: Sequences and Series
  67. 8.1: Sequences
  68. 8.2: Infinite Series
  69. 8.3: Integral and Comparison Tests
  70. 8.4: Ratio and Root Tests
  71. 8.5: Alternating Series and Absolute Convergence
  72. 8.6: Power Series
  73. 8.7: Taylor Polynomials
  74. 8.8: Taylor Series
  75. 8.E: Applications of Sequences and Series (Exercises)
  76. 9: Curves in the Plane
  77. 9.1: Conic Sections
  78. 9.2: Parametric Equations
  79. 9.3: Calculus and Parametric Equations
  80. 9.4: Introduction to Polar Coordinates
  81. 9.5: Calculus and Polar Functions
  82. 9.E: Applications of Curves in a Plane (Exercises)
  83. 10: Vectors
  84. 10.1: Introduction to Cartesian Coordinates in Space
  85. 10.2: An Introduction to Vectors
  86. 10.3: The Dot Product
  87. 10.4: The Cross Product
  88. 10.5: Lines
  89. 10.6: Planes
  90. 10.E: Applications of Vectors (Exercises)
  91. 11: Vector-Valued Functions
  92. 11.1: Vector–Valued Functions
  93. 11.2: Calculus and Vector-Valued Functions
  94. 11.3: The Calculus of Motion
  95. 11.4: Unit Tangent and Normal Vectors
  96. 11.5: The Arc Length Parameter and Curvature
  97. 11.E: Applications of Vector Valued Functions (Exercises)
  98. 12: Functions of Several Variables
  99. 12.1: Introduction to Multivariable Functions
  100. 12.2: Limits and Continuity of Multivariable Functions
  101. 12.3: Partial Derivatives
  102. 12.4: Differentiability and the Total Differential
  103. 12.5: The Multivariable Chain Rule
  104. 12.6: Directional Derivatives
  105. 12.7: Tangent Lines, Normal Lines, and Tangent Planes
  106. 12.8: Extreme Values
  107. 12.E: Applications of Functions of Several Variables (Exercises)
  108. 13: Multiple Integration
  109. 13.1: Iterated Integrals and Area
  110. 13.2: Double Integration and Volume
  111. 13.3: Double Integration with Polar Coordinates
  112. 13.4: Center of Mass
  113. 13.5: Surface Area
  114. 13.6: Volume Between Surfaces and Triple Integration
  115. 13.E: Applications of Multiple Integration (Exercises)
  116. 14: Appendix
  117. 14.1: Section 1-
  118. 14.2: Section 2-
  119. 14.3: Section 3-
  120. 14.4: Section 4-
  121. 14.5: Section 5-
  122. 14.6: Section 6-
  123. Back Matter
  124. Index
  125. Glossary
  126. Detailed Licensing