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Calculus by David Guichard (Improved)

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Calculus by David Guichard (Improved)

This is an improved version of LibreTexts edition of Calculus by David Guidhard which has been edited by Terry Betteridge. Many interactive figures have been added as well as correcting misprints.

CalculusMathematics
Author
Terry Betteridge, Editor
Publisher
LibreTexts
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 132 sections
  1. 01: Analytic Geometry
  2. 1.01: Prelude to Analytic Geometry
  3. 1.02: Lines
  4. 1.03: Distance Between Two Points Circles
  5. 1.04: Functions
  6. 1.05: Shifts and Dilations
  7. 02: Instantaneous Rate of Change- The Derivative
  8. 2.01: The Slope of a Function
  9. 2.02: An Example
  10. 2.03: Limits
  11. 2.04: The Derivative Function
  12. 2.05: Adjectives for Functions
  13. 03: Rules for Finding Derivatives
  14. 3.01: The Power Rule
  15. 3.02: Linearity of the Derivative
  16. 3.03: The Product Rule
  17. 3.04: The Quotient Rule
  18. 3.05: The Chain Rule
  19. 04: Transcendental Functions
  20. 4.01: Trigonometric Functions
  21. 4.02: The Derivative of sin x
  22. 4.03: A Hard Limit
  23. 4.04: The Derivative of sin x - II
  24. 4.05: Derivatives of the Trigonometric Functions
  25. 4.06: Exponential and Logarithmic Functions
  26. 4.07: Derivatives of the Exponential and Logarithmic Functions
  27. 4.08: Implicit Differentiation
  28. 4.09: Inverse Trigonometric Functions
  29. 4.10: Limits Revisited
  30. 4.11: Hyperbolic Functions
  31. 05: Curve Sketching
  32. 5.01: Maxima and Minima
  33. 5.02: The First Derivative Test
  34. 5.03: The Second Derivative Test
  35. 5.04: Concavity and Inflection Points
  36. 5.05: Asymptotes and Other Things to Look For
  37. 06: Applications of the Derivative
  38. 6.01: Optimization
  39. 6.02: Related Rates
  40. 6.03: Newton's Method
  41. 6.04: Linear Approximations
  42. 6.05: The Mean Value Theorem
  43. 07: Integration
  44. 7.01: Two Examples
  45. 7.02: The Fundamental Theorem of Calculus
  46. 7.03: Some Properties of Integrals
  47. 08: Techniques of Integration
  48. 8.01: Substitution
  49. 8.02: Powers of sine and cosine
  50. 8.03: Trigonometric Substitutions
  51. 8.04: Integration by Parts
  52. 8.05: Rational Functions
  53. 8.06: Numerical Integration
  54. 8.07: Additional exercises
  55. 09: Applications of Integration
  56. 9.01: Area Between Curves
  57. 9.02: Distance Velocity and Acceleration
  58. 9.03: Volume
  59. 9.04: Average Value of a Function
  60. 9.05: Work
  61. 9.06: Center of Mass
  62. 9.07: Kinetic energy and Improper Integrals
  63. 9.08: Probability
  64. 9.09: Arc Length
  65. 9.10: Surface Area
  66. 10: Polar Coordinates and Parametric Equations
  67. 10.01: Polar Coordinates
  68. 10.02: Slopes in Polar Coordinates
  69. 10.03: Areas in Polar Coordinates
  70. 10.04: Parametric Equations
  71. 10.05: Calculus with Parametric Equations
  72. 11: Sequences and Series
  73. 11.01: Prelude to Sequences and Series
  74. 11.02: Sequences
  75. 11.03: Series
  76. 11.04: The Integral Test
  77. 11.05: Alternating Series
  78. 11.06: Comparison Test
  79. 11.07: Absolute Convergence
  80. 11.08: The Ratio and Root Tests
  81. 11.09: Power Series
  82. 11.10: Calculus with Power Series
  83. 11.11: Taylor Series
  84. 11.12: Taylor's Theorem
  85. 11.13: Additional Exercises
  86. 12: Three Dimensions
  87. 12.01: The Coordinate System
  88. 12.02: Vectors
  89. 12.03: The Dot Product
  90. 12.04: The Cross Product
  91. 12.05: Lines and Planes
  92. 12.06: Other Coordinate Systems
  93. 13: Vector Functions
  94. 13.01: Space Curves
  95. 13.02: Calculus with Vector Functions
  96. 13.03: Arc length and Curvature
  97. 13.04: Motion Along a Curve
  98. 14: Partial Differentiation
  99. 14.01: Functions of Several Variables
  100. 14.02: Limits and Continuity
  101. 14.03: Partial Differentiation
  102. 14.04: The Chain Rule
  103. 14.05: Directional Derivatives
  104. 14.06: Higher order Derivatives
  105. 14.07: Maxima and minima
  106. 14.08: Lagrange Multipliers
  107. 15: Multiple Integration
  108. 15.01: Volume and Average Height
  109. 15.02: Double Integrals in Cylindrical Coordinates
  110. 15.03: Moment and Center of Mass
  111. 15.04: Surface Area
  112. 15.05: Triple Integrals
  113. 15.06: Cylindrical and Spherical Coordinates
  114. 15.07: Change of Variables
  115. 16: Vector Calculus
  116. 16.01: Vector Fields
  117. 16.02: Line Integrals
  118. 16.03: The Fundamental Theorem of Line Integrals
  119. 16.04: Green's Theorem
  120. 16.05: Divergence and Curl
  121. 16.06: Vector Functions for Surfaces
  122. 16.07: Surface Integrals
  123. 16.08: Stokes's Theorem
  124. 16.09: The Divergence Theorem
  125. 17: Differential Equations
  126. 17.01: First Order Differential Equations
  127. 17.02: First Order Homogeneous Linear Equations
  128. 17.03: First Order Linear Equations
  129. 17.04: Approximation
  130. 17.05: Second Order Homogeneous Equations
  131. 17.06: Second Order Linear Equations
  132. 17.07: Second Order Linear Equations II