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Calculus

External

Calculus

Mathematics
Author
Eric Hutchinson
Publisher
College of Southern Nevada
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 129 sections
  1. 01: Functions and Graphs (Precalculus Review)
  2. 1.01: Review of Functions
  3. 1.02: Basic Classes of Functions
  4. 1.03: Trigonometric Functions
  5. 1.04: Inverse Functions
  6. 1.05: Exponential and Logarithmic Functions
  7. 02: Limits and Continuity
  8. 2.01: Limit of a Function and Limit Laws
  9. 2.02: The Precise Definition of a Limit
  10. 2.03: One-Sided Limits
  11. 2.04: Continuity
  12. 2.05: Limits Involving Infinity Asymptotes of Graphs
  13. 03: Differentiation
  14. 3.01: Defining the Derivative
  15. 3.02: The Derivative as a Function
  16. 3.03: Differentiation Rules
  17. 3.04: The Derivative as a Rate of Change
  18. 3.05: Derivatives of Trigonometric Functions
  19. 3.06: The Chain Rule
  20. 3.07: Implicit Differentiation
  21. 3.08: Derivatives of Inverse and Logarithmic Functions
  22. 3.09: Inverse Trigonometric Functions
  23. 3.10: Related Rates
  24. 3.11: Linearization and Differentials
  25. 04: Applications of Derivatives
  26. 4.01: Maxima and Minima
  27. 4.02: The Mean Value Theorem
  28. 4.03: The First Derivative Test
  29. 4.04: The Second Derivative Test and Curve Sketching
  30. 4.05: Indeterminate Forms and L'Hopital's Rule
  31. 4.06: Applied Optimization Problems
  32. 4.07: Newton's Method
  33. 05: Integration
  34. 5.01: Antiderivatives
  35. 5.02: Approximating Areas with Limits of Finite Sums
  36. 5.03: The Definite Integral
  37. 5.04: The Fundamental Theorem of Calculus
  38. 5.05: Substitution with Indefinite Integrals
  39. 5.06: Substitution with Definite Integrals
  40. 06: Applications of Definite Integrals
  41. 6.01: Volumes Using Cross-Sections
  42. 6.02: Volumes Using Cylindrical Shells
  43. 6.03: Arc Length
  44. 6.04: Areas of Surfaces of Revolution
  45. 6.05: Work
  46. 6.06: Moments and Centers of Mass
  47. 07: Integrals and Transcendental Functions
  48. 7.01: The Logarithm Defined as an Integral
  49. 7.02: Exponential Change and Separable Differential Equations
  50. 7.03: Hyperbolic Functions
  51. 08: Techniques of Integration
  52. 8.01: Integration by Parts
  53. 8.02: Trigonometric Integrals
  54. 8.03: Trigonometric Substitutions
  55. 8.04: Integration of Rational Functions by Partial Fractions
  56. 8.05: Integral Tables and Computer Algebra Systems
  57. 8.06: Numerical Integration
  58. 8.07: Improper Integrals
  59. 09: Infinite Sequence and Series
  60. 9.01: The Binomial Series and Applications of Taylor Series
  61. 9.02: Sequences
  62. 9.03: Infinite Series
  63. 9.04: The Integral Test
  64. 9.05: Comparison Tests
  65. 9.06: The Ratio and Root Tests
  66. 9.07: Alternating Series Absolute and Conditional Convergence
  67. 9.08: Power Series
  68. 9.09: Taylor and Maclaurin Series
  69. 9.10: Convergence of Taylor Series
  70. 10: Parametric Equations and Polar Coordinates
  71. 10.01: Parametrizations of Plane Curves
  72. 10.02: Calculus with Parametric Curves
  73. 10.03: Polar Coordinates
  74. 10.04: Graphing in Polar Coordinates
  75. 10.05: Areas and Lengths in Polar Coordinates
  76. 10.06: Conics in Polar Coordinates
  77. 11: Vectors and the Geometry of Space
  78. 11.01: Three-Dimensional Coordinate Systems
  79. 11.02: Vectors
  80. 11.03: The Dot Product
  81. 11.04: The Cross Product
  82. 11.05: Lines and Planes in Space
  83. 11.06: Cylinders and Quadric Surfaces
  84. 12: Vector-Valued Functions and Motion in Space
  85. 12.01: Curves in Space and Their Tangents
  86. 12.02: Integrals of Vector Functions Projectile Motion
  87. 12.03: Arc Length in Space
  88. 12.04: Curvature and Normal Vectors of a Curve
  89. 12.05: Tangential and Normal Components of Acceleration
  90. 12.06: Velocity and Acceleration in Polar Coordinates
  91. 13: Partial Derivatives
  92. 13.01: Functions of Several Variables
  93. 13.02: Limits and Continuity in Higher Dimensions
  94. 13.03: Partial Derivatives
  95. 13.04: The Chain Rule
  96. 13.05: Directional Derivatives and Gradient Vectors
  97. 13.06: Tangent Planes and Differentials
  98. 13.07: Extreme Values and Saddle Points
  99. 13.08: Lagrange Multipliers
  100. 14: Multiple Integrals
  101. 14.01: Double and Iterated Integrals over Rectangles
  102. 14.02: Double Integrals over General Regions
  103. 14.03: Area by Double Integration
  104. 14.04: Double Integrals in Polar Form
  105. 14.05: Triple Integrals in Rectangular Coordinates
  106. 14.06: Moments and Centers of Mass
  107. 14.07: Triple Integrals in Cylindrical and Spherical Coordinates
  108. 14.08: Substitutions in Multiple Integrals
  109. 15: Integration in Vector Fields
  110. 15.01: Line Integrals
  111. 15.02: Vector Fields and Line Integrals- Work Circulation and Flux
  112. 15.03: Path Independence Conservative Fields and Potential Functions
  113. 15.04: Green's Theorem in the Plane
  114. 15.05: Surfaces and Area
  115. 15.06: Surface Integrals
  116. 15.07: Stokes' Theorem
  117. 15.08: The Divergence Theorem and a Unified Theory
  118. 16: First-Order Differential Equations
  119. 16.01: Solutions Slope Fields and Euler's Method
  120. 16.02: First-Order Linear Equations
  121. 16.03: Applications
  122. 16.04: Graphical Solutions of Autonomous Equations
  123. 16.05: Systems of Equations and Phase Planes
  124. 17: Second-Order Differential Equations
  125. 17.01: Second-Order Linear Equations
  126. 17.02: Nonhomogeneous Linear Equations
  127. 17.03: Applications
  128. 17.04: Euler Equations
  129. 17.05: Power Series Solutions