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Calculus - Early Transcendentals

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Calculus - Early Transcendentals

CalculusMathematics
Author
LibreTexts
Publisher
LibreTexts
Source
LibreTexts
Language
EN
Category
Basic Sciences
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Contents· 136 sections
  1. 01: Functions and Models
  2. 1.01: Four Ways to Represent a Function
  3. 1.02: Mathematical Models- A Catalog of Essential Functions
  4. 1.03: New Functions from Old Functions
  5. 1.04: Exponential Functions
  6. 1.05: Inverse Functions and Logarithms
  7. 02: Limits and Derivatives
  8. 2.01: The Tangent and Velocity Problems
  9. 2.02: The Limit of a Function
  10. 2.03: Calculating Limits Using the Limit Laws
  11. 2.04: The Precise Definition of a Limit
  12. 2.05: Continuity
  13. 2.06: Limits at Infinity Horizontal Asymptotes
  14. 2.07: Derivatives and Rates of Change
  15. 2.08: The Derivative as a Function
  16. 03: Differentiation Rules
  17. 3.01: Derivatives of Polynomials and Exponential Functions
  18. 3.02: The Product and Quotient Rules
  19. 3.03: Derivatives of Trigonometric Functions
  20. 3.04: The Chain Rule
  21. 3.05: Implicit Differentiation
  22. 3.06: Derivatives of Logarithmic Functions
  23. 3.07: Rates of Change in the Natural and Social Sciences
  24. 3.08: Exponential Growth and Decay
  25. 3.09: Related Rates
  26. 3.10: Linear Approximations and Differentials
  27. 3.11: Hyperbolic Functions
  28. 04: Applications of Differentiation
  29. 4.01: Maximum and Minimum Values
  30. 4.02: The Mean Value Theorem
  31. 4.03: How Derivatives Affect the Shape of a Graph
  32. 4.04: Indeterminate Forms and l'Hospital's Rule
  33. 4.05: Summary of Curve Sketching
  34. 4.06: Graphing with Calculus and Calculators
  35. 4.07: Optimization Problems
  36. 4.08: Newton's Method
  37. 4.09: Antiderivatives
  38. 05: Integrals
  39. 5.01: Areas and Distances
  40. 5.02: The Definite Integral
  41. 5.03: The Fundamental Theorem of Calculus
  42. 5.04: Indefinite Integrals and the Net Change Theorem
  43. 5.05: The Substitution Rule
  44. 06: Applications of Integration
  45. 6.01: Areas Between Curves
  46. 6.02: Volumes
  47. 6.03: Volumes by Cylindrical Shells
  48. 6.04: Work
  49. 6.05: Average Value of a Function
  50. 07: Techniques of Integration
  51. 7.01: Integration by Parts
  52. 7.02: Trigonometric Integrals
  53. 7.03: Trigonometric Substitution
  54. 7.04: Integration of Rational Functions by Partial Fractions
  55. 7.05: Strategy for Integration
  56. 7.06: Integration Using Tables and Computer Algebra Systems
  57. 7.07: Approximate Integration
  58. 7.08: Improper Integrals
  59. 08: Further Applications of Integration
  60. 8.01: Arc Length
  61. 8.02: Area of a Surface of Revolution
  62. 8.03: Applications to Physics and Engineering
  63. 8.04: Applications to Economics and Biology
  64. 8.05: Probability
  65. 09: Differential Equations
  66. 9.01: Modeling with Differential Equations
  67. 9.02: Direction Fields and Euler's Method
  68. 9.03: Separable Equations
  69. 9.04: Models for Population Growth
  70. 9.05: Linear Equations
  71. 9.06: Predator-Prey Systems
  72. 10: Parametric Equations And Polar Coordinates
  73. 10.01: Curves Defined by Parametric Equations
  74. 10.02: Calculus with Parametric Curves
  75. 10.03: Polar Coordinates
  76. 10.04: Areas and Lengths in Polar Coordinates
  77. 10.05: Conic Sections
  78. 10.06: Conic Sections in Polar Coordinates
  79. 11: Infinite Sequences And Series
  80. 11.01: Sequences
  81. 11.02: Series
  82. 11.03: The Integral Test and Estimates of Sums
  83. 11.04: The Comparison Tests
  84. 11.05: Alternating Series
  85. 11.06: Absolute Convergence and the Ratio and Root Test
  86. 11.07: Strategy for Testing Series
  87. 11.08: Power Series
  88. 11.09: Representations of Functions as Power Series
  89. 11.10: Taylor and Maclaurin Series
  90. 11.11: Applications of Taylor Polynomials
  91. 12: Vectors and The Geometry of Space
  92. 12.01: Three-Dimensional Coordinate Systems
  93. 12.02: Vectors
  94. 12.03: The Dot Product
  95. 12.04: The Cross Product
  96. 12.05: Equations of Lines and Planes
  97. 12.06: Cylinders and Quadric Surfaces
  98. 13: Vector Functions
  99. 13.01: Vector Functions and Space Curves
  100. 13.02: Derivatives and Integrals of Vector Functions
  101. 13.03: Arc Length and Curvature
  102. 13.04: Motion in Space- Velocity and Acceleration
  103. 14: Partial Derivatives
  104. 14.01: Functions of Several Variables
  105. 14.02: Limits and Continuity
  106. 14.03: Partial Derivatives
  107. 14.04: Tangent Planes and Linear Approximations
  108. 14.05: The Chain Rule
  109. 14.06: Directional Derivatives and the Gradient Vector
  110. 14.07: Maximum and Minimum Values
  111. 14.08: Lagrange Multipliers
  112. 15: Multiple Integrals
  113. 15.01: Double Integrals over Rectangles
  114. 15.02: Double Integrals over General Regions
  115. 15.03: Double Integrals in Polar Coordinates
  116. 15.04: Applications of Double Integrals
  117. 15.05: Surface Area
  118. 15.06: Triple Integrals
  119. 15.07: Triple Integrals in Cylindrical Coordinates
  120. 15.08: Triple Integrals in Spherical Coordinates
  121. 15.09: Change of Variables in Multiple Integrals
  122. 16: Vector Calculus
  123. 16.01: Vector Fields
  124. 16.02: Line Integrals
  125. 16.03: The Fundamental Theorem for Line Integrals
  126. 16.04: Green's Theorem
  127. 16.05: Curl and Divergence
  128. 16.06: Parametric Surfaces and Their Areas
  129. 16.07: Surface Integrals
  130. 16.08: Stokes' Theorem
  131. 16.09: The Divergence Theorem
  132. 17: SecondOrder Differential Equations
  133. 17.01: Second-Order Linear Equations
  134. 17.02: Nonhomogeneous Linear Equations
  135. 17.03: Applications of Second-Order Differential Equations
  136. 17.04: Series Solutions of Differential Equations