Math 4A: Multivariable Calculus

by Kenn Huber

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This textbook covers a standard course in multivariable calculus. Studies include the three dimensional space, vectors, space curves, surfaces, multivariable functions, limits, partial derivatives, tangent planes, extrema, double and triple integration, changes of variables, line integrals, surface integrals, and the four major Theorems to connect these topics.

Description from LibreTexts.

Publisher
Irvine Valley College
Subjects
Mathematics
Licence
CC BY-NC 4.0, 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: Multivariable Precalculus
  7. 1.1: The Third Dimension
  8. 1.1: The 3D Axes
  9. 1.1: Distance Based Objects
  10. 1.1: Vectors in the Plane and Space
  11. 1.1: Practice Set
  12. 1.2: Vector Products
  13. 1.2: The Dot Product
  14. 1.2: The Cross Product
  15. 1.2: Practice Set
  16. 1.3: Lines and Planes
  17. 1.3: Lines
  18. 1.3: Planes
  19. 1.3: Practice Set
  20. 1.4: Famous Surfaces
  21. 1.4: Cylindrical and Quadric Surfaces
  22. 1.4: Practice Set
  23. 1.5: Polar, Cylindrical, and Spherical Coordinates
  24. 1.5: Cylindrical and Spherical Coordinates
  25. 1.5: Practice Set
  26. 1.6: Space Curves
  27. 1.6: Vector-Valued Functions
  28. 1.6: Calculus of Vector-Valued Functions
  29. 1.6: Practice Set
  30. 1.7: Applications of Space Curves
  31. 1.7: Arc Length and Curvature
  32. 1.7: Motion in Space
  33. 1.7: Practice Set
  34. 2: Functions of Several Variables
  35. 2.1: Multivariable Functions
  36. 2.1: Functions of Several Variables
  37. 2.1: Surfaces
  38. 2.1: Practice Set
  39. 2.2: Multivariable Limits
  40. 2.2: Limits and Continuity
  41. 2.2: Practice Set
  42. 2.3: Multivariable Differentiation
  43. 2.3: Partial Derivatives
  44. 2.3: Tangent Planes and Linear Approximations
  45. 2.3: Practice Set
  46. 2.4: More on Multivariable Derivatives
  47. 2.4: The Chain Rule for Multivariable Functions
  48. 2.4: Directional Derivatives and the Gradient
  49. 2.4: Practice Set
  50. 2.5: Vector Fields and Derivatives
  51. 2.5: Vector Fields
  52. 2.5: Divergence and Curl
  53. 2.5: Practice Set
  54. 2.6: Multivariable Extrema
  55. 2.6: Maxima/Minima Problems
  56. 2.6: Absolute Extrema
  57. 2.6: Lagrange Multipliers
  58. 2.6: Practice Set
  59. 3: Multiple Integration
  60. 3.1: Double Integrals
  61. 3.1: Iterated Integrals and Area
  62. 3.1: Double Integration and Volume
  63. 3.1: Practice Set
  64. 3.2: Triple Integrals and Polar Double Integrals
  65. 3.2: Triple Integrals
  66. 3.2: Double Integrals in Polar Coordinates
  67. 3.2: Practice Set
  68. 3.3: Change of Variables in 2 Dimensions
  69. 3.3: Change of Variables in Double Integrals
  70. 3.3: Practice Set
  71. 3.4: Change of Variables in 3 Dimensions
  72. 3.4: Change of Variables in Triple Integrals
  73. 3.4: Triple Integrals in Cylindrical and Spherical Coordinates
  74. 3.4: Practice Set
  75. 3.5: Integrals on a Line
  76. 3.5: Line Integrals
  77. 3.5: Practice Set
  78. 3.6: Integrals of Real Functions on a Surface
  79. 3.6: Surface Integrals
  80. 3.6: Practice Set
  81. 3.7: Integrals of Vector Fields on a Surface
  82. 3.7: Orientation and Flux
  83. 3.7: Practice Set
  84. 4: Vector Calculus Theorems
  85. 4.1: The Fundamental Theorem of Line Integrals
  86. 4.1: FTCLI
  87. 4.1: Practice Set
  88. 4.2: Green's Theorem
  89. 4.2: Green’s Theorem
  90. 4.2: Practice Set
  91. 4.3: Stokes' Theorem
  92. 4.3: Stokes’ Theorem
  93. 4.3: Practice Set
  94. 4.4: The Divergence Theorem
  95. 4.4: The Divergence Theorem
  96. 4.4: Practice Set
  97. Back Matter
  98. Index
  99. Glossary
  100. Detailed Licensing
  101. Detailed Licensing