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Math 4A: Multivariable Calculus

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Math 4A: Multivariable Calculus

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.

Mathematics
Author
Kenn Huber
Publisher
Irvine Valley College
Source
LibreTexts
License
CC BY-NC
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 91 sections
  1. 01: Multivariable Precalculus
  2. 1.01: The Third Dimension
  3. 1.1.01: The 3D Axes
  4. 1.1.02: Distance Based Objects
  5. 1.1.03: Vectors in the Plane and Space
  6. 1.1.04: Practice Set
  7. 1.02: Vector Products
  8. 1.2.01: The Dot Product
  9. 1.2.02: The Cross Product
  10. 1.2.03: Practice Set
  11. 1.03: Lines and Planes
  12. 1.3.01: Lines
  13. 1.3.02: Planes
  14. 1.3.03: Practice Set
  15. 1.04: Famous Surfaces
  16. 1.4.01: Cylindrical and Quadric Surfaces
  17. 1.4.02: Practice Set
  18. 1.05: Polar Cylindrical and Spherical Coordinates
  19. 1.5.01: Cylindrical and Spherical Coordinates
  20. 1.5.02: Practice Set
  21. 1.06: Space Curves
  22. 1.6.01: Vector-Valued Functions
  23. 1.6.02: Calculus of Vector-Valued Functions
  24. 1.6.03: Practice Set
  25. 1.07: Applications of Space Curves
  26. 1.7.01: Arc Length and Curvature
  27. 1.7.02: Motion in Space
  28. 1.7.03: Practice Set
  29. 02: Functions of Several Variables
  30. 2.01: Multivariable Functions
  31. 2.1.01: Functions of Several Variables
  32. 2.1.02: Surfaces
  33. 2.1.03: Practice Set
  34. 2.02: Multivariable Limits
  35. 2.2.01: Limits and Continuity
  36. 2.2.02: Practice Set
  37. 2.03: Multivariable Differentiation
  38. 2.3.01: Partial Derivatives
  39. 2.3.02: Tangent Planes and Linear Approximations
  40. 2.3.03: Practice Set
  41. 2.04: More on Multivariable Derivatives
  42. 2.4.01: The Chain Rule for Multivariable Functions
  43. 2.4.02: Directional Derivatives and the Gradient
  44. 2.4.03: Practice Set
  45. 2.05: Vector Fields and Derivatives
  46. 2.5.01: Vector Fields
  47. 2.5.02: Divergence and Curl
  48. 2.5.03: Practice Set
  49. 2.06: Multivariable Extrema
  50. 2.6.01: Maxima Minima Problems
  51. 2.6.02: Absolute Extrema
  52. 2.6.03: Lagrange Multipliers
  53. 2.6.04: Practice Set
  54. 03: Multiple Integration
  55. 3.01: Double Integrals
  56. 3.1.01: Iterated Integrals and Area
  57. 3.1.02: Double Integration and Volume
  58. 3.1.03: Practice Set
  59. 3.02: Triple Integrals and Polar Double Integrals
  60. 3.2.01: Triple Integrals
  61. 3.2.02: Double Integrals in Polar Coordinates
  62. 3.2.03: Practice Set
  63. 3.03: Change of Variables in 2 Dimensions
  64. 3.3.01: Change of Variables in Double Integrals
  65. 3.3.02: Practice Set
  66. 3.04: Change of Variables in 3 Dimensions
  67. 3.4.01: Change of Variables in Triple Integrals
  68. 3.4.02: Triple Integrals in Cylindrical and Spherical Coordinates
  69. 3.4.03: Practice Set
  70. 3.05: Integrals on a Line
  71. 3.5.01: Line Integrals
  72. 3.5.02: Practice Set
  73. 3.06: Integrals of Real Functions on a Surface
  74. 3.6.01: Surface Integrals
  75. 3.6.02: Practice Set
  76. 3.07: Integrals of Vector Fields on a Surface
  77. 3.7.01: Orientation and Flux
  78. 3.7.02: Practice Set
  79. 04: Vector Calculus Theorems
  80. 4.01: The Fundamental Theorem of Line Integrals
  81. 4.1.01: FTCLI
  82. 4.1.02: Practice Set
  83. 4.02: Green's Theorem
  84. 4.2.01: Greens Theorem
  85. 4.2.02: Practice Set
  86. 4.03: Stokes' Theorem
  87. 4.3.01: Stokes Theorem
  88. 4.3.02: Practice Set
  89. 4.04: The Divergence Theorem
  90. 4.4.01: The Divergence Theorem
  91. 4.4.02: Practice Set