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Math C280: Calculus III

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Math C280: Calculus III

Multivariable calculus including vectors, vector-valued functions, functions of several variables, partial derivatives, multiple integrals, calculus of vector fields, Green's Theorem, Stokes' Theorem, and the Divergence Theorem.

Mathematics
Author
Michael Everett
Publisher
Coastline College
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 97 sections
  1. 01: Vectors and the Geometry of Space
  2. 1.01: Vectors in the Plane
  3. 1.1E: Exercises for Vectors in the Plane
  4. 1.02: Vectors in Space
  5. 1.2E: Exercises for Vectors in Space
  6. 1.03: The Dot Product
  7. 1.3E: Exercises for The Dot Product
  8. 1.04: The Cross Product
  9. 1.4E: Exercises for The Cross Product
  10. 1.05: Equations of Lines and Planes in Space
  11. 1.5E: Exercises for Equations of Lines and Planes in Space
  12. 1.06: Quadric Surfaces
  13. 1.6E: Exercises for Quadric Surfaces
  14. 1.07: Cylindrical and Spherical Coordinates
  15. 1.7E: Exercises for Cylindrical and Spherical Coordinates
  16. 1.08: Chapter 11 Review Exercises
  17. 02: Vector-valued Functions
  18. 2.01: Vector-Valued Functions and Space Curves
  19. 2.1E: Exercises for Section 12.1
  20. 2.02: The Calculus of Vector-Valued Functions
  21. 2.2E: Exercises for Section 12.2
  22. 2.03: The Calculus of Vector-Valued Functions II
  23. 2.04: Motion in Space
  24. 2.4E: Exercises for Section 12.3
  25. 2.05: Arc Length and Curvature
  26. 2.5E: Exercises for Section 12.4
  27. 2.06: Acceleration and Kepler's Laws
  28. 2.6E: Exercises for Section 12.5
  29. 2.07: Review Exercises for Chapter 12
  30. 2.08: More Review Exercises for Chapter 12
  31. 03: Functions of Multiple Variables and Partial Derivatives
  32. 3.01: Introduction to Functions of Multiple Variables
  33. 3.02: Functions of Multiple Variables
  34. 3.2E: Functions of Multiple Variables (Exercises)
  35. 3.03: Limits and Continuity
  36. 3.3E: Exercises for Limits and Continuity
  37. 3.04: Partial Derivatives
  38. 3.4E: Partial Derivatives (Exercises)
  39. 3.05: Tangent Planes Linear Approximations and the Total Differential
  40. 3.5E: Tangent Planes Linear Approximations and the Total Differential (Exercises)
  41. 3.06: The Chain Rule for Functions of Multiple Variables
  42. 3.6E: The Chain Rule for Functions of Multiple Variables (Exercises)
  43. 3.07: Directional Derivatives and the Gradient
  44. 3.7E: Directional Derivatives and the Gradient (Exercises)
  45. 3.08: Taylor Polynomials of Functions of Two Variables
  46. 3.8E: Taylor Polynomials of Functions of Two Variables (Exercises)
  47. 3.09: Optimization of Functions of Several Variables
  48. 3.9E: Optimization of Functions of Several Variables (Exercises)
  49. 3.10: Constrained Optimization
  50. 3.10E: Optimization of Functions of Several Variables (Exercises)
  51. 3.11: Lagrange Multipliers
  52. 3.11E: Exercises for Lagrange Multipliers
  53. 3.12: Chapter 13 Review Exercises
  54. 04: Multiple Integration
  55. 4.01: Iterated Integrals and Area
  56. 4.1E: Iterated Integrals and Area (Exercises)
  57. 4.02: Double Integrals Over Rectangular Regions
  58. 4.2.01: Double Integrals Part 1 (Exercises)
  59. 4.03: Double Integrals Over General Regions
  60. 4.3.01: Double Integrals Part 2 (Exercises)
  61. 4.04: Double Integration with Polar Coordinates
  62. 4.4b: Double Integrals in Polar Coordinates
  63. 4.4E: Double Integrals in Polar Coordinates (Exercises)
  64. 4.05: Triple Integrals
  65. 4.5E: Triple Integrals (Exercises)
  66. 4.06: Triple Integrals in Cylindrical and Spherical Coordinates
  67. 4.6E: Exercises for Section 14.5
  68. 4.07: Calculating Centers of Mass and Moments of Inertia
  69. 4.7E: Exercises for Section 14.6
  70. 4.08: Change of Variables in Multiple Integrals (Jacobians)
  71. 4.8E: Exercises for Section 14.7
  72. 4.09: Review Exercises for Chapter 14
  73. 4.10: More Chapter 14 Review Exercises
  74. 05: Vector Fields Line Integrals and Vector Theorems
  75. 5.01: Introduction to Vector Field Chapter
  76. 5.02: Vector Fields
  77. 5.2E: Exercises for Section 15.1
  78. 5.03: Line Integrals
  79. 5.3.01: Line Integrals - Part 2
  80. 5.3E: Exercises for Section 15.2
  81. 5.04: Conservative Vector Fields
  82. 5.4E: Exercises for Section 15.3
  83. 5.05: Green's Theorem
  84. 5.5E: Exercises for Section 15.4
  85. 5.06: Divergence and Curl
  86. 5.6E: Divergence and Curl (Exercises)
  87. 5.07: Surface Integrals
  88. 5.7E: Exercises for Section 15.6
  89. 5.08: Stokes' Theorem
  90. 5.8E: Exercises for Section 15.7
  91. 5.09: The Divergence Theorem
  92. 5.9E: Exercises for Section 15.8
  93. 06: Appendices
  94. 6.01: Trigonometric Identities
  95. 6.02: Table of Derivatives
  96. 6.03: Table of Integrals
  97. 6.04: Table of Laplace Transforms