MATH 2514 Calculus III

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A standard course in multivariable calculus that starts with vectors operations and vector-valued functions, continues through functions of multiple variables, partial derivatives, multiple integration, vector fields, and vector theorems.

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Subjects
Mathematics
Licence
CC BY-NC-SA, 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. Chapter 11: Vectors and the Geometry of Space
  7. 11.1: Vectors in the Plane
  8. 11.1E: Exercises for Vectors in the Plane
  9. 11.2: Vectors in Space
  10. 11.2E: Exercises for Vectors in Space
  11. 11.3: The Dot Product
  12. 11.3E: Exercises for The Dot Product
  13. 11.4: The Cross Product
  14. 11.4E: Exercises for The Cross Product
  15. 11.5: Equations of Lines and Planes in Space
  16. 11.5E: Exercises for Equations of Lines and Planes in Space
  17. 11.6: Quadric Surfaces
  18. 11.6E: Exercises for Quadric Surfaces
  19. 11.7: Cylindrical and Spherical Coordinates
  20. 11.7E: Exercises for Cylindrical and Spherical Coordinates
  21. Chapter 11 Review Exercises
  22. Chapter 12: Vector-valued Functions
  23. 12.1: Vector-Valued Functions and Space Curves
  24. 12.1E: Exercises for Section 12.1
  25. 12.2: The Calculus of Vector-Valued Functions
  26. 12.2E: Exercises for Section 12.2
  27. 12.2B: The Calculus of Vector-Valued Functions II
  28. 12.3: Motion in Space
  29. 12.3E: Exercises for Section 12.3
  30. 12.4: Arc Length and Curvature
  31. 12.4E: Exercises for Section 12.4
  32. 12.5: Acceleration and Kepler's Laws
  33. 12.5E: Exercises for Section 12.5
  34. 12.E: Chapter 12 Review Exercises
  35. Chapter 12 Review Exercises
  36. Chapter 13: Functions of Multiple Variables and Partial Derivatives
  37. 13.0: Introduction to Functions of Multiple Variables
  38. 13.10: Lagrange Multipliers
  39. 13.10E: Exercises for Lagrange Multipliers
  40. 13.1: Functions of Multiple Variables
  41. 13.1E: Functions of Multiple Variables (Exercises)
  42. 13.2: Limits and Continuity
  43. 13.2E: Exercises for Limits and Continuity
  44. 13.3: Partial Derivatives
  45. 13.3E: Partial Derivatives (Exercises)
  46. 13.4: Tangent Planes, Linear Approximations, and the Total Differential
  47. 13.4E: Tangent Planes, Linear Approximations, and the Total Differential (Exercises)
  48. 13.5: The Chain Rule for Functions of Multiple Variables
  49. 13.5E: The Chain Rule for Functions of Multiple Variables (Exercises)
  50. 13.6: Directional Derivatives and the Gradient
  51. 13.6E: Directional Derivatives and the Gradient (Exercises)
  52. 13.7: Taylor Polynomials of Functions of Two Variables
  53. 13.7E: Taylor Polynomials of Functions of Two Variables (Exercises)
  54. 13.8: Optimization of Functions of Several Variables
  55. 13.8E: Optimization of Functions of Several Variables (Exercises)
  56. 13.9: Constrained Optimization
  57. 13.9E: Optimization of Functions of Several Variables (Exercises)
  58. Chapter 14: Multiple Integration
  59. 14.1: Iterated Integrals and Area
  60. 14.1E: Iterated Integrals and Area (Exercises)
  61. 14.2a: Double Integrals Over Rectangular Regions
  62. 14.2aE: Double Integrals Part 1 (Exercises)
  63. 14.2b: Double Integrals Over General Regions
  64. 14.2bE: Double Integrals Part 2 (Exercises)
  65. 14.3: Double Integration with Polar Coordinates
  66. 14.3b: Double Integrals in Polar Coordinates
  67. 14.3E: Double Integrals in Polar Coordinates (Exercises)
  68. 14.4: Triple Integrals
  69. 14.4E: Triple Integrals (Exercises)
  70. 14.4E: Triple Integrals (Exercises 2)
  71. 14.5: Triple Integrals in Cylindrical and Spherical Coordinates
  72. 14.6: Calculating Centers of Mass and Moments of Inertia
  73. 14.7: Change of Variables in Multiple Integrals (Jacobians)
  74. Chapter 14 Review Exercises
  75. Chapter 15: Vector Fields, Line Integrals, and Vector Theorems
  76. 15.0: Introduction to Vector Field Chapter
  77. 15.1: Vector Fields
  78. 15.1E: Vector Fields (Exercises)
  79. 15.2: Line Integrals
  80. 15.2: Line Integrals - Part 2
  81. 15.2E: Line Integrals (Exercises)
  82. 15.3: Conservative Vector Fields
  83. 15.3E: Conservative Vector Fields (Exercises)
  84. 15.4: Green's Theorem
  85. 15.4E: Green's Theorem (Exercises)
  86. 15.5: Divergence and Curl
  87. 15.5E: Divergence and Curl (Exercises)
  88. 15.6: Surface Integrals
  89. 15.7: Stokes' Theorem
  90. 15.8: The Divergence Theorem
  91. Chapter 15 Review Exercises
  92. Appendices
  93. Table of Derivatives
  94. Table of Integrals
  95. Table of Laplace Transforms