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Math 223 Calculus 3

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Math 223 Calculus 3

This book considers what happens when we broaden our view of what a function is to include functions that have more than one input, or that produce more than one result, or both. In particular, we consider what it means for such a function to have a limit, and how to differentiate or integrate such functions. In the course of learning these things, we will also encounter many applications of so-called multivariable and vector-valued functions in the natural and social sciences.

Mathematics
Publisher
LibreTexts
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 81 sections
  1. 01: Vectors in Space
  2. 1.01: Vectors in the Plane
  3. 1.1E: Exercises for Section 1.1
  4. 1.02: Vectors in Three Dimensions
  5. 1.2E: Exercises for Section 1.2
  6. 1.03: The Dot Product
  7. 1.3E: Exercises for Section 1.3
  8. 1.04: The Cross Product
  9. 1.4E: Exercises for Section 1.4
  10. 1.05: Equations of Lines and Planes in Space
  11. 1.5E: Exercises for Section 1.5
  12. 1.06: Quadric Surfaces
  13. 1.6E: Exercises for Section 1.6
  14. 1.07: Cylindrical and Spherical Coordinates
  15. 1.7E: Exercises for Section 1.7
  16. 1.08: Chapter 1 Review Exercises
  17. 02: Vector-Valued Functions
  18. 2.01: Vector-Valued Functions and Space Curves
  19. 2.1E: Exercises for Section 2.1
  20. 2.02: Calculus of Vector-Valued Functions
  21. 2.2E: Exercises for Section 2.2
  22. 2.03: Arc Length and Curvature
  23. 2.3E: Exercises for Section 2.3
  24. 2.04: Motion in Space
  25. 2.4E: Exercises for Section 2.4
  26. 2.05: Chapter 2 Review Exercises
  27. 03: Differentiation of Functions of Several Variables
  28. 3.01: Functions of Several Variables
  29. 3.1E: Exercises for Section 3.1
  30. 3.02: Limits and Continuity
  31. 3.2E: Exercises for Section 3.2
  32. 3.03: Partial Derivatives
  33. 3.3E: Exercises for Section 3.3
  34. 3.04: Tangent Planes and Linear Approximations
  35. 3.4E: Exercises for Section 3.4
  36. 3.05: The Chain Rule for Multivariable Functions
  37. 3.5E: Exercises for Section 3.5
  38. 3.06: Directional Derivatives and the Gradient
  39. 3.6E: Exercises for Section 3.6
  40. 3.07: Maxima Minima Problems
  41. 3.7E: Exercises for Section 3.7
  42. 3.08: Lagrange Multipliers
  43. 3.8E: Exercises for Section 3.8
  44. 3.09: Chapter 3 Review Exercises
  45. 04: Multiple Integration
  46. 4.01: Double Integrals over Rectangular Regions
  47. 4.1E: Exercises for Section 4.1
  48. 4.02: Double Integrals over General Regions
  49. 4.2E: Exercises for Section 4.2
  50. 4.03: Double Integrals in Polar Coordinates
  51. 4.3E: Exercises for Section 4.3
  52. 4.04: Triple Integrals
  53. 4.4E: Exercises for Section 4.4
  54. 4.05: Triple Integrals in Cylindrical and Spherical Coordinates
  55. 4.5E: Exercises for Section 4.5
  56. 4.06: Calculating Centers of Mass and Moments of Inertia
  57. 4.6E: Exercises for Section 4.6
  58. 4.07: Change of Variables in Multiple Integrals
  59. 4.7E: Exercises for Section 4.7
  60. 4.08: Chapter 4 Review Exercises
  61. 05: Vector Calculus
  62. 5.01: Vector Fields
  63. 5.1E: Exercises for Section 5.1
  64. 5.02: Line Integrals
  65. 5.2E: Exercises for Section 5.2
  66. 5.03: Conservative Vector Fields
  67. 5.3E: Exercises for Section 5.3
  68. 5.04: Greens Theorem
  69. 5.4E: Exercises for Section 5.4
  70. 5.05: Divergence and Curl
  71. 5.5E: Exercises for Section 5.5
  72. 5.06: Surface Integrals
  73. 5.6E: Exercises for Section 5.6
  74. 5.07: Stokes Theorem
  75. 5.7E: Exercises for Section 5.7
  76. 5.08: The Divergence Theorem
  77. 5.8E: Exercises for Section 5.8
  78. 5.09: Chapter 5 Review Exercises
  79. 06: Appendices
  80. 6.A: Table of Derivatives
  81. 6.B: Table of Integrals