MCC: MTH 212 Calculus III

by Paul Seeburger

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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.

Description from LibreTexts.

Publisher
Monroe Community College
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. Chapter 11: Vectors and the Geometry of Space
  2. 11.1: Vectors in the Plane
  3. 11.1E: Exercises for Vectors in the Plane
  4. 11.2: Vectors in Space
  5. 11.2E: Exercises for Vectors in Space
  6. 11.3: The Dot Product
  7. 11.3E: Exercises for The Dot Product
  8. 11.4: The Cross Product
  9. 11.4E: Exercises for The Cross Product
  10. 11.5: Equations of Lines and Planes in Space
  11. 11.5E: Exercises for Equations of Lines and Planes in Space
  12. 11.6: Quadric Surfaces
  13. 11.6E: Exercises for Quadric Surfaces
  14. 11.7: Cylindrical and Spherical Coordinates
  15. 11.7E: Exercises for Cylindrical and Spherical Coordinates
  16. 11R: Chapter 11 Review Exercises
  17. Chapter 12: Vector-valued Functions
  18. 12.1: Vector-Valued Functions and Space Curves
  19. 12.1E: Exercises for Section 12.1
  20. 12.2: The Calculus of Vector-Valued Functions
  21. 12.2E: Exercises for Section 12.2
  22. 12.2B: The Calculus of Vector-Valued Functions II
  23. 12.3: Motion in Space
  24. 12.3E: Exercises for Section 12.3
  25. 12.4: Arc Length and Curvature
  26. 12.4E: Exercises for Section 12.4
  27. 12.5: Acceleration and Kepler's Laws
  28. 12.5E: Exercises for Section 12.5
  29. 12R: Review Exercises for Chapter 12
  30. More Review Exercises for Chapter 12
  31. Chapter 13: Functions of Multiple Variables and Partial Derivatives
  32. 13.0: Introduction to Functions of Multiple Variables
  33. 13.1: Functions of Multiple Variables
  34. 13.1E: Functions of Multiple Variables (Exercises)
  35. 13.2: Limits and Continuity
  36. 13.2E: Exercises for Limits and Continuity
  37. 13.3: Partial Derivatives
  38. 13.3E: Partial Derivatives (Exercises)
  39. 13.4: Tangent Planes, Linear Approximations, and the Total Differential
  40. 13.4E: Tangent Planes, Linear Approximations, and the Total Differential (Exercises)
  41. 13.5: The Chain Rule for Functions of Multiple Variables
  42. 13.5E: The Chain Rule for Functions of Multiple Variables (Exercises)
  43. 13.6: Directional Derivatives and the Gradient
  44. 13.6E: Directional Derivatives and the Gradient (Exercises)
  45. 13.7: Taylor Polynomials of Functions of Two Variables
  46. 13.7E: Taylor Polynomials of Functions of Two Variables (Exercises)
  47. 13.8: Optimization of Functions of Several Variables
  48. 13.8E: Optimization of Functions of Several Variables (Exercises)
  49. 13.9: Applications of Optimization, Constrained Optimization, and Absolute Extrema
  50. 13.9E: Optimization of Functions of Several Variables (Exercises)
  51. 13.10: Lagrange Multipliers
  52. 13.10E: Exercises for Lagrange Multipliers
  53. 13R: Chapter 13 Review Exercises
  54. Chapter 14: Multiple Integration
  55. 14.1: Iterated Integrals and Area
  56. 14.1E: Iterated Integrals and Area (Exercises)
  57. 14.2a: Double Integrals Over Rectangular Regions
  58. 14.2aE: Double Integrals Part 1 (Exercises)
  59. 14.2b: Double Integrals Over General Regions
  60. 14.2bE: Double Integrals Part 2 (Exercises)
  61. 14.3: Double Integration with Polar Coordinates
  62. 14.3b: Double Integrals in Polar Coordinates
  63. 14.3E: Double Integrals in Polar Coordinates (Exercises)
  64. 14.4: Triple Integrals
  65. 14.4E: Triple Integrals (Exercises)
  66. 14.5: Triple Integrals in Cylindrical and Spherical Coordinates
  67. 14.5E: Exercises for Section 14.5
  68. 14.6: Calculating Centers of Mass and Moments of Inertia
  69. 14.6E: Exercises for Section 14.6
  70. 14.7: Change of Variables in Multiple Integrals (Jacobians)
  71. 14.7E: Exercises for Section 14.7
  72. 14R: Review Exercises for Chapter 14
  73. More Chapter 14 Review Exercises
  74. Chapter 15: Vector Fields, Line Integrals, and Vector Theorems
  75. 15.0: Introduction to Vector Field Chapter
  76. 15.1: Vector Fields
  77. 15.1E: Exercises for Section 15.1
  78. 15.2: Line Integrals
  79. 15.2: Line Integrals - Part 2
  80. 15.2E: Exercises for Section 15.2
  81. 15.3: Conservative Vector Fields
  82. 15.3E: Exercises for Section 15.3
  83. 15.4: Green's Theorem
  84. 15.4E: Exercises for Section 15.4
  85. 15.5: Divergence and Curl
  86. 15.5E: Divergence and Curl (Exercises)
  87. 15.6: Surface Integrals
  88. 15.6E: Exercises for Section 15.6
  89. 15.7: Stokes' Theorem
  90. 15.7E: Exercises for Section 15.7
  91. 15.8: The Divergence Theorem
  92. 15.8E: Exercises for Section 15.8
  93. Appendices
  94. Trigonometric Identities
  95. Table of Derivatives
  96. Table of Integrals
  97. Table of Laplace Transforms