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MATH 241: Calculus 3

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MATH 241: Calculus 3

An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss.

Mathematics
Author
Justin Wyss-Gallifent
Publisher
University of Maryland
Source
LibreTexts
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 50 sections
  1. 01: Vectors in Space
  2. 1.0E: 1.E: Vectors in Space (Exercises)
  3. 1.01: Prelude to Vectors in Space
  4. 1.02: Vectors in the Plane
  5. 1.03: Vectors in Three Dimensions
  6. 1.04: The Dot Product
  7. 1.05: The Cross Product
  8. 1.06: Equations of Lines and Planes in Space
  9. 1.07: Quadric Surfaces
  10. 1.08: Cylindrical and Spherical Coordinates
  11. 02: Vector-Valued Functions
  12. 2.0E: 2.E: Vector-Valued Functions (Exercises)
  13. 2.01: Prelude to Vector-Valued Functions
  14. 2.02: Vector-Valued Functions and Space Curves
  15. 2.03: Calculus of Vector-Valued Functions
  16. 2.04: Arc Length and Curvature
  17. 2.05: Motion in Space
  18. 03: Differentiation of Functions of Several Variables
  19. 3.0E: 3.E: Differentiation of Functions of Several Variables (Exercises)
  20. 3.01: Prelude to Differentiation of Functions of Several Variables
  21. 3.02: Functions of Several Variables
  22. 3.03: Limits and Continuity
  23. 3.04: Partial Derivatives
  24. 3.05: Tangent Planes and Linear Approximations
  25. 3.06: The Chain Rule for Multivariable Functions
  26. 3.07: Directional Derivatives and the Gradient
  27. 3.08: Maxima
  28. Minima Problems
  29. 3.09: Lagrange Multipliers
  30. 04: Multiple Integration
  31. 4.0E: 4.E: Multiple Integration (Exercises)
  32. 4.01: Prelude to Multiple Integration
  33. 4.02: Double Integrals over Rectangular Regions
  34. 4.03: Double Integrals over General Regions
  35. 4.04: Double Integrals in Polar Coordinates
  36. 4.05: Triple Integrals
  37. 4.06: Triple Integrals in Cylindrical and Spherical Coordinates
  38. 4.07: Calculating Centers of Mass and Moments of Inertia
  39. 4.08: Change of Variables in Multiple Integrals
  40. 05: Vector Calculus
  41. 5.0E: 5.E: Vector Calculus (Exercises)
  42. 5.01: Prelude to Vector Calculus
  43. 5.02: Vector Fields
  44. 5.03: Line Integrals
  45. 5.04: Conservative Vector Fields
  46. 5.05: Green’s Theorem
  47. 5.06: Divergence and Curl
  48. 5.07: Surface Integrals
  49. 5.08: Stokes’ Theorem
  50. 5.09: The Divergence Theorem