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Multidimensional Calculus

Educator Edition

ContributorUniversity of Rochester
CourseMTH 164, Multidimensional Calculus
Equations of lines and planes, quadric surfaces, space curves, partial derivatives, linear approximation, directional derivatives, extrema, Lagrange multipliers, double/triple integrals including cylindrical and spherical coordinates. Line, surface, and volume integrals, divergence theorem, Stokes' theorem.
TextbookCalculus (Early Transcendentals), 8th or earlier edition, James Stewart; or a textbook of your choice.

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Syllabus

  1. Three-Dimensional Coordinate Systems; Vectors; Dot Product
  2. Dot Product; Cross Product; Equations of Lines and Planes
  3. Quadric Surfaces and Cylinders; Vector Functions and Space Curves; Derivatives and Integrals of Space Curves
  4. Arc Length and Curvature; Motion in Space; Functions of Several Variables
  5. Functions of Several Variables; Limits and Continuity; Partial Derivatives
  6. Partial Derivatives
  7. Maximum and Minimum Values; Lagrange Multipliers
  8. Multiple Integrals; Iterated Integrals
  9. Double Integrals over General Regions; Change of Variables in Multiple Integrals; Polar Coordinates
  10. Integration in Polar Coordinates; Applications of Double Integrals; Triple Integrals; Integrals in Spherical Coordinates
  11. Vector Fields; Line Integrals; FTC for Line Integrals Against Gradient Fields; Green's Theorem
  12. Green's Theorem; Curl and Div; Parametric Surfaces
  13. Surface Integrals; Stoke's Theorem; Divergence Theorem

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