Multidimensional Calculus

used at University of Rochester

Educator Edition

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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Problem Sets

  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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