|Contributor||University of Rochester|
|Course||MTH 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.
|Textbook||Calculus (Early Transcendentals), 8th or earlier edition, James Stewart; or a textbook of your choice.|
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- Three-Dimensional Coordinate Systems; Vectors; Dot Product
- Dot Product; Cross Product; Equations of Lines and Planes
- Quadric Surfaces and Cylinders; Vector Functions and Space Curves; Derivatives and Integrals of Space Curves
- Arc Length and Curvature; Motion in Space; Functions of Several Variables
- Functions of Several Variables; Limits and Continuity; Partial Derivatives
- Partial Derivatives
- Maximum and Minimum Values; Lagrange Multipliers
- Multiple Integrals; Iterated Integrals
- Double Integrals over General Regions; Change of Variables in Multiple Integrals; Polar Coordinates
- Integration in Polar Coordinates; Applications of Double Integrals; Triple Integrals; Integrals in Spherical Coordinates
- Vector Fields; Line Integrals; FTC for Line Integrals Against Gradient Fields; Green's Theorem
- Green's Theorem; Curl and Div; Parametric Surfaces
- Surface Integrals; Stoke's Theorem; Divergence Theorem
This is a multi-student, educator license. You will be able to manage an online classroom of your students, and monitor their progress.