Multivariable Calculus Common Topics List1
1. Multivariable Functions
2. 3-D space
(a) Distance
(b) Equations of planes, spheres, etc.
(c) Two-variable function graphs
(d) Sections, level curves, and contour diagrams
3. Vectors
(a) Arithmetic on vectors, graphically and by components
(b) Dot Product and projection
(c) Cross Product
4. Limits are more complicated than in the one-variable case
5. Partial Derivatives
(a) Compute using the definition of partial derivatives
(b) Compute using differentiation rules
(c) Approximate given a contour diagram or other info about a function
(d) Estimate signs from real-world desciption
(e) Find the tangent plane
(f) Compute higher-order partials
(g) Mixed partials are equal under certain conditions
6. Directional derivatives
(a) Estimate from contour diagram
(b) Compute using limit definition
(c) Compute using dot product with the gradient
7. Gradient
(a) Compute the gradient
(b) Points in the direction of fastest increase
(c) Length is the directional derivative in that direction
(d) Perpendicular to level set
(e) Draw gradient vector given a contour diagram
1This list was approved by the department on 4/10/19
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