Math 209: Multivariate Calculus

How do you notate vectors

With an arrow on top of the variable. (Set 1 Material)

What does a vector have

Magnitude and Direction (Set 1 Material)

What is the dot product

If vector a = < a₁ , a₂ , a₃ > and vector b = < b₁, b₂ , b₃ > then a “dot” b = (a₁b₁) + (a₂b₂) + (a₃b₃) (Set 1 Material)

What is the cross product

If vector a = < a₁ , a₂ , a₃ > and vector b = < b₁, b₂ , b₃ > then a x b = < a₂b₃ - a₃b₂ , -1(a₁b₃ - a₃b₁) , a₁b₂ - a₂b₁ > (Set 1 Material)

Do the dot product and cross products result in numbers or vectors

The dot product will result in a number. The cross product results in a vector. (Set 1 Material)

(Set 1 Material)

What is the equation

(Set 1 Material)

(Set 1 Material)

(Set 2 Material)

What is the gradient of a function

(Set 3 Material)

What is the formula for the directional derivative of f in the direction of v at the point p. 

(Set 3 Material)

Given a real valued function f(x,y) whose partials exists, are are continuous, the tangent plane to the graph of f at (a , b , f(a,b)) is what

(Set 4 Material)

How do you determine maximums and minimums of multivariable functions

(Set 4 Material)

What are the equations must you use for the system of equations for Lagrange multipliers

(Set 5 Material)