Studied by 10 peopleDistance formula
Equation of sphere of center
Midpoint of 2 points
can also include z for 2pts in 3-space
Completing the square
Angle b/w vectors
Orthagonal Projection
Cross Product
Area of a Parallelogram
Area of Triangle
Volume of parallepiped
or cross product of the three vectors
Parametric equation
Distance b/w line and point
Equation of a plane in 3-space
Planes given by 3-points
Distance b/w point and plane
ellipsoid
hyperboloid w/one sheet
hyperboloid w/two sheets
Elliptic cone
Elliptic parabaloid
Hyperbolic parabaloid
Equation of tangent line
Distance
Displacement
Arc length
Arc length parametrization
Identify reference point (end pt) by value of pt
Use Arc length formula
find t in terms of s
In R(t) replace t value in s from step 3
Unit vectors (T(t))
Unit vectors (B(t))
Unit vectors (N(t))
Curvature
Curvature in y = f(x) form
Limit and Continuity
Polar coordinates to evaluate limit
Continuity
Partial derivative
Chain rule for derivative
Chain rule for partial derivative
Directional derivative
Theorem: directional derivative
Local linear approximation
Equation of tangent plane
maximum/minimum
Double Integral
Polar Coordinates
Theorem: polar coordinates
Triple Integral
Volume (using triple integral)
Volume (using double integral)
Cylindrical coordinates
same as polar coord. except z=z and integrate by z first (also has same jacobian of R)
Spherical coordinates
Spherical coordinates jaacobian
Jacobian of T
Jacobian Theorem
Theorem: change of variables
Area (with double integral)
Vector field notation
Theorem: conservative vector field in 2-space
Divergence
Curl of F (vector field)
Parametric Curve
Line Integral
Line integral of vector valued function
Conservative vector field (3-space)
Potential function
Theorem: line integral
Green’s Theorem
Note
Flashcard