MATH 12 CLASS 4 NOTES, SEP 28 2011
Contents
1. Lines in R3
2. Intersections of lines in R3
3. The equation of a plane
4. Various problems with planes
4.1. Intersection of planes with planes or lines
4
MATH 12 CLASS 5 NOTES, SEP 30 2011
Contents
1. Vector-valued functions
2. Dierentiating and integrating vector-valued functions
3. Velocity and Acceleration
1
3
4
Over the past two weeks we have devel
MATH 12 CLASS 5 NOTES, SEP 30 2011
Contents
1. Arc length of curves
1
1. Arc length of curves
Now that we know how to take derivatives of vector-valued functions, we briey
describe how to solve a natu
MATH 12 CLASS 7 NOTES, OCT 4 2011
Contents
1. Plotting functions of several variables
2. Limits of functions of several variables
3. Computer systems for 3D graphing
1
3
5
1. Plotting functions of sev
MATH 12 CLASS 8 NOTES, OCT 7 2011
Contents
1. Partial Derivatives
2. Higher partial derivatives
3. Tangent planes
1
3
3
Now that we have some idea of how to dene a limit for multivariable functions, a
MATH 12 CLASS 9 NOTES, OCT 10 2011
Contents
1. Tangent planes
2. Denition of dierentiability
3. Dierentials
1
3
4
1. Tangent planes
Recall that the derivative of a single variable function can be inte
MATH 12 CLASS 10 NOTES, OCT 12 2011
Contents
1. Directional derivatives
2. The gradient
1
2
Quick links to denitions/theorems
Directional derivative denition
Gradient denition
Computing the directi
MATH 12 CLASS 11 NOTES, OCT 14 2011
Contents
1. The direction of maximum increase
Suppose we have a function f (x, y ) and a point (a, b) we are interested in. If we
think about the surface z = f (x,