MAT 213: Calculus III, Section D01
Solutions distributed in class.
Answer key (odd-numbered text problems).
The Greek Alphabet.
A review of some trigonometry.
Topics to review from Calc I and Calc II.
Practice sheet: converting to polar coordinates.
Two magnitude calculations.
Example 7 on p 804.
Dot products and angles.
Lines in R^2 and the dot product.
Cauchy-Schwarz and Triangle Inequalities.
SUMMARY: dot product.
One determinant computed six ways.
Determinants and the Laplace expansion.
The cross product.
The distance between two lines in three-dimensional space.
A brief summary of conic sections.
A brief summary of quadric surfaces.
A diagram of the conic sections.
Partial proof of Rule 5 (page 858).
A discussion of rule#6 (page 858).
Speed and arclength.
Reparametrization by arclength: an example.
Curvature and acceleration.
Why the formula #10 on the curvature/acceleration handout is often so hard to use.
Comparing Calc I and Calc III limit laws.
Examples involving path limits.
Galileo, Kepler, and Newton.
Some basic facts about inequalities.
Linearization and differentials: the one-dimensional case (text sec. 3.10).
Differentiating a function of two variables.
The Chain Rule in higher dimensions.
Gradients and level sets.
Comparing Calc I and Calc III max/min rules.
The Extreme Value Theorem in the Plane.
Further properties of the gradient.
Proof of Clairaut's Theorem.
Integrating f(x,y)=g(x)h(y) over a rectangle.
The "chart method" for certain integrals.
An integral iterated -dydx and -dxdy.
The area of a polar rectangle.
Notes on center of mass in the plane.
Calculating the area of a hemisphere.
Cylindrical and spherical coordinates.
Moment of inertia.
Conversions among rectangular/cylindrical/spherical coordinates.
Worksheet: practice in coordinate conversion.
Why conservative vector fields are gradient fields.
Some topics from Chapter 16.