## MAT 213: Calculus III, Section D01

## Spring 2017

Syllabus.

Solutions distributed in class.

Day-by-day summary.

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).

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.

The "chart method" for certain integrals.

An integral iterated -dydx and -dxdy.

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.