MAT2500 [Jantzen] Handout Log
Occasionally handouts will attempt clarification of some point to aid in your learning.
A log of these will be kept here, with links to .pdf scanned copies of
handwritten handouts for your convenience. Some will only be online handouts,
which makes the term "handouts" a bit questionable. The current list may be
updated during the semester.
You are responsible for all asking bob for all paper handouts you missed
receiving due to class absences, or you must print these scans to
substitute them.
From MAT1500 and precalc [not handed out in paper form]:
 rules of algebra.
 understanding function notation,
functional relationships.
 trigonometry and the unit circle.
 inverse trig functions.
 solving a functional relationship
between two variables for the input variable.
From MAT1500/1505:
 You are expected to know this basic stuff without hesitation or by using
technology when needed:
calculus I and II: basic
functions [algebra summary]
[print combo]
MAT 2500
Course bureaucracy:

Welcome email with WebAssign class codes,
sent weekend before classes start.

student schedule sheet section
[01,
04] [you can print these to fill out in advance]
 Course information sheet
(final version ready 4th day of class?)
Course content:
vector calculus
 online only: reminder of calc 2 problem in 3space: volume in
two overlapping spheres [Maple]
 decomposing a vector with respect to a direction
[flip side: angle between vectors][Maple]
 describing lines and planes
 online only: distances between points, lines and planes

online only: vector products and length, area, volume

online only: key idea of vectorvalued
functions and the tangent vector

online only: arclength and arclength
parametrization
 geometry of curves
 spacecurve curvature and acceleration [osculating circle][plane curve]
 online only: osculating circle
 online only: decomposing a vector with respect to a direction
revisited
"multivariable calculus"
 derivatives of 2D and 3D functions
 linear approximations and
differentials
 online only: the tangent plane and the linear
approximation and differentials
 online only: partial derivatives and changing
coordinate exercise

online only:
chain rule: second derivative exercise

multivariable derivative and differential notation
 2D 2nd derivative test
integration
 double integrals: describing a region of the plane
 example of iterating triple integral 6
different ways
 exercise in setting up triple integrals in Cartesian
coordinates

polar coordinate regions of
the plane and integration
 cylindrical and spherical
coordinates
[online only: comparison with polar
coordinates]

cylindrical and spherical regions of space and
their bounding surfaces: examples

cylindrical and spherical triple integral:
examples

radial integration diagrams for simple circles
and lines (cylinders, spheres, planes)

integration over 2D and 3D regions of the plane and
space

distributions of stuff: density, moments,
center of gravity, centroid, probability
 online only: progress report: where we've been and where
we're going (to end)
vector integration

line integrals of scalars and vectors

"antidifferentiation" in multivariable calculus
(potential function for conservative vector field)
 divergence and curl

*
geometrical interpretation of Green's
Theorem: Gauss and Stokes

interpretation of divergence and curl (2d)

optional: surface integral examples

optional: worked examples of Gauss and Stoke's Theorem

fun:
equianglespiralshell.mw]
[Duke
website]
29dec2015 [course
homepage]