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. Most will only be on-line handouts,
which makes the term "handouts" a bit questionable. The current list may be
updated during the semester.
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 instructionis,
sent two days before classes start.
- Course information sheet
(syllabus)
Course content:
vector calculus
- on-line only: reminder of calc 2 problem in 3-space: volume in
two overlapping spheres [Maple]
- the dot product
- decomposing a vector with respect to a direction
[flip side: angle between vectors][Maple]
on-line only: projection animation
- describing lines and planes
- on-line only: distances between points, lines and planes
- on-line only: vector products and length, area, volume
- on-line only: key idea of vector-valued
functions and the tangent vector
- on-line only: arclength and arclength
parametrization
- geometry of curves
- spacecurve curvature and acceleration [osculating circle][plane curve]
- on-line only: osculating circle
- on-line only: decomposing a vector with respect to a direction
revisited
"multivariable calculus"
- derivatives of 2D and 3D functions
- linear approximations and
differentials
- on-line only: the tangent plane and the linear
approximation and differentials
- on-line only: partial derivatives and changing
coordinate exercise
- on-line only:
chain rule: second derivative exercise
- multivariable derivative and differential notation
- on-line only: directional derivative
graphical representation
- 2D 2nd derivative test
integration
- double integrals: describing a region of the plane
[graphic representation of a double integral][entering
multiple integrals in Maple]
[partial
integration graphical representation]
- 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
[on-line only:
integrating over circles not centered on the origin]
- distributions of stuff: density, moments,
center of gravity, centroid, probability
- inverse trig centroid example
- cylindrical and spherical
coordinates
[on-line only: comparison with polar
coordinates]
- cylindrical and spherical regions of space and
their bounding surfaces: examples
- cylindrical and spherical triple integral:
examples
[on-line only:
triple cartesian integrals converted to spherical/cylindrical coords]
- radial integration diagrams for simple circles
and lines (cylinders, spheres, planes)
- integration over 2D and 3D regions of the plane and
space [summary]
- on-line only: progress report: where we've been and where
we're going (to end)
- summary of understanding
multiple integration regions of integration
[how
to graphically represent boundaries of triple integrals in 3d graphics?]
[interactive visualization of triple integral
limits of integration]
vector integration
- line integrals of scalars and vectors
- vector
line integrals
- "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 integrals for fun [parametrized
surfaces]
- optional: surface integration examples---PDFs and Maple worksheets:
- fun:
equianglespiralshell.mw]
[Duke
website]
Topic Notes
21-aug-2022 [course
homepage]