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 on-line handouts, which makes the term "handouts" a bit questionable. The current list may be updated during the semester. Handouts marked "online only" are not printed and distributed in normal nonpandemic times, implying more importance to the rest.

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.
- 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:

- examples 1&2: surface area and centroid of
hemisphere,
Gauss law example,

plus wedge of cylinder Stewart 16.7.example3;

example3: parabola of revolution (Stewart16.7.23 expanded into Gauss/Stokes examples) - example 4: rotated parabolic cylinder example.

- examples 1&2: surface area and centroid of
hemisphere,
Gauss law example,
- fun:
equianglespiralshell.mw]
**[Duke website]**

*11-may-2020* [course
homepage]