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 on-line 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]:

1. rules of algebra.
2. understanding function notation, functional relationships.
3. trigonometry and the unit circle.
4. inverse trig functions.
5. solving a functional relationship between two variables for the input variable.

From MAT1500/1505:

1. 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:

1. Welcome email with WebAssign class codes, sent weekend before classes start.
2. student schedule sheet section [01, 04]  [you can print these to fill out in advance, or pick one up in the first class]
3. Course information sheet (final version ready 4th day of class?)
   
   Course content:
   
   vector calculus
4. on-line only: reminder of calc 2 problem in 3-space: volume in two overlapping spheres [Maple]
5. the dot product
6. decomposing a vector with respect to a direction [flip side: angle between vectors][Maple]
   on-line only: projection animation
7. describing lines and planes
8. on-line only: distances between points, lines and planes
9. on-line only: vector products and length, area, volume
10. on-line only: key idea of vector-valued functions and the tangent vector
11. on-line only: arclength and arclength parametrization
12. geometry of curves
13. spacecurve curvature and acceleration [osculating circle][plane curve]
14. on-line only: osculating circle
15. on-line only: decomposing a vector with respect to a direction revisited
    
    "multivariable calculus"
16. derivatives of 2D and 3D functions
17. linear approximations and differentials
18. on-line only: the tangent plane and the linear approximation and differentials
19. on-line only: partial derivatives and changing coordinate exercise
20. on-line only: chain rule: second derivative exercise
21. multivariable derivative and differential notation
22. on-line only: directional derivative graphical representation
23. 2D 2nd derivative test
    
    integration
24. double integrals: describing a region of the plane
      [graphic representation of a double integral][entering multiple integrals in Maple]
      [partial integration graphical representation]
25. example of iterating triple integral 6 different ways
26. exercise in setting up triple integrals in Cartesian coordinates
27. polar coordinate regions of the plane and integration
    [on-line only: integrating over circles not centered on the origin]
28. distributions of stuff: density, moments, center of gravity, centroid, probability
29. inverse trig centroid example
30. cylindrical  and spherical coordinates
    [on-line only: comparison with polar coordinates]
31. cylindrical and spherical regions of space and their bounding surfaces: examples
32. cylindrical and spherical triple integral: examples
     [on-line only: triple cartesian integrals converted to spherical/cylindrical coords]
33. radial integration diagrams for simple circles and lines (cylinders, spheres, planes)
34. integration over 2D and 3D regions of the plane and space [summary]
35. on-line only: progress report: where we've been and where we're going (to end)
    
    
36. 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
37. line integrals of scalars and vectors
38.  vector line integrals
39. "antidifferentiation" in multivariable calculus (potential function for conservative vector field)
40. divergence and curl
41. geometrical interpretation of Green's Theorem: Gauss and Stokes
42. interpretation of divergence and curl (2d)
43. optional: surface integrals for fun [parametrized surfaces]
44. 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.
    
    
45. fun: equianglespiralshell.mw] [Duke website]

23-apr-2016 [course homepage]