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. Handouts marked "online only" are not printed and distributed in normal nonpandemic times, implying more importance to the rest.

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

Topic Notes

• double integrals
• triple integrals
• line integrals (and optional surface integrals)

11-may-2020 [course homepage]