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Different reparameterizations
All-in-one review/exer .pdf
Coordinates and grids
Cylindrical/spherical coord's
Rect/polar grid in plane
Rect/cylindr/spher.grid in 3D
General procedure
Finding limits of integration
Slices versus projections
Coord change and Jacobian
Exercises
Illustrated samples
Skew pyramid 6 ways
Wedge cut out of tree
Cone 36 ways
Vector fields
Gradient fields & irrotational
Flux across curve
Flux across surface
Linear vector fields
Green's theorem in plane
Greens thm: applications
Gauss' divergence theorem
Gauss' divergence thm: Applications
Stokes' thm for surfaces in 3d
Formulas and notation
Directory listing
MAPLE worksheets
JAVA vector field analyzer
static slideshow
only: JAVA program
Definitions
Relationships
Calculate potential 1
Calculate potential 2
Calculate potential 3
Chainrule / fund thm
General picture
Zooming
R-sum and calc I integral
practical calculation
Example: 2D-electric
dA for surface
dA for graph z=f(x,y)
dA for sphere
Defn of linearity
Defn of linear vec field
Formulas for lin vec field
Conject: Lin vf & polygon
Slope and scalar curl
Lin vf: translation invariance
Linear vf and line segment
Linear vf and rectangle
Linear vf and rectangle II
Linear vf and triangle
Linear vf and polygon
Polygon: "telescoping sum"
Region with holes
Linear vector fields
Subtracting the drift
Defn differentiability
Defn scalar curl
Calc I: Fundamental theorem
Sketch pf nonlinear vf
Sketch pf work, no words
Sketch pf flux, no words
Traditional proof (induction)
Unification: Differential forms
Duality in 2d: elec and magn
What to use Greens thm for?
Summary: Line integrals
Greens: typical use
Greens and Laplacian I
Greens and Laplacian II
Greens and Laplacian III
Greens and Laplacian IV
Const field, closed surface
Linear field, closed surface
Linear field: Observations
Linear field: Looking ahead
Linear field: Top and bottom
Def differentiability, div
Divergence thm w/ words
Divergence thm w/ applic
Sketch of proof
Sketch of proof (2)
Taylor expansion
Typical -- most simple
Typical -- not closed
Which direction?
Electric field, cylinder: all
fluxcal2.mws
Electric field, cylinder: I
Electric field, cylinder: II
Electric field, cylinder: III
Electric field, cylinder: IV
Electric field, cylinder: V
Electric field, cylinder: VI
Stokes I
Stokes II
Stokes III
Linear II
Linear III
Linear IV
Linear V
Linear to nonlinear I
Linear to nonlinear II
Stokes IV
Stokes V
Stokes VI
Stokes' theorem
Typical use
Evaluating line integrals
Notation for surface integrals
Evaluating surface integrals
There is only one: Stokes'
= fundamental theorem
Typical uses compared