still thursday

09 January 2025, thurs

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.no dreams last night,

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.math:

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.path/ line integral focus

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.start in x,y plane, potential paths: lines, simple polynomials (to include roots)

..and simple logs and exponents (functions)

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.now, have a simple surface (curve) over the x,y plane, line the plane z=1

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.now, integrate along the line and under the curve to find the area of the

..'wall' under the surface (curve) and along the line,

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.now, these 'wall' areas won't be the same...

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.how to calculate ... difficult, ,,, integral in terms of 't', line to be

..parametric_i_zied,

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.so now there's ... blah

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. example, z=1, y=x, ... integrate along the line y=x from (1,0) to

..(0,1) for say a time of 1 second/ unit/ whatever ... under the plane z=1

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.geometric method, ... distance along y=x is √2, , distance under z=1 is one, so area

.. of a square is LxW, so √2 x 1 = √2

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.integration method ... need to review 'parametric_i_zing' a curve in the plane, ...

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.more to come ...

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.daily events: groceries, skateboard, walk, light rail , library, telephone

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.end