This document is a collection of detailed lecture notes from a university-level course on Multivariable Calculus and Physics. It covers essential topics including lines, planes, and surfaces, projectile motion, limits, partial derivatives, optimization, and integration techniques in various coordin...
,The Riemann integralR for y = f (x)
b
Recall the definition of a f (x) dx:
,Double Riemann sums
We want to calculate the volume inside a rectangular region
R = {(x, y) : a ≤ x ≤ b, c ≤ y ≤ d} underneath the surface
z = f (x, y).
, Double Riemann sums
We want to calculate the volume inside a rectangular region
R = {(x, y) : a ≤ x ≤ b, c ≤ y ≤ d} underneath the surface
z = f (x, y).
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