Daniel Ingebretson
University of Illinois at Chicago
July 8, 2024
,Areas as double integrals
Z b
Notice that dx =
a
, Areas as double integrals
Z b
Notice that dx =
a
If R is a region in the xy plane, then
ZZ
area of R = dA.
R
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 coordinate systems (polar, cylindrical, and spherical). Each section of the document is dedicated to a specific topic, providing both theoretical explanations and practical examples. The notes are well-structured to facilitate easy learning and revision, making them an excellent resource for students preparing for exams or needing a thorough review of the material.
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