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Calculus 3

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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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Institution
University Of Illinois - Chicago
Course
MATH 210 (MATH210)










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Institution
University Of Illinois - Chicago
Course
MATH 210 (MATH210)
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Uploaded on
August 18, 2024
Number of pages
19
Written in
2024/2025
Type
Class notes
Professor(s)
Daniel ingebretson
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Math 210 Lecture 9: Optimization and
Lagrange multipliers

Daniel Ingebretson

University of Illinois at Chicago


July 1, 2024

,Unbounded domains
What’s the absolute maximum of f (x) = 1 − x 2 on
−∞ < x < ∞?

, Example: optimization on an unbounded domain
Find the point on the plane x + 2y + z = 2 closest to the
point (2, 0, 4).
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