#maths #calculus #multivariable #multivariablecalculus #perspective #some #someπ #learn #learning #intuition #intuitive
In this video, I introduce the concept of a line integral from multivariable calculus by building it up intuitively from integration in single-variable calculus. Math is all about expanding previous knowledge into new domains, after all! I also try to present the intuition behind line integrals, and finally demonstrate a practical calculation of a line integral for an ordinary function: z = x^2 + y^2, over line segment y = x extending from (1,1) to (3,3).
Enjoy!
Chapters:
0:00 Intro
1:48 Prerequisites
2:09 Video Outline
2:33 Integration in Single-Variable Calculus
5:27 Line Integrals - Intuition
10:33 Line Integrals - How To Calculate
17:42 Line Integrals - Example Calculation
19:24 Side Note
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