Скачать или смотреть Concept of a Functional and Function Spaces | Calculus of Variations

What is the difference between a function and a functional? In this video, we dive into the fundamental concepts of the Calculus of Variations. We visualize how functionals map entire curves to single numbers and explore how to measure the "size" of a function using Norms in C^p spaces.


Timecide:
0:00 - Intro
0:15 - What is a Functional?
0:47 - Function vs. Functional
1:28 - Example: The Definite Integral
2:00 - Function Spaces (C^p on [a,b])
2:55 - Defining the Norm
3:25 - Example: Calculating the Norm of sin(x)


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   • Linear Differential Equation Solution: (xy...  

   • Method of Characteristics: Solving PDE (x(...  

   • Fourier Series Expansion of f(x) = x | Cal...  

   • Laplace Transform of f(t) = (cos(3t) - 1) ...  

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