Concept of a Functional and Function Spaces | Calculus of Variations скачать в хорошем качестве

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) Instagram: https://www.instagram.com/math_infini... TikTok:   / math.infinitum   Telegram: https://t.me/MathInfinitum    • Theorem: Every Convergent Sequence is Boun...      • Solving Differential Equation xy\,dx + (x+...      • Does it Converge or Diverge? Integral of 1...      • Integral of 1/x^2: Power Rule with Negativ...      • Complex Analysis: Finding the Laurent Seri...      • Metric Spaces: Definition, Axioms, and Exa...      • Residue Calculation for Higher-Order and S...      • Evaluating Definite Complex Integral from ...      • 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) ...   #CalculusOfVariations #math #Manim #functionalanalysis #mathematics #engineeringmath #advanced #calculus #Integral #Equations #variations #Norm #definitions #Sine #examples #Spaces #Physics #functional #function