The Weierstrass Function: Continuous Everywhere, Differentiable Nowhere скачать в хорошем качестве

The Weierstrass Function: Continuous Everywhere, Differentiable Nowhere

In 1872, Karl Weierstrass presented a mathematical "monster"—a function that is continuous at every point but differentiable nowhere. This counterexample fundamentally changed how mathematicians understand Real Analysis. In this video, we visualize the construction of the Weierstrass function using Manim, strictly define continuity and differentiability, and perform a step-by-step integration of this fractal curve. Timecode: 0:00 Introduction: The Weierstrass Function: Definition 1:07 Continuity of a Function 3:10 Differentiability of a Function 4:28 The Weierstrass Function (Graph) 5:56 Integration of the Weierstrass Function 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) ...   #Weierstrass #function #calculus #real #analysis #Continuous #everywhere #differentiable #nowhere #epsilon #delta #math #animation #manim #infinite #series #fractal #geometry #higher #education