Lectures related to Piecewise linear function

Covers the definition and integration of piecewise continuous functions on intervals.

Covers the concept of piecewise linear interpolation and the importance of dividing intervals correctly.

Explores Fourier series, Dirichlet theorem, and convergence properties in periodic functions.

Covers the integration of limit expansions and continuous functions by pieces.

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

Covers integration techniques for series and functions, including power series and piecewise functions.

Explains spline interpolation and error analysis in approximating data points using piecewise linear and spline methods.

Covers smooth piecewise arcs integration and the importance of closed paths.

Explores constructing a piecewise continuous function using degree 2 interpolation by intervals.

Explores approximation methods and weak variational forms in numerical methods.

Explores the application of Fourier series and the challenges of using multiple methods to solve problems.

Explores linear and non-linear functions in optimization, emphasizing their distinct characteristics and implications in solving problems.

Covers the composition of piecewise functions and introduces the signum and Heaviside functions.

Explores the finite element method's global approach, including shape functions and systematization.

Covers the discussion of the function f(x) = |2x-1| -x²+1 on a given domain and its continuity, zeros, and derivatives.

Introduces Laplace transforms, their properties, and applications in solving differential equations.

Explores the theory and applications of Fourier series, including convergence properties and piecewise-defined functions.

Explores convex functions, affine transformations, pointwise maximum, minimization, Schur's Lemma, and relative entropy in mathematical optimization.

Covers polynomial interpolation, error analysis, stability, and piecewise linear interpolation using equally distributed nodes.

Discusses distributions, the Laplace transform, and their applications in mathematical analysis.