Lectures related to Maximal Solutions in Advanced Analysis II

Covers various examples of calculating the volume of a body of revolution.

Stochastic Simulation: Uncertainty Quantification

Explores uncertainty quantification using Quasi Monte Carlo methods and discrepancy measures for integral approximation and volume estimation.

Jensen's Inequality

Covers Jensen's inequality, stating that the convex function of the average is less than or equal to the average of the function.

Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Lagrange Multiplier and DuBois-Reymond Equation

Explores Lagrange multiplier method and DuBois-Reymond equation in optimization.

Elliptic Problems: Model and Deformation

Covers elliptic problems related to a model and deformation, discussing concepts such as the model problem and deformation energy.

Cauchy Problem: Existence and Uniqueness of Solutions

Covers the Cauchy problem, focusing on the existence and uniqueness of solutions to differential equations.

Deficiency in Cupliere Sulposous

Explores deficiency in cupliere sulposous through mathematical functions and variable relationships.

Equidistribution of CM Points

Explores the joint equidistribution of CM points in a coherent manner.

Taylor's Formula: Convexity, Inflection Points

Explores Taylor's formula, uniqueness of Taylor series, Mean Value Theorem, inflection points, and convexity.

Analysis I: Indeterminate Forms and Gendarmes' Role

Covers indeterminate forms, logarithmic functions, and the 'role of the gendarmes' theorem.

Boundary Problems in 1D: Part 1

Covers the resolution of boundary problems in 1D, focusing on mathematical concepts and equations.

Advanced Analysis: Differential Equations Overview

Covers the fundamentals of differential equations, their properties, and methods for finding solutions through various examples.

Introduction to Tempered Distributions

Introduces tempered distributions, covering acceleration, force, impulse, and short duration shocks.

Injective Functions: Properties and Examples

Covers the properties of injective functions and demonstrates their proofs through examples and visual aids.

Hamiltonian Homeomorphisms on Surfaces

Explores the action of Hamiltonian homeomorphisms on surfaces and discusses related mathematical concepts.

Differential Equations: General Solutions and Methods

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Uniqueness of Solutions: Cauchy-Lipschitz Theorem

Covers the uniqueness of solutions in differential equations, focusing on the Cauchy-Lipschitz theorem and its implications for local and global solutions.

Cauchy-Lipschitz Theorem

Explores the Cauchy-Lipschitz theorem for differential equations and its proof.

Geometric Expansion of Crom-Conrelation

Explores the geometric expansion of the crom-conrelation, focusing on mathematical formulas and correlation analysis.