Lectures related to Stochastic Simulation: Uncertainty Quantification

Explores the Fokker-Planck and KPZ equations in stochastic processes and random growth models.

Stochastic Simulation: Low-Discrepancy Point Sets

Explores low-discrepancy point sets in stochastic simulation and their construction algorithms.

Geometric Meanings: Euclidean Division and Divine Proportion

Explores the historical and mathematical significance of Euclidean Division and the Divine Proportion in geometry and art.

Conformal Blocks: Understanding Young Diagrams and Weight States

Covers conformal blocks, Young diagrams, and their significance in weight states.

Residue Theorem: Applications in Complex Analysis

Discusses the residue theorem and its applications in calculating complex integrals.

Boundary Problems in 1D: Part 1

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

Improper Integrals: Fundamental Concepts and Examples

Covers improper integrals, their definitions, properties, and examples in two and three dimensions.

Introduction to Tempered Distributions

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

Duplication of the Cube

Delves into the historical challenge of duplicating the cube, exploring construction methods, misattributions, and geometric concepts.

Elliptic Problems

Covers the concept of elliptic problems and their applications in various scenarios.

Complex Analysis: Derivatives and Integrals

Provides an overview of complex analysis, focusing on derivatives, integrals, and the Cauchy theorem.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Verification and validation

Covers the verification and validation process in numerical flow simulation, ensuring credibility of simulation outcomes.

Analytical Mechanics: Newton's Three Laws

Introduces the mathematical approach to analytical mechanics, emphasizing Newton's three laws for a complete description of phenomena.

Mechanics: Introduction and Calculus

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Proof of Delta Function Properties

Explores the proof of properties related to the delta function in mathematical analysis.

Geometric Expansion of Crom-Conrelation

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

Mathematical Rigor and Course Organization

Emphasizes mathematical rigor, clear communication, and exercise organization in teaching methods.

Computational Science and Engineering: Master Program Overview

Outlines the Master in Computational Science and Engineering program at EPFL, detailing its structure, projects, and career opportunities for graduates.

Integration Techniques: Fundamental Theorems and Methods

Discusses integration techniques, focusing on integration by parts and substitution methods, with practical examples and theoretical insights.