Lectures related to Elliptic Problems

Duplication of the Cube

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

Residue Theorem: Applications in Complex Analysis

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

Reformulating Problems: Tools and Intuition

Focuses on open problems and the importance of reformulating problems with better tools and intuition.

Finite Differences and Finite Elements: Variational Formulation

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

Conformal Blocks: Understanding Young Diagrams and Weight States

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

Laplacian: Basics and Examples

Covers the basics of the Laplacian operator applied to scalar fields and its importance in mathematical models.

Advanced Analysis II: Cauchy Problem and Differential Equations

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on solution uniqueness.

Taylor Series and Secant Method: Numerical Analysis Techniques

Discusses the Taylor series and secant method, focusing on their applications in numerical analysis and root-finding techniques.

Mathematical Rigor and Course Organization

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

Introduction: Mathematical background

Covers basics of modeling for micro/nano devices and emphasizes the importance of computational thinking in understanding and improving device design.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Riemann Sphere: Correlations and Conditions

Covers the Riemann sphere, focusing on its conditions and correlation functions in mathematical and physical contexts.

Geometric Meanings: Euclidean Division and Divine Proportion

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

Linear Algebra: Injective Functions

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

Fourier Transform and Differential Equations

Discusses the Fourier transform and its application to solving differential equations, focusing on the wave equation and its transformations.

End-to-End Vector: Lecture 4

Explores the concept of end-to-end vector and its practical implications.

Root Finding Methods: Secant, Newton, and Fixed Point Iteration

Covers numerical methods for finding roots, including secant, Newton, and fixed point iteration techniques.

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.

Energy Systems Optimization

Explores energy systems modeling, optimization, and cost analysis for efficient operations.

Limits of Sequences

Covers the concept of limits of sequences, including definitions, examples, boundedness, and more.