Introduction to Theory and Numerics of Partial Differential Equations - Lecture 3
Explore numerical methods for solving partial differential equations, focusing on techniques essential for gravitational wave astronomy and computational relativity.
Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 1
Explore advanced harmonic analysis concepts: Nikodym sets and maximal functions associated with spheres. Gain insights from expert Jongchon Kim in this comprehensive lecture.
Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 2
Explores advanced concepts in harmonic analysis, focusing on Nikodym sets and maximal functions related to spheres. Builds on previous lecture, deepening understanding of these mathematical structures.
Sharp Fourier Restriction onto the Parabola and the Cubic Monomial - Lecture 1
Explore sharp Fourier restriction estimates for parabola and cubic monomial curves, advancing understanding in harmonic analysis and algebraic geometry applications.
Sharp Fourier Restriction onto the Parabola and the Cubic Monomial - Lecture 2
Explores sharp Fourier restriction estimates for parabola and cubic monomial curves, advancing understanding of harmonic analysis and polynomial methods in mathematical research.
The Variance of a General Class of Multiplicative Functions in Short Intervals
Explore the variance of multiplicative functions in short intervals, applying Fourier analysis and rational point counting to derive asymptotic estimates for k-free numbers and other functions.
Numerical Integration of ODEs with Forward Euler and Backward Euler in Python and Matlab
Explore Forward and Backward Euler integration methods for ODEs using Python and Matlab. Compare stability, error, and implementation on a spring-mass-damper system with analytic solutions.
Deriving Forward Euler and Backward-Implicit Euler Integration Schemes for Differential Equations
Explore Forward and Backward Euler integration methods for ODEs, including derivations, error sources, and stability analysis. Gain insights into numerical integration techniques for solving differential equations.
Numerical Simulation of Ordinary Differential Equations - Integrating ODEs
Explore numerical integration of ODEs to analyze nonlinear systems and generate trajectories. Learn techniques for solving complex dynamics where analytic methods fall short.
Linearizing Around a Fixed Point - Control Bootcamp
Explore linearization of nonlinear systems around fixed points, demonstrated with a simple pendulum example using both manual calculations and MATLAB implementation.
Distance Problems and Their Many Variants - Lecture 2
Explores distance problems in harmonic analysis, focusing on variants and recent developments. Discusses polynomial methods and discrete approaches, offering insights for researchers in the field.
Nikodym Sets and Maximal Functions Associated with Spheres - Lecture 2
Explores advanced concepts in harmonic analysis, focusing on Nikodym sets and maximal functions related to spheres. Builds on recent developments in the field.
Circuits - Linear Algebra for Physics with Python
Explore linear algebra applications in circuit analysis using Python, enhancing problem-solving efficiency for STEM students and professionals.
How Much Math Do You Need to Know to Solve an Initial Value Problem - SIAM PDE Seminar
Explore mathematical techniques for solving nonlinear Schrödinger equations, from harmonic analysis to dynamical systems, focusing on long-time dynamics and energy transfer in initial value problems.
Orthogonality Sampling Methods for Electromagnetic Inverse Scattering Problems
Exploring orthogonality sampling methods for electromagnetic inverse scattering problems, focusing on implementation simplicity, noise robustness, and applications in 2D and 3D experimental data.
Bayesian Reimaging of Sparsity in Inverse Problems - SIAM-IS Virtual Seminar
Bayesian approach to sparse inverse problems in imaging and dictionary learning, featuring efficient computational framework and hierarchical prior models for sparsity promotion and automatic model reduction.
Bayesian Reimaging of Sparsity in Inverse Problems - IMAGINE Seminar Series
Explore Bayesian approaches to sparse inverse problems in imaging and dictionary learning, focusing on efficient computational frameworks and hierarchical prior models.
A Fourier Transform for Abelian Fibrations
Explore Fourier transform theory for abelian fibrations, extending Beauville decomposition and examining perverse filtration applications in algebraic geometry and motivic theory.
Partial Orders, Maxels, and Möbius Functions in Posets
Explores partial orders, maxels, and Möbius functions in advanced mathematics, connecting Boolean algebra to circuit analysis and introducing novel notation for negative numbers.
How the Algebra of Boole Simplifies Circuit Analysis - Part 3
Explore Boolean algebra's role in simplifying circuit analysis, covering logic gates, algebraic expressions, and symmetry considerations for efficient circuit equivalence determination.
The Algebra of Boole and Boolean Algebra - Key Differences - Part 1
Introduction to the Algebra of Boole, focusing on the bifield of two elements and n-tuples. Explores its role in circuit analysis and contrasts it with Boolean algebra, highlighting implications for 20th-century mathematics.