Laplace Transform and ODEs with Forcing and Transfer Functions
Explore Laplace transforms, ODEs, and transfer functions in engineering mathematics, focusing on spring-mass-damper systems and frequency response analysis.
Vectorized Integration and the Lorenz Equation
Explore vectorized integration and the Lorenz equation, focusing on chaos, turbulence, and uncertainty in engineering mathematics, with practical MATLAB implementations.
Sparse Identification of Nonlinear Dynamics - SINDy
Explore a novel algorithm combining machine learning and sparse regression to identify nonlinear differential equations from measurement data, with applications in dynamical systems.
The Mathematical Essence of Aging - Theoretically Speaking
Explore mathematical models of aging using large-scale medical data, revealing seasonal hormone patterns and insights into age-related diseases, with implications for optimal treatment strategies.
Prelinear Algebra - Essential Concepts for Linear Algebra
Comprehensive introduction to vectors, trigonometry, and geometry as foundational concepts for Linear Algebra, with applications in various fields like physics, economics, and machine learning.
Commensurators of Thin Subgroups
Explores commensurators of thin subgroups in discrete group theory, discussing key theorems, propositions, and strategies for constructing examples and analyzing group actions.
The Power of Sampling by Peter W. Glynn
Explore sampling methods in statistics, computation, and engineering. Learn about their history, applications, and advantages in overcoming dimensional challenges and creating scalable algorithms.
Mathematical and Statistical Modelling in the Fight to Control Tuberculosis by Emma McBryde
Exploring mathematical models to combat tuberculosis, from basic concepts to advanced simulations. Insights on disease dynamics, latency, mortality, and regional applications in the Asia Pacific.
Uncertainty Quantification of Quantum Chemical Methods - IPAM at UCLA
Explore uncertainty quantification in quantum chemistry, covering error estimation, benchmarking, and machine learning approaches for improved accuracy in computational methods.
Deployment of Autonomous Fleet Mobility Services at Scale
Explores deployment scenarios and network impacts of autonomous fleet mobility services, discussing optimization challenges, integration with existing transit, and potential societal benefits.
On the 5-Vertex Model
Exploration of the 5-vertex model, a generalization of lozenge tiling, discussing free energy, surface tension, and probabilities. Insights into asymptotic algebraic combinatorics and lattice path models.
Solving High Dimensional HJ Equations Using Generalized Hopf-Lax Formulas vs Using Machine Learning
Explore advanced techniques for solving high-dimensional Hamilton-Jacobi equations, comparing generalized Hopf-Lax formulas with machine learning approaches in control and differential games.
Asymmetry in Dynamics
Explore symmetries in dynamical systems and progress on Smale's conjecture about generic smooth systems having only trivial symmetries. Delve into complex analytic, Hamiltonian, and smooth dynamics.
Branching Random Walks - Two Conjectures and a Theorem by Parthanil Roy
Explore branching random walks, their applications, and long-term behavior. Delve into conjectures and theorems with mathematician Parthanil Roy in this engaging lecture on probability theory.
Introduction to Dynamical Systems - Lecture 2
Explore non-smooth dynamical systems, bifurcations, and complex networks. Learn about border collision, switched systems, and applications in engineering and natural phenomena.
Introduction to Dynamical Systems - Lecture 1
Explore dynamical systems, from linear ODEs to nonlinear chaos. Learn about equilibrium points, eigenvalues, attractors, and bifurcations. Gain insights into Lorenz systems, Poincaré maps, and iterative methods.
Optimization and Modeling in AP Calculus
Learn techniques for solving optimization and modeling problems in calculus, including practical applications and step-by-step solutions for various real-world scenarios.
Related Rate Problems in AP Calculus
Learn strategies for solving related rate problems, including soap bubbles, cylindrical tanks, right triangles, conical tanks, and street light scenarios using similar triangles.
Measuring Speed - Average and Instantaneous Velocity - Part 1
Explore average and instantaneous velocity concepts through practical examples and data analysis techniques in this engaging calculus lesson.
Approximate Matrix Eigenvalues, Subspace Iteration With Repeated Random Sparsification
Explore efficient matrix eigenvalue approximation using subspace iteration and random sparsification, with applications in quantum chemistry and high-dimensional problems.
Random Algebraic Dynamics in Complex Dimension 2
Explore dynamics of automorphism groups on projective surfaces, covering measure classification, orbit closures, and finite orbits. Techniques from geometry and dynamical systems are discussed.