Models for Dynamical Systems in Dimensions 1 and 2 - Lecture 1
Explore dynamical systems in 1D and 2D, focusing on Milnor-Thurston's theorem and its potential 2D analog for surface diffeomorphisms. Delve into connections with Teichmüller Theory and 3-manifold topology.
Counting Periodic Orbits of One-Dimensional Maps - Lecture 2
Delve into the mathematics of counting periodic orbits in one-dimensional maps. Explore connections to number theory and thermodynamic formalism, focusing on interval and complex rational maps.
Generalized Pseudo-Anosov Maps from Holomorphic Dynamics
Explore the connection between quadratic polynomial dynamics and surface homeomorphisms, focusing on generalized pseudo-Anosov extensions of Hubbard tree dynamics.
Dynamical Complexity in the Rössler System
Uncover the analytical connection between Rössler equations and the logistic family. Explore periodic orbits, topologies, and complex dynamics in this mathematical exploration of chaotic attractors.
Monotonicity of Entropy in Families of Interval Maps - Lecture 1
Explore the transfer operator, holomorphic motions, and entropy monotonicity in interval maps. Gain insights into applications in rational dynamics and quadratic families.
Equilibrium States Through Potential Theory - Lecture 2
Dive into equilibrium states for rational maps and endomorphisms, exploring their construction through potential theory and their statistical properties in thermodynamic formalism.
Models for Dynamical Systems in Dimensions 1 and 2 - Lecture 3
Explore dynamical systems in 1D and 2D, focusing on Milnor-Thurston's theorem and its potential 2D analogue for surface diffeomorphisms. Delve into connections with Teichmüller Theory and 3-manifold topology.
Models for Dynamical Systems in Dimensions 1 and 2 - Lecture 2
Explore models for dynamical systems in 1D and 2D, focusing on Milnor-Thurston's theorem and its potential 2D analogue for surface diffeomorphisms.
Homogeneous Second-Order Linear Differential Equations
Explore second-order linear differential equations, covering auxiliary equations, reduction of orders, and linear dependence/independence of functions in this comprehensive tutorial.
Foundation of Scientific Computing
Explore the fundamentals of scientific computing through a comprehensive series of lectures, covering essential concepts and techniques for computational problem-solving in scientific research.
Optimal Control, Guidance and Estimation
Comprehensive exploration of optimal control theory, guidance systems, and estimation techniques for aerospace applications, covering LQR, dynamic programming, and Kalman filters.
Advanced Control System Design for Aerospace Vehicles
Comprehensive exploration of advanced control systems for aerospace vehicles, covering classical and modern techniques, flight dynamics, optimization, and adaptive designs for enhanced aircraft performance.
A Second Course in Differential Equations
Explore advanced topics in ordinary differential equations, including linear systems, eigenvalues, numerical methods, and Python implementations for solving complex ODEs.
APEX Calculus - Differential Equations
Comprehensive exploration of differential equations, covering basics, separable and linear equations, and real-world applications through modeling. Ideal for calculus students seeking practical understanding.
Scientific Computing I
Explore scientific computing through Python, covering numerical methods, data analysis, and machine learning, with practical applications in physics and mathematics.
Mathematics
Comprehensive screencasts on advanced mathematical concepts, including equations, matrices, and regression analysis, with practical applications using Excel and POLYMATH software.
Applications of Calculus to Mechanics
Explore calculus applications in mechanics, covering circular motion, pendulums, and banked tracks. Learn to analyze forces, velocities, and accelerations in various scenarios.
Sparse Nonlinear Dynamics Models with SINDy - The Library of Candidate Nonlinearities
Explores advanced techniques for SINDy algorithm, including control variables, bifurcation parameters, rational functions, dimensionality reduction, and symmetry constraints in nonlinear dynamics modeling.
Normal Forms for Vector Fields
Introduction to normal forms for vector fields, focusing on simplifying nonlinear terms and determining topological equivalence. Covers theory, examples, and applications in dynamical systems analysis.
Center Manifolds for Hamiltonian Systems and PDEs - Lorenz System Bifurcation, Part 2
Explore center manifolds in Hamiltonian systems and PDEs, including Lorenz system bifurcation, unstable directions, and applications to flame front evolution and celestial mechanics.
Center Manifold Theory - Computing Center Manifolds
Explore center manifold theory for dynamical systems, focusing on computing and approximating center manifolds. Learn to analyze stability and dynamics near equilibrium points using Taylor series expansions and tangency conditions.