Partial Differential Equation - CF & PI
Explore homogeneous and non-homogeneous partial differential equations, focusing on complementary functions and particular integrals. Learn general methods and rules for solving PDEs.
Advanced Calculus - Multivariable Calculus
Comprehensive exploration of advanced calculus concepts, from differential equations to multivariable calculus, including series, vector functions, optimization, and integral theorems.
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.
Chemistry 361B
Comprehensive exploration of quantum mechanics, covering complex numbers, differential equations, atomic models, Schrödinger equation, and molecular structures. Ideal for advanced chemistry students.
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.
Differential Equations
Comprehensive exploration of differential equations, covering first and second-order equations, applications in physics and engineering, and advanced solution methods like Laplace transforms and power series.
Analysis II Video Lectures
Comprehensive video lectures on advanced mathematical analysis, covering topology, continuity, differentiation, manifolds, and more, with applications to various mathematical concepts.
Differential Equations - Vol 1
Explore fundamental concepts and applications of ordinary differential equations, including solving techniques, graphing, and real-world applications in mixing, cooling, and electrical circuits.
Differential Equations - Vol 2
Comprehensive exploration of second-order differential equations, covering linear ODEs, Wronskian test, homogeneous and non-homogeneous equations, and various solution methods.
Laplace Transform
Master Laplace Transform: definition, essential transforms, inverse transforms, and applications in solving differential equations. Gain practical skills through extensive problem-solving exercises.
Mathematics
Comprehensive screencasts on advanced mathematical concepts, including equations, matrices, and regression analysis, with practical applications using Excel and POLYMATH software.
Solving the Wave Equation with Separation of Variables and Guitar String Physics
Explore wave equation solutions using separation of variables, with applications to guitar string physics. Gain insights into optics, acoustics, and fundamental physics concepts.
Deriving the Wave Equation
Comprehensive derivation of the Wave Equation, exploring its applications in physics and engineering, with examples from guitar strings to illustrate key concepts.
PDE 101 - Separation of Variables or How I Learned to Stop Worrying and Solve Laplace's Equation
Explore the powerful Separation of Variables technique for solving PDEs, focusing on Laplace's equation in 2D for steady-state heat distribution, with applications in physics and engineering.
Sparse Nonlinear Models for Fluid Dynamics with Machine Learning and Optimization
Exploring SINDy algorithm for developing efficient nonlinear models in complex fluid flows, with applications in various fields including bluff body wakes, thermal convection, and magnetohydrodynamics.
Friction and Phase Portraits - Coulomb Friction - Cone of Friction - Falling Broom - Spinning Top
Explore Coulomb friction, phase portraits, and 3D rigid body dynamics. Analyze friction effects on equilibrium, falling objects, and spinning tops using experiments and mathematical models.
Phase Portraits from Potential Energy - Bifurcations - Constraint Forces from Lagrange Multipliers
Explore phase portraits, bifurcations, and constraint forces in dynamical systems. Learn graphical methods, analyze system behavior changes, and understand Lagrangian mechanics with practical applications.
Lagrange’s Equations with Conservative and Non-Conservative Forces - Phase Space Introduction
Explore Lagrange's equations for conservative and non-conservative forces, rigid body systems, and phase space analysis. Learn to solve and classify motions using advanced analytical dynamics techniques.
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.
Stability of Periodic Orbits - Floquet Theory - Stable and Unstable Invariant Manifolds
Explore stability of periodic orbits using Floquet theory. Learn about monodromy matrices, Floquet multipliers, and invariant manifolds in Hamiltonian systems. Understand the foundations of chaos in dynamical systems.
Hamiltonian Normal Forms, Lie Series Method for Transformations - Infinite-Dimensional Hamiltonians
Explore Hamiltonian normal forms, Lie series transformations, and infinite-dimensional systems. Learn to simplify complex dynamics and analyze PDEs like shallow water equations.