Steve Brunton Courses

Complex Analysis - Examples of Complex Integrals

Explore practical applications of complex integration theorems through challenging examples, enhancing your understanding of advanced mathematical concepts.

• YouTube
• 22 minutes
• Self-Paced
• Free Video

Complex Analysis - Complex Residues

Explore the residue theorem and learn to compute complex contour integrals around singular points, culminating in the integral of f(z)=1/z.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Complex Analysis - Integrals in the Complex Plane

Explore contour integration in complex analysis, covering theorems, continuous deformation, and integration around singularities for a deeper understanding of complex functions.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Complex Analysis - Analytic Functions Solve Laplace's Equation

Explore how analytic complex functions' real and imaginary parts solve Laplace's equation, introducing harmonic functions in this in-depth mathematical analysis.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Complex Analysis - Analytic Functions and Cauchy-Riemann Conditions

Explore analytic complex functions and learn to test for analyticity using Cauchy-Riemann conditions in this comprehensive mathematical exploration.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Complex Analysis - Roots of Unity and Rational Powers of Z

Explore complex logarithms and exponentials to compute fractional powers of complex numbers, including nth roots of unity and special cases like the square root of i.

• YouTube
• 35 minutes
• Self-Paced
• Free Video

Complex Analysis - Functions of a Complex Variable, f(z)

Explore complex functions including monomials, exponentials, and trigonometric functions. Learn about Taylor series and important identities in complex analysis.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

Numerical Integration of Chaotic Dynamics - Uncertainty Propagation & Vectorized Integration

Explore chaos and uncertainty propagation in dynamical systems through numerical integration. Learn efficient vectorization techniques in Python and MATLAB for faster computations.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Coding a Fourth-Order Runge-Kutta Integrator in Python and Matlab

Learn to implement a 4th-order Runge-Kutta integrator in Python and Matlab, and apply it to simulate the chaotic Lorenz 1963 system. Gain practical coding skills for numerical integration.

• YouTube
• 37 minutes
• Self-Paced
• Free Video

Runge-Kutta Integrator Overview - All Purpose Numerical Integration of Differential Equations

Comprehensive introduction to Runge-Kutta schemes for numerical integration of differential equations, covering RK2 and RK4 methods with intuitive explanations and visual representations.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

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.

• YouTube
• 31 minutes
• Self-Paced
• Free Video

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.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

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.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

Differential Equations with Forcing: Method of Variation of Parameters

Learn to solve forced linear differential equations using the powerful method of variation of parameters, replacing unknown coefficients with time-dependent functions based on external forcing.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Differential Equations with Forcing: Method of Undetermined Coefficients

Learn to solve linear differential equations with external forcing using the method of undetermined coefficients. Understand homogeneous solutions, particular solutions, and how to combine them for a complete solution.

• YouTube
• 20 minutes
• Self-Paced
• Free Video