Steve Brunton Courses

ODEs with External Forcing - Inhomogeneous ODEs

Explore inhomogeneous ODEs and external forcing in engineering mathematics, covering key concepts and applications for solving complex differential equations.

• YouTube
• 50 minutes
• On-Demand
• Free Video

2x2 Systems of ODEs - With Eigenvalues and Eigenvectors, Phase Portraits

Explore 2x2 systems of ODEs, eigenvalues, eigenvectors, and phase portraits in engineering mathematics. Learn to analyze and visualize complex dynamical systems.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Linearization of Nonlinear ODEs, 2x2 Systems, Phase Portraits

Explore linearization techniques for nonlinear ODEs, analyze 2x2 systems, and visualize phase portraits in this advanced engineering mathematics lecture.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Eigenvalues, Eigenvectors, and Dynamical Systems

Explore eigenvalues, eigenvectors, and dynamical systems in engineering mathematics, focusing on their applications and significance in solving complex problems.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Higher-Order ODEs, Characteristic Equation, Matrix Systems of First Order ODEs

Explore higher-order linear ODEs, characteristic equations, and matrix systems of first-order equations in engineering mathematics, with accompanying notes and MATLAB code.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Taylor Series and Solutions to First and Second Order Linear ODEs

Explore Taylor series and solutions to linear ODEs, enhancing your understanding of engineering mathematics with practical applications and MATLAB code examples.

• YouTube
• 53 minutes
• On-Demand
• Free Video

SVD Part 2

Explore advanced concepts of Singular Value Decomposition (SVD) in data analysis and dimensionality reduction, building on fundamental principles to enhance understanding of matrix factorization techniques.

• YouTube
• 49 minutes
• On-Demand
• Free Video

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video