Steve Brunton Courses

Potential Flow, Stream Functions, and Examples

Explore potential flow, stream functions, and Laplace's equation with practical examples in fluid dynamics. Gain insights into fundamental concepts and their applications.

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

Div, Grad, and Curl

Explore fundamental vector calculus concepts: divergence, gradient, and curl. Learn their applications in engineering mathematics through clear explanations and examples.

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

Linear Algebra in 2D and 3D - Inner Product, Norm of a Vector, and Cross Product

Explore fundamental concepts of linear algebra in 2D and 3D spaces, including inner product, vector norms, and cross product, essential for engineering mathematics applications.

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

Gauss's Divergence Theorem

Explore Gauss's Divergence Theorem in engineering mathematics, understanding its applications and significance in vector calculus and fluid dynamics.

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

Directional Derivative, Continuity Equation, and Examples of Vector Fields

Explore directional derivatives, continuity equations, and vector field examples in engineering mathematics, enhancing understanding of fluid dynamics and electromagnetic theory applications.

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

Numerical Solutions to ODEs - Forward and Backward Euler

Explore numerical methods for solving ordinary differential equations, focusing on Forward and Backward Euler techniques in engineering mathematics applications.

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

Numerical Integration and Numerical Solutions to ODEs

Explore numerical methods for integration and solving ordinary differential equations, enhancing your computational skills in engineering mathematics.

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

Numerical Differentiation and Numerical Integration

Explore numerical differentiation and integration techniques in engineering mathematics, covering key concepts and practical applications for solving complex problems.

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

Numerical Differentiation Using Finite Difference

Explore numerical differentiation techniques using finite difference methods, with practical applications in engineering mathematics and accompanying Matlab code examples.

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

Degenerate Systems of Equations and Non-Normal Energy Growth

Explore degenerate equation systems and non-normal energy growth in engineering mathematics, focusing on key concepts and practical applications in dynamic systems analysis.

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

ODEs with External Forcing and the Convolution Integral

Explore inhomogeneous ODEs and convolution integrals, learning to solve differential equations with external forcing for advanced engineering applications.

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

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video