Explore Runge-Kutta integration methods for solving ordinary differential equations (ODEs) and delve into the fascinating Lorenz equation in this 49-minute lecture from the Engineering Mathematics course at the University of Washington. Begin with an introduction to the Forward Euler scheme, progress through second-order Runge-Kutta methods, and examine various types of Runge-Kutta integrators. Investigate vector fields and implicit schemes before focusing on the Lorenz equation and its renowned attractor. Access supplementary materials, including lecture notes and MATLAB code for simulations, to enhance your understanding of these advanced mathematical concepts and their applications in engineering.