Explore the intricacies of particle trajectories in time-varying vector fields through this 49-minute lecture from the Engineering Mathematics course at the University of Washington. Delve into topics such as PCA examples, vector fields with varying frequencies, mesh grids, and integration techniques. Learn to plot new vector fields, integrate particles, and visualize their movements using multidimensional arrays in MATLAB. Discover practical applications like determining optimal pollution dumping locations and optimizing code performance. Access accompanying MATLAB code for hands-on practice with double gyre vector fields and integration methods. Gain valuable insights into particle stencils and patches, enhancing your understanding of complex mathematical concepts in engineering.