Differential Equations and Dynamical Systems Modeling in Engineering

This course will provide students with an introduction to differential equations in the context of electrical and systems engineering. Students will gain a foundation in the use of differential equations to describe, model and engineer systems and devices. The course will cover fundamental mathematical principles of ordinary differential equations including: (i) existence of solutions, (ii) elementary solution strategies, and (iii) the conceptual foundation for frequency domain solution techniques. An introduction to early concepts in dynamical systems theory, such as state-space analysis, equilibria and stability, will also be provided. Finally, students will obtain an initial introduction to partial differential equations in ESE in the context of wave propagation. Mathematical developments will be closely accompanied by computational implementations and numerical simulations. Further, students will engage several case studies, in which students will use the mathematical theory to perform analysis and design within ESE contexts spanning systems, circuits and applied physics.