Differential equations are a foundational component of modern quantitative math, science, and engineer. From their primitive origins in the studies of Johannes Kepler and Galileo Galilei, the use of differential equations spread and diversified to become one of the most ubiquitous concepts in science and engineering. Today, differential equations are used every day in almost every field concerned with dynamic phenomena, including robotics, astromechanics, movie and computer-game special-effects design, neurobiology, biopharmaceuticals, global financial, rocketry, public health management, and more.
Topics will include Green functions, boundary-value problems, symmetry theory, special functions, stability and bifuration theory, qualitative analysis, numerical approximation, computer algebra, complexity theory, asymptotic approximation, boundary layers, along with connections to adjacent subjects like difference equations, PDEs, stochastic ODEs, and Filipov systems, with applications to physics, chemistry, biology, optimization, and economics.
Prerequisites: Calculus, basic differential equations, and matrix algebra.
For more information, feel free to contact Prof. Reluga at tcr2@psu.edu