Numerical Simulation

Mathematical equations, whether simple or complex, govern all real-world dynamical systems, from the periodic motion of a pendulum to the turbulent flow over the wing of an airplane or the population dynamics of species in the wild. While some of these equations can be solved easily by hand, for other equations, the calculations can quickly get complicated and tedious. The goal of this course is for students to gain an understanding of how to solve mathematical equations with a high degree of precision using modern computational methods. This course will cover topics including function evaluation, interpolation, extrapolation, and regression; solution of linear and nonlinear equations; numerical optimization, differentiation, and integration; and solution of differential equations and eigenvalue problems. Students learn several critical tools from calculus and linear algebra, including series expansion, linearization, numerical analysis, and stability analysis, which have far-reaching impacts across science and engineering fields. After building mathematical proficiency, students build programming proficiency through practice simulating real-world systems using their toolkit of numerical methods. On the whole, students will leave the course well-equipped to tackle computational problems in a wide variety of disciplines ranging from artificial intelligence to aerospace engineering.