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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.

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Session Three
Accepting Applications
at the time of application
Scheduled Class Time*

08:00 AM - 11:00 AM (PDT)

*The course will meet for two hours daily (Monday–Friday) for a live class during this window of time. The exact time will be set closer to the program start. In addition to the live meeting times, students will engage in out-of-class learning assignments such as assigned readings, group work, pre-recorded online lectures, and more.


Beginner-level proficiency in a programming language. Pre-calculus- or calculus-level mathematics background. (Note: all necessary mathematics will be covered in the course, so dedicated students without this background are also welcome.)