This course explores the numerical algorithms at the core of many of the fundamental as well as advanced computational techniques used in Space Engineering. Engineers routinely use Commercial-Off-The-Shelf (COTS) software tools for creating mission orbits, computing trajectories, and analyze subsystems such as GNC, Communication, and Propulsion. The focus of this course is to develop the mathematical principles and numerical methods behind many of those commonly-used, often times as “black box”, COTS tools, as well as introduce state-of-the-art ones from the current research literature. Students will be exposed to topics such as Numerical Optimization, Differential Correction, Finite Difference and Complex-Step Derivative computation, Stochastic Differential Equations and more. Applications ranging from accurate Orbit Propagation, Launch Vehicle Trajectory Optimization, RF Link Design, Propulsion System sizing and others will be studied through in-class discussions and homework assignments. Students are expected to be comfortable in programming with MATLAB, Python or similar simulation platforms, and must have been exposed to the mathematical topics of Linear Algebra, Differential Equations, Calculus, and elementary Probability through prior coursework.