Applied mathematics
Applied mathematics uses mathematical ideas and methods to formulate, analyze, and solve problems in science, engineering, industry, and other fields.
Mathematical modeling: The process of representing a real-world system or problem with mathematical structures. It turns practical questions into equations, variables, and assumptions that can be analyzed.
Computational fluid dynamics: The numerical simulation of fluid motion using computational methods. It applies mathematical models and numerical algorithms to flows around vehicles, buildings, and turbines.
Dimensional analysis: The use of physical dimensions to derive relations, check equations, and reduce variables. It can simplify a model before detailed calculation and expose inconsistent assumptions.
Pure mathematics: The study of mathematical structures and ideas primarily for their internal properties and relationships. Its questions need not begin with a practical problem, unlike the usual starting point here.
Differential equation: An equation relating an unknown function to one or more of its derivatives. Differential equations describe changing quantities in physical, biological, and engineered systems.
Operations research: The use of mathematical models and algorithms to improve decisions in complex systems. It directs optimization toward scheduling, routing, logistics, and resource allocation.
Finite element method: A numerical method that approximates solutions by dividing a domain into smaller elements. It converts complex boundary-value problems into solvable systems of equations.
Theoretical physics: The branch of physics that develops mathematical theories to explain and predict physical phenomena. It shares mathematical tools with applied mathematics but is organized around physical theory.
Linear algebra: The study of vectors, vector spaces, linear transformations, and systems of linear equations. Vectors and matrices encode data, transformations, and coupled unknowns in applied problems.
Control theory: The study of how to make dynamic systems behave as desired through feedback and control inputs. Its mathematical models help stabilize and steer machines, processes, and other changing systems.