Applied Mathematics Examples

Definition: Applied mathematics problems are mathematical problems which importance is self-evident.

Applied math is a group of methods aimed for solution of problems in sciences, engineering, economics, or medicine. These methods are originated by Newton, Euler, Lagrange, Gauss and other giants. Modern areas of applied math include Mathematical physics, Mathematical biology, Control theory, Aero-space engineering, optimal planning, math finance. There is a fuzzy boundary between applied math and engineering and at the other side, between applied and pure mathematics. Applied math discovers new problems which could become subjects of pure math (like geodesics), or develop to become a new engineering discipline (like elasticity theory). Study of applied math requires expertise in many areas of mathematics and science, physical intuition and common sense, and collaboration skills. Applied math allows for many approaches to the problem, a choice of objectives, and variety of methods.
Definition: Success in applied math is a new elegant model that catches the phenomenon and novel clever methods to solve it.

Approaches to applied math

In the majority of applied problems, one need to build mathematical model of a phenomenon, solve this model, and develop the recommendations for improvement of the performance.

Math modeling

Typically we deal with large systems (thousands of variables, equations and inequalities). A clever model separates the main phenomenon from the noise and allows for analytic treatment of the problem, followed by extensive numerical development. There may be several models suggested for the same phenomena with various level of details: No one need a one-to-one geographical map. The art of simplification is to make the problem solvable but not trivial. All models have ranges of applicability (Take for example the ideal gas model, compare with the black hole model).