Computational applied mathematics consists roughly of using mathematics for allowing and improving computer computation in applied mathematics. Computational mathematics may also refer to the use of computers for mathematics itself. This includes the use of computers for mathematical computations (computer algebra), the study of what can (and cannot) be computerized in mathematics (effective methods), which computations may be done with present technology (complexity theory), and which proofs can be done on computers.Development and analysis of algorithms for use in all areas of applied mathematics, science and engineering. These areas include medical imaging, atmospheric modeling, fluid dynamics, and social and biological systems modeling.Numerical solutions of differential equations, inverse problems, optimization, scientific computing, approximation theory, and uncertainty quantification. Applications include astrophysics, atmospheric science, solar cell research, environmental fluid dynamics, ground water flow (porous media), hydrodynamics of soft matter (lipids, proteins) at interfaces, and flows in microgravity, imaging and signal processing.
Computational mathematics involves mathematical research in mathematics as well as in areas of science where computing plays a central and essential role, and emphasizes algorithms, numerical methods, and symbolic computations.
Computational applied mathematics consists roughly of using mathematics for allowing and improving computer computation in applied mathematics. Computational mathematics may also refer to the use of computers for mathematics itself. This includes the use of computers for mathematical computations (computer algebra), the study of what can (and cannot) be computerized in mathematics (effective methods), which computations may be done with present technology (complexity theory), and which proofs can be done on computers (proof assistants)