Scientific computation
Scientific computation is an interdisciplinary field in which realistic mathematical models combined with scientific computing methods are used to study, usually through computer simulation and modeling, systems of real-world scientific. Scientific computing is an indispensable part of almost all scientific investigation and technological development.

As computing technology has become increasingly powerful and increasingly available, and as the basic sciences and engineering have advanced, computer modeling and simulation have become progressively more recognized as engines of economic growth and scientific advancement.

Computer simulation and modeling are now used in virtually every area of science and engineering such as specific application areas, e.g. mathematical and statistical finance, applications of machine learning, fluid mechanics, finite element methods, biomedical modeling, electrical and electronics engineers, aeronautical engineers, mechanical engineers, astronomers, astrophysicists and so on.

Computational scientists synthesize scientific programming and mathematical skills along with knowledge of application fields to computationally model systems of interest. Areas of mathematics such as calculus, differential equations, statistics, and linear algebra form the basic language in which science and engineering are practiced. Additional required skills include high performance computing, scientific programming, simulation methods, specialized scientific computing packages and tools, and animation and visualization of results.

Maxima is a CAS (Computer Algebra System), similar to systems like Mathematica and Maple, designed for the manipulation of algebraic expressions. But you can use Maxima for manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations (ODE), systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Read more