Название: One Hundred Physics Visualizations Using MATLAB, 2nd Edition
Автор: Dan Green
Издательство: World Scientific Publishing
Год: 2025
Страниц: 310
Язык: английский
Формат: pdf (true)
Размер: 50.3 MB

The MATLAB tools have evolved from scripts, to Apps and at present to Live code. The Live package is preferred because it combines text and equations with MATLAB code all in a single site. The results of that code, formerly shown separately, also appear in line and in this way the user can vary the parameters of the specific problem and explore immediately how the solutions vary in response. For this reason, the Live scheme is used exclusively in this edition. These awards have altered the choices made in the hundred problems that are addressed in this revised volume. The problems are a bit more complex than those of the first addition, but the content is more topical and the MATLAB tools are up to the work asked of the Live scripts.

Indeed, the aim of this book is to use the ensemble of symbolic and numeric tools available in the MATLAB suite of programs to illustrate representative numerical solutions to about one hundred problems spanning several physics topics. The student typically works through the demonstration and alters the inputs using a Live script. This tool combines text, equations and solutions as figures and numerical or symbolic output all in a single Live script. The parametric variation is enabled using the Live tools of “edit fields”, “dropdown menus” and numerical “sliders”.

MATLAB is a good vehicle for the computational tasks. It has a compiler, editor and debugger which are very useful and user friendly. The HELP utility is very extensive as is the complete documentation set. The MATLAB language is similar to a modern C++ or Python language. Indeed code conversion between MATLAB and Python is available which expands the pool of possible users of this text. MATLAB is a vector/matrix language which makes coding simple. Data is easily imported and exported in a variety of formats.

MATLAB contains many special functions. Matrices and linear algebra are covered well. Curve fitting, polynomials and fast Fourier transforms are supplied. Numerical integration packages are available. Differential equations, symbolic, ordinary and partial, as well as numerical solutions are available for both initial value and boundary value versions. MATLAB also has symbolic mathematics. Within that package, calculus, linear algebra, algebraic equations and differential equations are covered. It is easy to combine a symbolic treatment of a problem with a numerical display of the solution when that is desirable. In this way converting from symbols to numbers is easily achieved.

Finally, and very importantly, MATLAB has an extensive suite of display packages. One can make bar, pie, histogram and simple data plots. There are several contour and surface plots which are possible. The time evolution of solutions can be made into “movies” that illustrate the speed of a process. These extensive visualization tools are crucial in that the student can plot, vary parameters and then re-plot. There are two and three dimensional plots of all types available.

The reader is not limited to MATLAB. There are many home institutions with a site-wide MATLAB license which gives students access to the scripts. One is not limited to the language either. For example, the free software package, Python, can be used since translation Apps of MATLAB scripts are also freely available.

Many tools are included with MATLAB. That fact drives the decision to use MATLAB tools to avoid unnecessary algebraic tedium in this text. Most problems are solved explicitly using the symbolic math tools. In general numerical results use the extensive MATLAB library of special functions and of numeric solvers of ordinary and differential equations.