Study of Linear and Nonlinear Models with Mathematica

The book is devoted to the problems of modeling physical systems and fields using the tools and capabilities of the 'Mathematica' software package. In the process of teaching classical courses in mechanics and mathematical physics, one often has to overcome significant difficulties associated with the cumbersomeness of the mathematical apparatus, which more than once distracts from the essence of the problems under consideration. The use of the 'Mathematica' package, which has a rich set of analytical and graphic tools, makes the presentation of classic issues related to modeling and interpretation of physical processes much more transparent. This package enables the visualization of both analytical solutions of nonlinear differential equations and solutions obtained in the form of infinite series or special functions.The textbook consists of two parts that can be studied independently of each other. The first part deals with the issues of nonlinear mechanics and the theory of oscillations. The second part covers linear problems of classical mathematical physics and nonlinear evolution models describing, inter alia, transport phenomena and propagation of waves. The book contains the codes of programs written in the 'Mathematica' package environment. Supplementary materials of programs illustrating and often complementing the presented material are available on the publisher's website.

這本書專注於使用「Mathematica」軟體套件的工具和功能來建模物理系統和場。在教授經典力學和數學物理課程的過程中，我們常常需要克服與數學工具繁瑣性相關的重大困難，這些困難多次分散了對問題本質的關注。使用具有豐富分析和圖形工具的「Mathematica」套件，可以使與物理過程建模和解釋相關的經典問題的呈現更加透明。該套件能夠可視化非線性微分方程的解析解，以及以無窮級數或特殊函數形式獲得的解析解。本教材由兩個部分組成，可以獨立學習。第一部分涉及非線性力學和振動理論的問題。第二部分涵蓋了經典數學物理的線性問題和描述傳輸現象和波傳播等非線性演化模型。本書包含在「Mathematica」套件環境中編寫的程式碼。出版商網站上提供了補充材料，這些材料以程式碼形式展示並經常補充所呈現的內容。