دانلود کتاب ملزومات پایتون – حل مسئله نمادین و عددی در مهندسی

Python is a computer language that has grown in a few years to be the most popular language by a wide margin. That popularity has been due to its modular, object-oriented nature and by its rich set of resources for many disciplines, including new fields such as neural networks and artificial intelligence. The free, open-source nature of the language has also contributed to its success. There are many Python books available, covering the language from very basic to advanced levels or dealing with specific applications. These books typically are about how to use Python to develop computer programs. Students and professionals in engineering and the sciences do have an interest in developing such programming skills, but they also have a strong interest in using computers directly as a tool to solve problems in much the same way that hand-held calculators are used. This book will teach you how to set up and use Python in a calculator-like mode for interactively solving problems numerically and symbolically and for displaying results. The primary target audience is engineering students, but the approach is also highly relevant for students in other technical disciplines and for professionals in engineering and other scientific fields. Using Python interactively is a challenge because it is highly modular with similar or redundant capabilities contained in different modules and because there are many integrated development environments (IDEs) available in which to do problem-solving. This book will use the Spyder IDE because it has three key features: bullet The IPython Console. The console is a computer window for running Python functions, commands, and scripts and for plotting results. This console performs the role of a “calculator” keyboard for entry and display. bullet Variable Explorer Window. This window provides a tool for inspecting variables and other objects directly in the IDE. In that role it acts as visual representation of our “calculator” storage. The same window can also perform other functions such as getting help, debugging programs, displaying plots, and showing files. bullet Scientific Libraries Integration. Spyder provides built-in support for four impor-tant scientific tools: NumPy, which is a package (a collection of modules) for doing numerical calculations, SymPy, a package for doing symbolic calculations, and SciPy, which is a package for solving differential equations, eigenvalue prob-lems, statistics, and much more. The fourth package, MatplotLib, is a library of plotting and other visualization tools that are very similar to the widely used plotting capabilities of MATLAB®. The book will also present a strategy for dealing with the complex, modular computing environment that Python represents. The strategy consists of (1) importing the functions contained in NumPy, SymPy, SciPy, and MatplotLib in a manner that makes the use of those functions as direct as possible (like how functions are used in a calculator) and (2) renaming functions, when necessary, to avoid conflicts between the packages. We will also add a few functions that are particularly useful in engi-neering and scientific applications. All these changes are implemented in a Python calculator script that is run at the beginning of a computer session. As you will see in the many worked examples, the Python environment set up by the calculator script will provide a simple but highly interactive foundation for solving engineering and scientific problems. In many respects this book is a companion of the book Lester W. Schmerr Jr, MATLAB Essentials, Symbolic and Numeric Problem-Solving in Engineering, Springer, 2025, which describes the use of MATLAB in the same calculator-like fashion. Chapter 1 is an introduction to the Python language and the many variable types and operations that one normally encounters in engineering and the sciences. The chapter also introduces you to the computing environment of the Python calculator and describes some essential plotting capabilities with MatplotLib. A set of exercises is available at the end of this chapter (and all other chapters) to allow you to test your understanding of the topics presented and become familiar with Python. Chapter 2 is a discussion of vectors, both from a Python standpoint and from a physical standpoint. The vector dot product and vector cross product are described in physical and geometrical terms and engineering examples of vector problems are given to reinforce those descriptions. Chapter 3 is a discussion of arrays and matrices and their use in applications. Arrays and matrices, as defined in Python, have behaviors that are sometimes different from what engineers and scientists normally expect so the discussions in this chapter will allow you to recognize and understand those differences. Eigenvalue problems, which are commonly found in engineering, are covered in a matrix-vector form. Chapter 4 is a discussion of the solution of simultaneous linear algebraic equations. Both numerical and symbolic solutions are covered. Simple examples, where results can be interpreted graphically, are used to help understand the nature of the solutions. The case where the number of equations equals the number of unknowns as well as the cases of overdetermined and underdetermined systems are examined from both mathematical and physical standpoints. A unique part of chapter four is the presentation of a new way to solve the underdetermined systems present in statically indeterminate engineering structures with Python. Chapter 5 covers the solutions of non-linear equations. Root-solving and the solution of simultaneous non-linear equations are discussed. Numerical and symbolic solutions are obtained. Examples are used to illustrate how non-linearities occur in common engineering problems. Chapter 6 describes the numerical solution of ordinary differential equations with a highly popular Runge-Kutta type of solver that can be applied to many engineering problems. This solver is used to discuss the main issues encountered in obtaining solutions. The ability to control numerical errors in the solution is examined, an important topic that is typically not covered in other texts. Symbolic solutions of ordinary differential equations are also obtained. Examples taken from engineering dynamics are used in many of the examples and exercises. In particular, the motion of a spring-pendulum is used to show how numerical solutions can reveal important and unexpected motions and how those motions can be displayed through animations. Chapter 7 extends the brief discussion of plotting given in chapter one. More details are given on how one can control and modify a plot and how to obtain multiple plots, specialized plots, and three-dimensional plots. More advanced symbolic plot-ting is also covered. An approach where plots are used to produce animations is described. Chapter 8 examines the method of finite differences to solve two partial differential equations—the 1-D wave equation and the 1-D heat equation. For the wave equa-tion the effects of boundary conditions on the reflected waves present are discussed including a perfectly absorbing boundary condition that makes the boundary trans-parent to the incident waves. It is also demonstrated that there exists a “magic time step” in the finite difference method where the numerical finite difference solution is essentially an exact solution. Animations are used to describe the wave motion. For the heat equation the 1-D temperature variations in a wall are described under a set of boundary conditions at the two sides of the wall. Animations are again used to illustrate the temperature changes. Since the boundary conditions chosen are inde-pendent of time, the temperature profile in the wall is shown to eventually reach a “steady-state” condition where the temperature profile in the wall never changes. Finally, an appendix provides more detailed information on the functions included in the interactive Python environment and on the use of animations. This book will provide many of the tools needed to solve problems with Python in a direct and interactive manner. It is written as a valuable resource for engineering students, practicing engineers, and researchers but it can also be used productively by those in other scientific fields. An Exercise Solutions Manual, with detailed solu-tions for all the exercises, and Python functions and scripts described in the text are available from the publisher https://go.sn.pub/ib17co. They can also be obtained from the author by sending an e-mail to lschmerr@iastate.edu with the subject title “Python Materials.”