文件名称:
MatheMatical Objects in c++
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上传时间: 2012-12-24
详细说明： MatheMatical Objects in c++: computational tools in a Unified Object-Oriented approach Preface Mathematics can be viewed as the philosophy of abstract objects. Indeed, mathematics studies all sorts of useful objects, from numbers to multilevel hierarchies and more general sets, along with the relations and functions as-sociated with them. The approach used in this book is to focus on the objects, rather than on thefunctions that use them. After all, the objects are the main building bricks ofthe language of mathematics. The C+ + implementation of the objects makesthem far more understandable and easy to comprehend. This book shows the strong connection between the theoretical nature of mathematical objects and their practical C++ implementation. For exam-ple, the theoretical principle of mathematical induction is used extensively to define useful recursive C++ objects. Furthermore, algebraic and geometrical objects are implemented in several different ways. Moreover, highly unstruc-tured computational objects such as oriented and onoriented graphs, two-and three-dimensional meshes, and sparse stiffness and mass matrices are im-plemented in short and well-debugged code segments. The book is intended for undergraduate and graduate students in math, applied math, computer science, and engineering who want to combine the theoretical and practical aspects. Because the book assumes no background in mathematics, computer science, or any other field, it can serve as a text book in courses in discrete mathematics, computational physics, numerical methods for PDEs, introduction to C for mathematicians and engineers, introduction to C++ for mathematicians and engineers, and data structures. Parts I–II introduce elementary mathematical objects, such as numbers and geometrical objects. These parts are aimed at beginners, and can be skipped bymore experienced readers. Part III provides the required theoretical background, including preliminary definitions, algorithms, and simple results. Part IV teaches C from a mathematical point of view, with an emphasis on recursion. Part V teaches C++ from a mathematical point of view, using templates to implement vectors and linked lists. Part VI implements more complex objects such as trees, graphs, and triangulations. Finally, Part VII implements yet more advanced objects, such as 3-D meshes, polynomials of two and three variables, sparse stiffness and mass matrices to linearize 3-D problems, and 3-D splines. Each chapter ends with relevant exercises to help comprehend the material. Fully explained solutions are available in the appendix. The original code is also available at www.crcpress.com. Yair Shapira August 2008 ...展开收缩
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