Calculation Methods and Practice

Author: Tian Xianghong
Publisher:
Publish Date: 2004-04-01
Features: This book is suitable for full-time and part-time students of computer majors in vocational and technical colleges, as well as non-mathematics major engineering students or adult education undergraduates. During the writing process of this book, many teachers from the Computer Information Management Teaching and Research Office of Longpan College, Jinling Institute of Technology, provided care and support, and the author expresses deep gratitude here. Due to the author's limited ability, it is inevitable that there are shortcomings and errors in the book. The author sincerely invites readers to point out any mistakes. Contact information of the author: avatian@sohu.com. This book is one of the series textbooks for vocational and technical colleges organized and compiled under the guidance of the China Higher Vocational and Technical Education Research Association by the Xidian University Press. When introducing algorithms, this book strives to present them from simple to complex, intentionally omitting complex and tedious theoretical proofs and derivations, focusing on the understanding and application of algorithms. The main content of this book includes basic concepts, principles, and algorithms of error knowledge, numerical solutions of nonlinear equations, numerical solutions of linear equations, interpolation methods, curve fitting and least squares methods, numerical differentiation and integration, and numerical solutions of ordinary differential equations. The book includes flowcharts of main algorithms and their C language program implementations. Each chapter provides a sufficient number of exercises, and reference answers are provided for some of them. The last chapter (Computational Practice) is designed for students to understand and practice algorithms. This book can be used as a textbook or reference book for undergraduates of non-mathematics majors in ordinary universities, vocational college students of computer majors, and undergraduates and vocational college students of adult education. It can also be used as a reference book for relevant engineering technicians and self-learners. This book is accompanied by an electronic teaching plan, which is provided free of charge. Since 1999, with the acceleration of the popularization of higher education, higher vocational education has shown rapid development. The Party and the State attach great importance to the reform and development of higher vocational education and have issued a series of relevant laws, regulations, documents, etc., to regulate and promote the healthy and orderly development of higher vocational education. At the same time, society's understanding of higher vocational and technical education is continuously strengthening, and the importance of applied technical talents and their cultivation is being recognized by more and more people. Currently, higher vocational and technical education accounts for half of higher education in terms of the number of schools, enrollment, and number of graduates, becoming an important part of higher education and playing an extremely important role in the cause of socialist construction in China. While higher vocational education is developing rapidly, there are also many pressing issues to be addressed. The main one is to cultivate a group of middle-aged and young teaching and research personnel with "dual-teacher quality" in accordance with the training objectives of higher vocational education; to write a series of characteristic textbooks for basic courses and main professional courses; and to create a group of excellent teaching schools, characteristic majors, and training bases. To solve the current problem of insufficient high-quality higher vocational textbooks in the fields of information and electromechanical, Xidian University Press and the China Higher Vocational and Technical Education Research Association have jointly planned and organized the writing of more than 100 kinds of series textbooks for vocational and technical colleges in two rounds. The selection of these textbooks was based on thorough research on teaching plans and curriculum settings in nearly 30 higher vocational and technical colleges across the country. The writing of the textbooks was conducted through an open bidding process to attract as many outstanding authors as possible to participate in bidding and writing. On this basis, a series of expert editorial committees were held to review the writing outlines of the textbooks, propose modifications and improvements to the winning outlines, and determine the chief editors and chief reviewers. This series of textbooks focuses on the principle of "emphasizing technical ability training" in higher vocational and technical education, aligning with the target positioning, and emphasizes breakthroughs in originality, practicality, and readability to reflect the characteristics of higher vocational textbooks. The first round of textbooks included 36 titles, all of which were completed by 2001. Based on the use, they are relatively suitable for the needs of higher vocational colleges and are widely welcomed by schools, with repeated reprints. Among them, "Internet Practical Technology and Web Production" has been reprinted six times in just over two years and won the second prize of the 2002 Excellent Textbook Award for Ordinary Universities of the Ministry of Education. The second round of textbooks is expected to be fully completed by 2004. Textbook construction is one of the main tasks of basic construction in higher vocational colleges and an important foundation for teaching content reform. Therefore, relevant higher vocational colleges attach great importance to textbook construction and organize teachers to actively participate in the writing of textbooks, working hard to develop higher vocational textbooks from nothing to something, from something to better, to special. We sincerely hope that teachers engaged in higher vocational education, while teaching and educating, will organize and work together to write high-quality textbooks for higher vocational education, making positive contributions to the introduction of a series of characteristic and high-quality higher vocational textbooks. With the development of modern science and technology and the widespread application of computer and network technology, the speed of information dissemination has significantly increased, and numerical calculation methods are no longer limited to pure mathematics but have also been widely used in engineering practice. Therefore, ordinary engineering technicians and designers in all walks of life need to use numerical calculation methods. As college students in the information age, it is even more important for them to understand the knowledge of numerical calculation methods, especially for college students of computer majors, adult education undergraduates, and self-examination undergraduates, as learning numerical calculation methods is more important for them to face future practical applications. Currently, there are many textbooks on computational methods, but most are suitable for undergraduates and postgraduates of science and engineering majors, with high requirements for the foundation of higher mathematics, which are not very suitable for students of higher vocational and technical colleges. Therefore, this textbook reduces many proofs of mathematical methods and focuses more on the implementation of numerical calculation methods, aiming to help students understand algorithms and master various numerical calculation methods proficiently. This book is divided into 8 chapters. Chapters 1 to 7 systematically introduce various commonly used numerical calculation methods, including the main principles, ideas, and implementation of algorithms. Each chapter is accompanied by a large number of examples and a certain number of exercises, with reference answers provided to help readers further understand and master various numerical calculation methods through the study of examples and exercises. This part is recommended to be taught with 32 to 40 class hours. Chapter 8 is Computational Practice, used for students' computer practice. Through these practice problems, students can have a deeper understanding of various numerical calculation methods. To more effectively guide students' computer practice and facilitate self-study, flowcharts of main algorithms and programs written in standard C language are provided for each practice problem, along with practice exercises for computer practice. It is recommended that the time for students' computer practice be 12 to 18 class hours.