Calculation Method Typical Examples and Solutions

Author: Gao Peiwang/Rui Yongjun (editors)
Publisher:
Publishing Date: 2003-11-01
Features: The main feature of this course is the abundance of algorithmic formulas and rigorous theoretical analysis. As a result, many students find it challenging to grasp the key points during the learning process, especially when applying the knowledge to solve specific problems flexibly. In reality, each algorithm has its corresponding mathematical background, principles, and fundamental framework. However, the construction ideas of certain algorithms are similar, serving as extensions and generalizations of one another. For example, the Gaussian quadrature formula for numerical integration can be regarded as an extension of the Newton-Cotes formula, where the integration nodes transition from fixed to determined. Based on this, the book categorizes these algorithms into a group and lists them sequentially in the content summary, thereby better assisting students in connecting, understanding, memorizing, and broadening their perspectives. This book is compiled based on the teaching syllabus of "Computational Methods" for engineering majors. During the writing process, it references various computational methods textbooks and exercise collections published in China in recent years, as well as a large number of self-study examination questions and graduate entrance examination questions from key universities in China. It selects nearly 500 typical problems and provides detailed analysis and solutions. The book consists of ten chapters, covering all the essential content required for "Computational Methods" in engineering. The first nine chapters provide key knowledge points, content summaries, typical examples and methods, exercises, problem-solving guidance, and solutions, making it convenient for readers to use.
Key Knowledge Points: According to the teaching syllabus requirements, the book outlines different levels of expectations for each knowledge point in each chapter—understanding, mastering, and proficiently mastering—allowing readers to clearly identify the learning priorities.
Content Summary: Briefly summarizes the main knowledge points of each chapter, enabling readers to systematically grasp the basic concepts, important theorems, and key algorithms within a relatively short period.
Typical Examples and Methods: To help students flexibly apply their knowledge to analyze and solve problems while mastering problem-solving techniques, this section categorizes typical problems based on the characteristics of each chapter and exam focus. It summarizes several typical question types, accompanied by 1–3 examples, providing corresponding problem-solving approaches and methods to achieve the goal of learning by analogy and comprehensive understanding. These examples are suitable for comprehensive course review and reference for various preparatory purposes.
Exercises: Primarily includes synchronous training questions and comprehensive training questions. The synchronous exercises are based on commonly used domestic textbooks and combine key knowledge points of each chapter, providing questions for synchronous training during the course to deepen understanding and mastery. The comprehensive training questions are more challenging and carefully selected to systematically master the content of each chapter or even the entire book, offering strong comprehensiveness and flexibility. They are suitable for comprehensive course review and reference for various preparatory purposes.
Solutions: Provides detailed solutions and guidance for synchronous training questions, as well as concise solutions for comprehensive training questions, for reference when solving problems.
Finally, the book also includes two mock exams and two authentic graduate entrance examination questions with reference answers. The mock exams are suitable for undergraduate students to assess their foundational knowledge upon completing the course, while the graduate entrance examination questions are designed for candidates preparing for graduate entrance exams and individuals seeking master's degrees through part-time studies to review the "Numerical Analysis" subject.