Penetrate Postgraduate Entrance Exam Mathematics: Economics: Economics

Author: Mou Junlin
Publisher:
Publish Date: 2003-08-01
Features: The systematicity and uniqueness of this book are crucial in mathematics, where cleverness triumphs over brute force. The author has meticulously studied and summarized the wisdom of numerous mathematical elites of this era to overcome the limitations of individual thinking. The sole purpose is to help students easily grasp the shortcut for passing the postgraduate entrance exam and change the fate of candidates. The book's distinctive feature lies in establishing a living problem framework based on the intrinsic connections of each point in the syllabus. To enable candidates to master this brand-new problem framework, we have enhanced its internal connections from the following four aspects:
1. A Fresh and Rational Chapter Arrangement: We have abandoned the traditional method of arranging content according to textbook chapters and instead integrated related chapters. This allows readers to achieve a comprehensive understanding through comparative analysis. For example, following the textbook order, there is an intermediate chapter on indefinite integrals between the derivatives of single-variable and multi-variable functions. Students often struggle to see the intrinsic connection between single-variable and multi-variable function differentiation, yet both share similarities in problem-solving methods and thinking. Therefore, we have combined these two chapters. Similarly, in linear algebra, proof problems are scattered across various chapters such as determinants, matrices, vectors, and linear equations. Students find it difficult to grasp the overall picture, so we have consolidated them into a single chapter—Proof Problems in Linear Algebra. The specific chapter arrangement and its rationale are detailed in the "Chapter Arrangement of This Book".
2. Grouping Similar Problem-Solving Methods into Types: Within each chapter and section, we categorize examples with similar problem-solving methods into types, summarizing each section into several or a dozen types. The advantages of this approach are:
- Fewer problem types per section, with strong internal connections among them, making them easier to master compared to a scattered collection of dozens of examples.
- Each type includes several similar sub-problems, allowing students to analyze and master them from different angles, thereby grasping the essence of each type. Through our summarization, all problem types can be fully presented in a single table, giving candidates confidence in mastering them. See the "Table of Contents".
3. Problem-Solving Method Explanations: We generally introduce basic methods first, followed by special methods, while summarizing a series of basic problem-solving steps to provide readers with a clear thought process. These steps help you quickly find a solution and improve efficiency. For example, when calculating limits, non-standard problems should first be converted into standard ones, often using logarithmic identities, substitution, or common denominator methods. Then, apply L'H?pital's Rule where possible, while noting that factors that can be solved should be addressed first.
4. Two Important Appendices: At the beginning of the book, we have compiled two key appendices: Basic and Important Theorems and Basic Problem Types and Solving Methods. These are the essence of the book. Many candidates struggle to remember trigonometric formulas or complex formulas before exams, yet finding a specific formula often requires flipping through several books, which is highly inconvenient. Additionally, without a clear and comprehensive understanding of various problem types, students may not have time to review but worry about not doing so. To address these challenges, we have carefully prepared these two appendices. This transforms study into a more memorization-based task, requiring only ten minutes of daily review to stabilize their mindset and avoid unnecessary anxiety—a crucial aspect!