Calculus Tutoring (Economic Application Mathematics Foundation (I) Renmin University Revised Edition (People's Daily Press))

Author: Yang Fuyun, Sun Huadong, Jiuzhang Series Course Group
Publisher:
Publish Date: 2005-08-20
Features: This book is a learning guide designed to accompany the "Fifteenth Five-Year Plan" national-level planning textbook "Calculus" (Second Edition) compiled by the Department of Applied Mathematics at Tongji University. As an essential component of advanced mathematics, Calculus is a mandatory foundational course for science and engineering students and a required subject for many postgraduate entrance examinations. The concepts in Calculus are complex and diverse, ranging from basic variables, functions, and limits to advanced derivatives, differentials, and integrals, forming an incredibly elegant and vast system. This system is not only rich in content but, more importantly, has a rigorous and flawless structure. As an introductory advanced mathematics course for university-level studies, many students find Calculus abstract and difficult to understand, struggling with grasping fundamental concepts and theorem conclusions. When it comes to solving problems, they often lack clear approaches and find it hard to get started. This guide aims to help students better master the basic concepts and theories of Calculus, integrate various problem-solving techniques and methods, and improve their ability to analyze and solve problems. The book is primarily composed of the following sections:
1. Basic Requirements. Based on the annual postgraduate entrance examination syllabus, it concisely summarizes the key points of each chapter, helping readers to have clear goals and focus during their study.
2. Content Summary. It explains the important properties, theorems, formulas, and conclusions in each chapter, providing detailed explanations and summaries for some challenging yet syllabus-relevant content. The goal is to enable students to learn the textbook analytically and master the knowledge.
3. Knowledge Network Diagram for Each Chapter. Each chapter includes a comprehensive knowledge network diagram that covers all key points, allowing students to grasp the framework structure of the chapter at a glance and fully understand the theoretical system of the textbook.
4. Typical Example Analysis. The book summarizes the important question types covered in the course, which are representative and derived from an in-depth analysis of past exams and postgraduate entrance examinations.
5. Full Solutions to After-Class Exercises. The textbook contains a rich variety of after-class exercises, ranging from basic to advanced, designed to help students understand fundamental concepts and theories from multiple perspectives and master basic problem-solving methods. We provide detailed solutions to all after-class exercises in the textbook.
6. Solutions to Experimental Problems. Given the widespread use of computers and the increasing sophistication of mathematical software, the textbook includes 14 mathematical experiments. We provide detailed solutions and explanations for these experimental problems. While other solutions may exist due to differing approaches, we offer one reference solution, and all experimental problem solutions are listed separately at the end of the book. During the writing process, we referred to the book "Calculus Learning Guide and Selected Problem Solutions" published by Higher Education Press, for which we express our sincere gratitude. Due to the tight schedule and the limited ability of the authors, there may be omissions in the book. We kindly invite readers to point out any errors or suggest improvements.