Knowledge Reserve of Advanced Mathematics and Problem-Solving Strategies

Author: Li Yong, Zhang Zuogang
Publisher:
Publish Date: 2001-01-01
Features: This book is a methodology for studying problem-solving techniques in advanced mathematics. Its content unfolds from two aspects:
1. Knowledge Reserve: It classifies advanced mathematics problems based on cognitive characteristics, such as explicit vs. implicit, direct vs. reverse, normal vs. abnormal, special vs. general, discrete vs. continuous. This aims to help readers break free from fixed thinking patterns, improve their cognitive methods, and make their thinking more scientific.
2. Strategy Reserve: It strengthens the awareness of planning problem-solving strategies and constructs 10 problem-solving thinking models—Exploration Model, Transfer Model, Reverse Model, Motion Model, Abnormal Model, External Transformation Model, Internal Transformation Model, Intermediate Transformation Model, Role-Reversal Model, and Flowering on a Tree Model—thereby forming a problem-solving strategy system.
The book is divided into 10 chapters, covering the following main topics:
- Differential Calculus of Univariate Functions
- Integral Calculus of Univariate Functions
- Inequalities and Function Zeros
- Vector Algebra and Space Analytic Geometry
- Differential Calculus of Multivariate Functions
- Multiple Integrals
- Line Integrals
- Surface Integrals
- Series
- Differential Equations
This book serves as a reference for undergraduate engineering students, a teaching resource for mathematics teachers, and a valuable study guide for candidates preparing for postgraduate entrance exams in science and engineering fields.