Calculus Problem Class Guidance

Author: Yan Zhanghang, Li Chaoxia, Liu Haozeng
Publisher:
Publish Date: 2005-05-01
Features: This book is a supplementary teaching material for the stereoscopic textbook "Advanced Mathematics." The main content of this book includes: summary of chapter content, classification and solutions of common problems, answers and hints for typical exercises, and self-assessment questions. The book is consistent with the main textbook in terms of chapter order, content presentation, problem-solving methods, and symbol markings. Its content provides abundant resources and materials for problem-solving classes in this course, greatly facilitating teachers' preparation and students' learning. This book can be used as a supplementary textbook for students in three-year or two-year vocational and technical colleges, adult colleges, and secondary schools affiliated with undergraduate universities, studying "Advanced Mathematics" in engineering, finance and economics, and management-related fields. Additionally, it holds high reference value for engineering technicians and economic management personnel.
Table of Contents
Table of Contents
Part One: Calculus of a Single Variable
Chapter 1: Functions, Limits, and Continuity
1 Section: Summary of Chapter Content
1 Section: Classification and Solutions of Common Problems
3 Section: Answers and Hints for Typical Exercises
8 Section: Self-Assessment (Alternative Exercises)
17
Chapter 2: Derivatives and Differentials
19 Section: Summary of Chapter Content
19 Section: Classification and Solutions of Common Problems
20 Section: Answers and Hints for Typical Exercises
22 Section: Self-Assessment (Alternative Exercises)
33
Chapter 3: Applications of Derivatives
35 Section: Summary of Chapter Content
35 Section: Classification and Solutions of Common Problems
36 Section: Answers and Hints for Typical Exercises
39 Section: Self-Assessment (Alternative Exercises)
51
Chapter 4: Integral Calculus of a Single Variable
53 Section: Summary of Chapter Content
53 Section: Classification and Solutions of Common Problems
54 Section: Answers and Hints for Typical Exercises
61 Section: Self-Assessment (Alternative Exercises)
71
Chapter 5: Applications of Definite Integrals
72 Section: Summary of Chapter Content
72 Section: Classification and Solutions of Common Problems
72 Section: Answers and Hints for Typical Exercises
77 Section: Self-Assessment (Alternative Exercises)
80
Part Two: Foundations of Multivariable Calculus
Chapter 6: Foundations of Multivariable Differential Calculus
81 Section: Summary of Chapter Content
81 Section: Classification and Solutions of Common Problems
82 Section: Answers and Hints for Typical Exercises
85 Section: Self-Assessment (Alternative Exercises)
96
Chapter 7: Multivariable Integral Calculus
98 Section: Summary of Chapter Content
98 Section: Classification and Solutions of Common Problems
99 Section: Answers and Hints for Typical Exercises
103 Section: Self-Assessment (Alternative Exercises)
116
Part Three: Foundations of Ordinary Differential Equations
Chapter 8: Ordinary Differential Equations
118 Section: Summary of Chapter Content
118 Section: Classification and Solutions of Common Problems
119 Section: Answers and Hints for Typical Exercises
123 Section: Self-Assessment (Alternative Exercises)
138
Part Four: Foundations of Infinite Series
Chapter 9: Infinite Series
140 Section: Summary of Chapter Content
140 Section: Classification and Solutions of Common Problems
142 Section: Answers and Hints for Typical Exercises
149 Section: Self-Assessment (Alternative Exercises)
162
Appendix: Self-Assessment Questions (Alternative Exercises)
Reference Answers
165
References
169