Basic Monotonicity Methods with Some Applications

This textbook covers basic tools from the theory of monotone operators and their applications to ordinary differential equations, with simple illustrations and inspiring applications for graduate students in mathematics. It also provides a smooth transition to studying more advanced topics.

Format: Paperback / softback
Length: 180 pages
Publication date: 02 September 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook delves into the realm of monotone operators, presenting a selection of fundamental tools alongside their diverse applications. By utilizing examples tailored to ordinary differential equations, the text elucidates the core concepts in a straightforward yet captivating manner. While maintaining a modest level of complexity, it presents inspiring examples that engage the reader and pique their interest. This textbook is particularly appealing to graduate students in mathematics who seek to acquire a solid foundation in the theory of monotone operators. Furthermore, it serves as a seamless gateway to exploring more advanced topics related to pseudomonotone operators and multivalued monotone operators, enabling students to delve deeper into the field of mathematics.

Introduction:
This textbook serves as a comprehensive introduction to the theory of monotone operators, encompassing a range of fundamental tools and their applications. By utilizing examples tailored to ordinary differential equations, the text elucidates the core concepts in a straightforward yet captivating manner. While maintaining a modest level of complexity, it presents inspiring examples that engage the reader and pique their interest. This textbook is particularly appealing to graduate students in mathematics who seek to acquire a solid foundation in the theory of monotone operators. Furthermore, it serves as a seamless gateway to exploring more advanced topics related to pseudomonotone operators and multivalued monotone operators, enabling students to delve deeper into the field of mathematics.

Examples:
The textbook provides a wealth of examples that illustrate the practical applications of monotone operators. These examples cover a wide range of topics, including optimization, control theory, and mathematical economics. Each example is carefully crafted to demonstrate the power and versatility of monotone operators in solving real-world problems. The accompanying explanations and diagrams further enhance the understanding of the concepts, making the material accessible to students with varying backgrounds in mathematics.

Applications:
The applications of monotone operators extend beyond the realm of ordinary differential equations. They find applications in various fields, such as optimization, control theory, and mathematical economics. Monotone operators play a crucial role in designing efficient algorithms for solving complex optimization problems, such as linear programming and nonlinear optimization. In control theory, monotone operators are used to design feedback control systems that stabilize systems and ensure desired performance. In mathematical economics, monotone operators are employed to model economic relationships and analyze market behavior.

Conclusion:
In conclusion, this textbook offers a comprehensive and engaging introduction to the theory of monotone operators. By presenting a selection of fundamental tools alongside their diverse applications, the text provides students with a solid foundation in the field. The examples and applications showcased in the textbook demonstrate the power and versatility of monotone operators in solving real-world problems. Whether you are a graduate student in mathematics seeking to expand your knowledge or an enthusiast interested in exploring the applications of monotone operators, this textbook is an invaluable resource.

Weight: 302g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030753078
Edition number: 1st ed. 2021