Description
“Applied Partial Differential Equations: Theory, Methods, and Applications” provides a comprehensive overview of the theory, numerical methods, and practical applications of partial differential equations (PDEs) in various scientific and engineering fields. The book is designed to serve as both a textbook for graduate-level courses and a reference for researchers and practitioners in the field.
Key Features:
Comprehensive Coverage:
The book covers a wide range of topics, including classical PDEs, numerical methods, applications in physics, engineering, biology, and finance, and advanced topics such as nonlinear equations and stochastic processes.
Theory and Methods:
Each topic is presented with a rigorous mathematical treatment, emphasizing fundamental principles, solution techniques, and theoretical insights.
Numerical Techniques:
The book includes detailed discussions of numerical methods for solving PDEs, including finite difference, finite element, spectral, and boundary integral methods, with practical examples and computational exercises.
Applications:
Numerous real-world examples and case studies demonstrate the relevance and applicability of PDEs in various scientific and engineering disciplines, such as fluid dynamics, heat transfer, electromagnetics, structural mechanics, and mathematical biology.
Exercises and Problems:
Each chapter includes exercises and problems ranging from basic concepts to advanced topics, allowing readers to test their understanding and develop problem-solving skills.
MATLAB and Python Code:
The book provides MATLAB and Python code snippets for implementing numerical algorithms and solving example problems, enabling readers to experiment with different methods and algorithms.
Target Audience:
● Graduate students and researchers in applied mathematics, engineering, physics, and computational science.
● Practitioners and professionals in industries such as aerospace, automotive, energy, environmental, and biomedical engineering.
● Educators teaching courses on partial differential equations, numerical methods, mathematical modelling, and scientific computing.
Overall, “Applied Partial Differential Equations: Theory, Methods, and Applications” offers a comprehensive and accessible treatment of PDEs, making it an essential resource for students, researchers, and practitioners interested in understanding and solving complex problems in science and engineering.
