This text introduces students to the mathematical models of Partial Differential Equations (PDEs) and the methods used for their numerical solution and optimization. It is designed for advanced students in Applied Mathematics, Engineering, Physical Science, and Computer Science, providing a comprehensive overview of essential concepts and techniques in these fields. The book aims to bridge the gap between theoretical understanding and practical application, equipping readers with the tools necessary to tackle complex problems.

The book is presented as an ideal text for advanced students, suggesting a rigorous and comprehensive approach to its subject matter. Its inclusion of numerous exercises and examples indicates a pedagogical focus, aiming to facilitate student learning and comprehension. The broad range of disciplines it serves—Applied Mathematics, Engineering, Physical Science, and Computer Science—points to its utility across various technical fields. The text is structured to familiarize students with both the theoretical underpinnings of numerical analysis and optimization and the practical methods for their application.