Mathematical Journey Through Differential Equations Of Physics, A

Physics and mathematics are intertwined, and this book aims to bridge the language barrier by introducing the beauty of mathematical physics. It showcases conceptual and mathematical commonalities across different physical theories, translating physical problems to concrete mathematical questions and explaining how to interpret the answers physically. The book alternates between mathematics- and physics-centric chapters, includes concrete examples from physics, and includes 76 exercises with solutions. Advanced material is sprinkled in to showcase how mathematics and physics augment one another.

Format: Paperback / softback
Length: 480 pages
Publication date: 10 October 2022
Publisher: World Scientific Publishing Co Pte Ltd

Mathematics serves as the universal language of physics, and over the years, physicists have evolved their own distinct dialect. The primary objective of this book is to dismantle this linguistic barrier and expose readers to the captivating realm of mathematical physics. It demonstrates how to harness the combined strengths of both approaches, with physicists frequently generating intriguing conjectures through a combination of intuition and insight, which can serve as the foundation for fascinating mathematical endeavors. Conversely, mathematicians possess the ability to discern commonalities between seemingly disparate fields, such as quantum mechanics and electromagnetism, and employ advanced analytical tools. Instead of being narrowly focused on a particular subject matter, this book showcases conceptual and mathematical similarities across diverse physical theories. It translates physical problems into concrete mathematical inquiries, guides readers through the process of answering them, and elucidates the physical implications of the solutions. For instance, when two Hamiltonians exhibit close similarities, why do their dynamics share similar characteristics? The book employs a balanced approach, alternating between chapters that prioritize mathematics and those that emphasize physics. It includes a wealth of concrete examples drawn from the realm of physics, as well as 76 exercises with comprehensive solutions. Recognizing that readers from both ends possess a foundational understanding of certain material, the book strategically incorporates advanced concepts to illustrate how mathematics and physics complement and enhance one another. Certain examples in this book are based on recent publications and encompass material that has not been extensively covered in other textbooks. This approach ensures that the content remains engaging and captivating for readers throughout the journey.

ISBN-13: 9789811227660