Overview

Purpose of the Book This book is intended for undergraduate students of physics, engineering, and related disciplines, as well as for readers seeking a clear and structured introduction to Special Relativity. Its primary objective is to present the fundamental concepts of the theory in a rigorous yet accessible manner, supported by a comprehensive collection of fully solved problems. Emphasis is placed on developing the reader's ability to apply the theoretical framework to practical situations and examination-type problems. Although the predictions of Special Relativity often contradict everyday intuition, their mathematical formulation is precise and consistent. Through systematic analysis and problem-solving, the reader is guided toward a deeper understanding of the physical principles governing spacetime and relativistic phenomena. The book is suitable both for self-study and as a supplementary text for university-level courses. The underlying philosophy of this and all the author's works is that a deep understanding of physics is achieved primarily through systematic problem-solving. For this reason, particular emphasis is placed on exercises and fully developed solutions, which serve as the main vehicle for mastering the theoretical concepts. Scope of the Book It should be emphasized that the notation of physical quantities is not unique and may vary across the literature. Particular attention must therefore be paid to the definitions and conventions adopted in this book. The first chapter provides a concise yet comprehensive introduction to the mathematical tools required for the development of the theory, including matrix algebra and the Einstein summation convention. The second chapter introduces transformations between inertial reference frames, leading to the general Galilean transformations and the classical concepts of space and time, while highlighting the limitations of classical (Newtonian) physics. The third chapter presents the postulates of Special Relativity and develops the Lorentz transformations, together with their physical implications, including time dilation and the relativity of simultaneity. The fourth chapter introduces the fundamental physical quantities of the theory, such as four-vectors and their applications in relativistic dynamics and particle processes. The fifth chapter provides an introduction to tensor calculus, allowing the formulation of the theory in a more general and elegant mathematical framework, and preparing the reader for further study in advanced topics such as General Relativity. The sixth chapter presents electrodynamics within the framework of Special Relativity, including Maxwell's equations in covariant form and the electromagnetic field tensor.

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