Introduction

When studying physics, we often encounter a vast array of materials that require careful reading and comprehension. However, it is not uncommon to struggle with fully understanding the derivation of all the equations presented. This can be due to various reasons: sometimes our personal limits hinder our understanding, and other times the authors possess a deeper insight into the physics and mathematics, allowing them to see things more clearly than we do.

Regardless of the reason, many of us have felt the need for a resource where fundamental equations are derived in a detailed and accessible manner. This project aims to address that need by providing a comprehensive platform where key equations are meticulously derived and explained. Our goal is to create a valuable tool for students and enthusiasts alike, helping them bridge the gap between complex theoretical concepts and practical understanding.

Physics is an incredibly vast field, and this project will only be able to cover some of its fundamental aspects. The topics selected for this project are those that the authors find personally most interesting and important. Some topics were chosen because the authors tutored students on specific subjects, such as the kinematics of rigid bodies, which led them to derive the Foucault Pendulum equation - a topic he was always interested in. Another example is the derivation of the Lorentz equations of special relativity. The authors read Einstein original 1905 paper and admired his genius in deriving the equations. However, they felt that additional work could be done to extend his formalism to a more general case. The authors aspire for this project to grow further with the help of the community, allowing for the addition of more topics in the future. By collaborating and sharing knowledge, they hope to create a valuable resource that continues to expand and evolve.

The topics that ideally would be covered in this project are the following:

The authors are far from contributing meaningfully to all of them. Hopefully, in the future, some contribution to each will be available for the reader.

This project is intended for readers with a solid understanding of mathematics and physics. It aims to provide detailed derivations and explanations of fundamental equations, which may be challenging for those without a strong background in these subjects. Undergraduate physics students at the beginning of their studies might find some sections particularly difficult. To fully benefit from this project, it is highly recommended that readers have a good grasp of linear algebra, multivariable calculus, and general physics principles. These mathematical tools are essential for understanding the complex derivations and concepts presented. By providing detailed explanations and derivations, the authors hope to make advanced topics more accessible to those with the necessary foundational knowledge.