Mastering Special and General Relativity: from the incompatibility between Galileo’s principle and Maxwell’s equations to the unraveling of the greatest “mathematical secrets” of the universe.
Students who take the course will learn the following:
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Understand the incompatibility between Galileo’s principle and Maxwell’s equations.
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Formulate Special Relativity and General Relativity consistently.
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Develop the mathematical intuition required to fully grasp and appreciate the contents of these subjects.
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Learn about Lagrangian mechanics and the Action Principle.
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Understand tensors and their applications in relativity.
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Derive Lorentz transformations in two different ways.
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Learn about the mathematics required to follow the part on General Relativity.
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Meet the prerequisite requirements, including Calculus and Multivariable Calculus.
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Develop skills in problem-solving, critical thinking, and mathematical reasoning.
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Build a strong foundation in advanced physics and mathematics, which can be applied in future studies or research.
Here are some benefits of taking the course on Special and General Relativity:
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Gain a deep understanding of the principles and concepts underlying Special and General Relativity, which are foundational to modern physics and astronomy.
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Develop strong mathematical skills required to fully grasp and appreciate the subject matter, including Lagrangian mechanics and tensor calculus.
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Learn how to derive important equations in Special and General Relativity, including the Lorentz transformations and the Einstein field equations.
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Gain insight into the implications of Special and General Relativity for our understanding of space, time, and gravity, and how these concepts are used in modern physics and astronomy.
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Engage with a challenging and stimulating subject matter, which can help to develop critical thinking skills and problem-solving abilities.
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Potentially open up opportunities for further study or research in the fields of physics, astronomy, or related areas.
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Gain a sense of satisfaction and accomplishment from tackling a complex and challenging subject and mastering its concepts and techniques.
Course description:
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We start by explaining the problem with Galileo’s principle and Maxwell’s equations and how this led to the formulation of Special Relativity.
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We expand the discussion to General Relativity and highlight the importance of mathematical intuition in fully grasping the concepts.
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We motivate every equation in the course to help students understand the underlying principles and theories.
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We provide a comprehensive explanation of Lagrangian mechanics and tensors, which are essential to understanding Special and General Relativity.
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We assume a prerequisite knowledge of Calculus and Multivariable Calculus, including the divergence theorem, vectors, dot and cross products, matrix multiplication, and determinants.
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We suggest some basic knowledge of Classical physics, including scalar potential, Newton’s laws, kinetic energy, energy conservation, and the wave equation.
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The first part of the course will focus on Lorentz transformations and derive them in two different ways, providing a simpler mathematics to follow along.
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The second part of the course will focus on General Relativity, where a pencil and paper are recommended to derive the equations, ensuring that students meet the prerequisite requirements.
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We provide students with a comprehensive understanding of Special and General Relativity and inspire them to appreciate and apply the theories.
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The course is designed for students who are passionate about physics and mathematics, especially those interested in pursuing higher education in these fields.