Mathematical intuition behind Special and General Relativity (Udemy.com)
Mastering Special and General Relativity: Calculus, Tensors, Lagrangian Mechanics, Einstein's ground-breaking articles
Created by: Emanuele Pesaresi
Last updated March 2026
What you will learn
- Special Relativity
- General Relativity
- Lagrangian mechanics
- tensors
- Lorentz transformations
- time dilation
- length contraction
- field equations
- how to construct a Lagrangian
- geodesics
- equivalence principle
- covariant formulation of physics
- covariant derivatives
- how to motivate EVERY equation in Special and General Relativity
- proof of E=mc^2
- why photons have momentum
How it compares
Against the other 503 rated Udemy courses in Teaching & Academics on CourseDuck:
- Rating4.4 out of 5higher than 27% of them
- Reviews205#358 of 504 by number of reviews
- Length18.8 hourslonger than 92% of them
- Last updatedMarch 2026more recently than 84% of them
Course Description
Mastering Special and General Relativity: from the incompatibility between Galileo's principle and Maxwell's equations to understanding the geometry of spacetime.
Students who take the course will learn the following:
Understand the incompatibility between Galileo's principle and Maxwell's equations.
Formulate Special Relativity and General Relativity consistently.
Develop the mathematical intuition required to fully grasp and appreciate the contents of these subjects.
Learn about Lagrangian mechanics and the Action Principle.
Understand tensors and their applications in relativity.
Derive Lorentz transformations in two different ways.
Learn about the mathematics required to follow the part on General Relativity.
Meet the prerequisite requirements, including Calculus and Multivariable Calculus.
Develop skills in problem-solving, critical thinking, and mathematical reasoning.
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:
Gain a deep understanding of the principles and concepts underlying Special and General Relativity, which are foundational to modern physics and astronomy.
Develop strong mathematical skills required to fully grasp and appreciate the subject matter, including Lagrangian mechanics and tensor calculus.
Learn how to derive important equations in Special and General Relativity, including the Lorentz transformations and the Einstein field equations.
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.
Engage with a challenging and stimulating subject matter, which can help to develop critical thinking skills and problem-solving abilities.
Potentially open up opportunities for further study or research in the fields of physics, astronomy, or related areas.
Gain a sense of satisfaction and accomplishment from tackling a complex and challenging subject and mastering its concepts and techniques.
Course description:
We start by explaining the problem with Galileo's principle and Maxwell's equations and how this led to the formulation of Special Relativity.
We expand the discussion to General Relativity and highlight the importance of mathematical intuition in fully grasping the concepts.
We motivate every equation in the course to help students understand the underlying principles and theories.
We provide a comprehensive explanation of Lagrangian mechanics and tensors, which are essential to understanding Special and General Relativity.
We assume a prerequisite knowledge of Calculus and Multivariable Calculus, including the divergence theorem, vectors, dot and cross products, matrix multiplication, and determinants.
We suggest some basic knowledge of Classical physics, including scalar potential, Newton's laws, kinetic energy, energy conservation, and the wave equation.
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.
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.
We provide students with a comprehensive understanding of Special and General Relativity and inspire them to appreciate and apply the theories.
The course is designed for students who are passionate about physics and mathematics, especially those interested in pursuing higher education in these fields.
Instructor Details
- 4.4 Rating
205 Reviews
Emanuele Pesaresi
I earned my PhD in Mechanics and Advanced Engineering Sciences in 2021, following a Bachelor’s (2015) and Master’s (2017) in Mechanical Engineering from the University of Bologna.
From 2018 to 2021, I served as the teaching tutor for the Mechanics of Machines course at the University of Bologna (Forlì branch).
Driven by a passion for mathematics, physics, and teaching, I enjoy guiding both high school and university students. My teaching philosophy emphasizes that, for engineers, mathematicians, and physicists, learning how to approach and solve problems logically is far more important than memorization. I aim to cultivate curiosity and critical thinking, encouraging students to question assumptions, explore concepts deeply, and build a robust understanding, rather than simply absorbing information.
For enquiries (such as tutoring requests or subject-related guidance) you can reach me via LinkedIn, email, my website, or the message boards of my courses.
You can also find updated versions of my courses on my website.
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Reviews
By Iuri Bachnivsky on 9/2/2026
This was a great intro to a really tough subject for me. I have tried to read some texts on the subject, but they gloss over details. Here Emanuele not only goes into detail but even stops a lot to remind us of what the different terms are and how they relate (such as whether or not something is a tensor). He really knows the subject matter well and I would love to take some of his other courses (which I already bought).
By Amos Elroy on 9/19/2024
The explanations are sometimes shorthand assuming certain prior knowledge. I had to pose and learn about Maxwell's equations for example before returning to the course. It would be easier if the sketches and equations were printed as they are hard to read in this format.
By Alexander Albus on 9/17/2024
The course was good and met my expectations. SR/GR are introduced in a less formal way and thus it is quite easy to follow with advanced calculus skills. Sometimes this comes at the expense of having to follow lengthy calculations, which is not very elegant. I still prefer the course this way. There are some redundancies (of the main part with the later section, where it is presented how Einstein did it - I wonder if it is necessary to present the material both ways). Sometimes I am lacking a bit a physical interpretations of the equations (or the mathematical "intuition" behind it). I would also appreciate to learn about the "plan of the argument", before a lengthy calculation is presented. This would help better to get the idea behind it and also encourage to really follow the calculations (because you understand why it's needed). But -as said- all-in-all I am happy about the course, because I could catch the essentials of the topics - even though being out of physics for 20 years;-)
By Paulo Renato Rodrigues on 12/2/2023
This course is being absolutely amazing! The professor provides information and derivations that I always wanted to have and in this course he gives us such information in a clear and mathematically precise way! Certainly I will follow this instructor for more courses like this. This course is comprehensive and marvelous! The content of this course went beyond my expectations! Congratulations and thank you Professor Emanulele Paresi!
By Gary Hedgcoxe on 5/11/2023
The information contained in this course pushed me to seek out additional resources because of its very interesting nature. I turned to 5 separate books to supplement the material, and, I have learned an enormous amount about physics and tensors in general. My mechanical engineering background did not prepare me, but I believe this has broadened my perspective and will be useful in my job, if for no other reason.
By Lisa Frey on 4/14/2023
I like the short, brief lectures. He is very thorough and wants us to understand the concepts, step-by-step, which is nice. He is a very good teacher. This is an absolutely fantastic course. He is very, very good at explaining the steps he goes through, and very methodical. I look forward to taking more classes from him! I still love the class! I was out for sometime due to a death in my family, but am glad to be back and able to spend time on this.
By Stephanie Beram on 1/13/2022
This course offers a lot of insight on both special and general relativity. If you are not very advanced in physics or math, the teacher develops the concepts and equations from simple arguments and builds on them. If you are more advanced, this course will provide you with a lot of intuition that might not be offered in a classroom setting. As a last year physics major that previously took GR, I am learning a lot from this course.
By Joshua Larson on 12/29/2021
I really liked the format and the instructor explained everything really well. I liked the overlays that showed when there were mistakes (mistakes in lectures are a great way to highlight the more challenging math-y bits). I wish there had been a few more concrete. examples. A lot of the math that happened here was pretty abstract, and it wasn't always that easy to connect it with physical or geometric intuition. For instance, it could be nice to show why a metric with 1 + 2phi/c^2 in the 00 position acts like a Newtonian potential, or to show an explicit calculation of the Ricci scalar of a sphere or some other easily-intuited manifold.
By Steve on 11/24/2021
The course could use more modern visualisation techniques as it is just the author writing equations on a piece of paper. It would also be good to have some numerical examples, at least for rank 2 tensors as the indice notation is a bit difficult to follow if you are a beginner in tensor algebra.
By Atley Anderson on 5/27/2021
I love physics, and I’ve always been interested in relativity and maths. So I decided to finally learn and fully understand the math and in depth physics of relativity. Just started this course, and it’s already so great! Thank you for posting this!
Quality Score
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Overall Score : 88 / 100






