Mastering Special and General Relativity: Calculus, Tensors, Lagrangian Mechanics, Einstein's ground-breaking articles | Discount Coupon for Udemy Course
Last updated 2/2023Course Language EnglishCourse Caption English [Auto]Course Length 18:55:47 to be exact 68147 seconds!Number of Lectures 95
This course includes:
19 hours hours of on-demand video
Full lifetime access
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Certificate of completion
15 additional resources
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
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: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.Who this course is for:students who want to motivate EVERY equation constituting the foundations of both Special and General Relativitystudents who aim to obtain a thorough understanding of the Lagrangian formulation of Physicsstudents interested in learning tensorsstudents who desire to learn Special Relativitystudents who desire to learn General Relativitymathematiciansphysicistsastronomersaerospace engineerscosmologists
Course Content:
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2 Lectures | 08:25
introduction: disagreement between electromagnetism and classical mechanics
04:16
Galileo's transformations
04:09
Note: at about 3:20 the velocity V is supposed to be V' actually, but I notice the error a few seconds later fortunately ;)
14 Lectures | 01:16:17
Lorentz trasformation derivation part 1
04:01
Lorentz trasformation derivation part 2 - Simultaneity
03:33
Lorentz trasformation derivation part 3
05:26
Lorentz transformation derivation part 4
04:06
Lorentz transformation derivation part 5
03:22
Lorentz transformation derivation part 6
03:15
Lorentz transformation derivation part 7
06:21
Lorentz invariant quantity
03:50
A different derivation of Lorentz transformations part 1
03:42
A different derivation of Lorentz transformations part 2: rotation matrices
03:11
A different derivation of Lorentz transformations part 3
03:28
A different derivation of Lorentz transformations part 4
02:38
A different derivation of Lorentz transformations part 5
04:53
Composition of velocities according to Galileo and Lorentz
24:31
2 Lectures | 12:59
Length contraction and time dilation
05:13
Non inertial frames and proper time
07:46
8 Lectures | 58:01
Introduction to Lagrangian mechanics
06:48
Lagrangian mechanics part 1
06:44
Lagrangian mechanics part 2
05:32
Lagrangian mechanics part 3
09:07
Lagrangian mechanics part 4
09:17
Additional comments on the Lagrangian, variation of the action
09:12
Derivation of the Hamiltonian
07:33
Definition of momentum
03:48
5 Lectures | 37:25
Lagrangian in Special Relativity
12:16
Derivation of Momentum in Special Relativity
07:53
Derivation of E=mc^2
08:22
Relation between Energy and momentum
05:12
Momentum of a Photon
03:42
3 Lectures | 21:15
Introduction to General Relativity: Einstein's "happiest" thought
05:20
Highlighting the need for Differential Geometry
03:15
Invariant in tensor notation
12:40
13 Lectures | 02:08:49
Tensor transformations part 1
16:08
Tensor transformations part 2
04:32
Higher rank tensors from lower rank tensors
17:03
Lower rank tensors from higher rank tensors
06:44
Transformation of Euclidean derivatives
06:48
Covariant Derivative
10:14
Some properties of the metric tensor
07:31
Christoffel symbol in terms of the metric tensor part 1
08:01
Christoffel symbol in terms of the metric tensor part 2
07:30
Covariant derivative of the metric tensor
06:26
Covariant derivative of a contravariant vector part 1
07:51
Covariant derivative of a contravariant vector part 2
16:01
Note#1: at about 6:41,as I've added in the notes of the last lecture, some tildes are wrong in some expressions, but I will correct them in this lecture.
Note#2: at 15:56 I mention the Ricci tensor: before the Ricci tensor we will introduce the Riemann tensor, but yeah....after that comes the Ricci tensor ;)
Proof that the covariant derivative of the metric tensor is zero
14:00
18 Lectures | 04:19:15
Equation of a geodesic
17:04
Geodesic and parallel transport
08:02
Riemann tensor part 1
26:44
Note: I will do another derivation of the Riemann tensor in the Appendix.
Some properties of : Riemann_tensor, Ricci tensor, Ricci scalar
09:22
Action in General Relativity
08:17
Invariant 4-volume element in the action
14:06
Determinant of the metric tensor
09:10
Variation of the action of gravity part 1
11:27
Variation of the action of gravity part 2
07:16
Variation of the action of gravity part 3
10:31
Note#1: at about 1:04, instead of 'v', there should be 'w'.
Note#2: at about 7:11 'v' should be replaced by 'w'.
Einstein field equations part 1
17:04
Einstein field equations part 2: another property of the Riemann tensor
12:56
Einstein field equations part 3: energy momentum tensor
16:39
Field equations in classical physics
12:37
Reducing General Relativity to Newtonian laws
12:29
Final form of the field equations
20:59
Gravitational time dilation
28:16
Shell theorem (used in Gravitational time dilation)
16:16
7 Lectures | 01:49:15
Lorentz transformations as derived by Einstein
26:48
The physical meaning that Einstein attributed to Lorentz transformations
07:05
How Einstein derived the composition of velocities in SR
11:46
How the Maxwell equations in vacuum transform in inertial frames
16:41
Relativistic Doppler effect, aberration, transformation of the energy
18:30
How Einstein derives his famous equation E=mc^2
08:49
Dynamics of an accelerated charged body
19:36
15 Lectures | 03:53:28
How Einstein shows that the inverse of the metric tensor is also a tensor
03:12
How Einstein shows the invariance of the infinitesimal volume element
04:54
How Einstein derives the equation of a geodetic line
10:26
How Einstein derives the concept of covariant derivative
14:45
General Relativity: rule of differentiation of determinants
12:58
How Einstein derives the concept of covariant divergence
16:49
Other important tensor expressions derived by Einstein in his paper on General
29:47
How Einstein derives the Riemann tensor in his paper on General Relativity
11:09
How Einstein derives the field equations in the absence of matter
04:54
How Einstein derives the field equations from the variation principle
26:42
How Einstein derives the field equations in the presence of matter
26:17
How Einstein derives the energy tensor of a frictionless adiabatic fluid
10:39
How Einstein derives Maxwell equations in covariant form
33:32
How Einstein shows that his theory of GR reduces to Newtonian physics
11:56
How Einstein calculates the deflection of a light ray due to gravity
15:28
1 Lectures | 47:53
How Einstein derives his General Relativity theory from Hamilton's principle
47:53
1 Lectures | 24:23
Cosmological considerations in GR: additional term in the field equations
24:23
2 Lectures | 42:29
Relativistic correction to the orbits of planets
29:41
Calculation of the bending of light-rays due to gravity
12:48
4 Lectures | 01:15:53
Rigorous proof that the variation of Christoffel symbol is a tensor
25:25
Proof that the Christoffel symbol is not a tensor
17:11
A more rigorous derivation of the Riemann tensor
19:36
A derivation of the geodetic equation without using the Variation Principle
13:41
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