- #1
bdj03001
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I'm currently taking a symmetry analysis course. It is really interesting. I would recommend it to any math major or anyone interested in ODE's and PDE'S. I am enjoying it very much.
Symmetry Analysis of Partial Differential Equations
- Thread starter bdj03001
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In summary: PDE's. It is recommended for math majors and those interested in ODE's and PDE's. Emmy Noether's theorem, discovered in 1918, also plays a role in this course. Overall, it is a fascinating subject worth exploring for anyone interested in these areas of math.
- #2
fourier jr
- 765
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is that anything like that "differential galois theory" where you look st symmetries in differential equations?
- #3
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I almost feel sorry that ever since Emmy Noether discovered the theorem in 1918,we physicists like to take a look at symmetries related to physical phenomena (and Lagrange & Hamilton actions & functions),and not to symmetries of PDE-s... 
:tongue2:
Daniel.
:tongue2: Daniel.
- #4
saltydog
Science Advisor
Homework Helper
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bdj03001 said:
Would you kindly briefly explain what this is? I'm interested in differential equations.
Thanks,
Salty
- #5
bdj03001
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dextercioby said:I almost feel sorry that ever since Emmy Noether discovered the theorem in 1918,we physicists like to take a look at symmetries related to physical phenomena (and Lagrange & Hamilton actions & functions),and not to symmetries of PDE-s...
Daniel.
This course is symmetry of PDE's
- #6
bdj03001
- 7
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fourier jr said:
Sorry I'm unfamiliar with "differential galois therory"
1. What is symmetry analysis of partial differential equations?
Symmetry analysis of partial differential equations is a mathematical method that involves identifying and exploiting the symmetries of a given partial differential equation (PDE). It allows us to reduce the number of independent variables in the equation, making it easier to solve and providing insight into the underlying physical behavior of the system.
2. Why is symmetry analysis important in studying PDEs?
Symmetry analysis is important because it helps us understand the underlying structure and behavior of PDEs. By identifying symmetries, we can simplify the equations and potentially find exact or approximate solutions. It also allows us to classify different types of PDEs and determine which techniques are most suitable for solving them.
3. What are the main techniques used in symmetry analysis of PDEs?
The main techniques used in symmetry analysis of PDEs include the Lie group method, the Lie point symmetry method, and the nonclassical method. These methods involve identifying infinitesimal generators of symmetries, using symmetry reduction techniques, and applying conservation laws to the PDEs.
4. Can symmetry analysis be applied to any type of PDE?
Yes, symmetry analysis can be applied to any type of PDE, including linear and nonlinear equations. However, the effectiveness of the methods may vary depending on the complexity of the PDE and the availability of symmetries.
5. What are some real-world applications of symmetry analysis of PDEs?
Symmetry analysis of PDEs has a wide range of applications in various fields, such as physics, engineering, and economics. It can be used to study heat conduction, fluid dynamics, elasticity, and many other physical phenomena. It is also useful in designing and optimizing systems and processes, such as in chemical reactions and control systems.
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