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Dens
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I am taking it in a few weeks, could someone tell me which topic are generally more challenging? PDE is Partial Differential Equations.
Thank you
Thank you
Dens said:I am taking it in a few weeks, could someone tell me which topic are generally more challenging? PDE is Partial Differential Equations.
Thank you
If it's a standard first quarter/semester course for me the most difficult aspect was Fourier analysis due to the different types of convergence. I had not taken real analysis so learning about uniform, pointwise and L convergences was more challenging the rest of the material.Dens said:I am taking it in a few weeks, could someone tell me which topic are generally more challenging? PDE is Partial Differential Equations.
Thank you
clope023 said:Navier Stokes or MHD Equations are unsolvable as far as I know.
It's not like those are separate chapters in books. Convolutions comes up, heavyside functions come up and sometimes you want to take their laplace transform, the dirac delta function comes up, etc, etc. They're used, yeah.Dens said:Is the concept of "Convolution", "unit-step functions in Laplace", or "dirac delta" heavily used in PDE? It's an intro class by the way...
Dens said:Is the concept of "Convolution", "unit-step functions in Laplace", or "dirac delta" heavily used in PDE? It's an intro class by the way...
The most common type of PDE is the linear second-order PDE, which includes the popular heat, wave, and Laplace equations. These equations are used to model physical phenomena such as heat diffusion, sound waves, and electrostatics.
PDEs are difficult to solve because they involve multiple independent variables and their derivatives. This makes it challenging to find exact solutions, and numerical methods must be used instead. Additionally, PDEs can exhibit complex behavior such as shock waves and oscillatory solutions, making them even more challenging to analyze.
The answer to this question may vary, as different people may find different topics more challenging. However, one of the most difficult topics in PDE is the theory of existence and uniqueness of solutions. This theory deals with proving the existence of a solution for a given PDE and determining if it is unique.
Some common techniques used to solve PDEs include separation of variables, Fourier series, Laplace transforms, and numerical methods such as finite difference and finite element methods. These techniques allow for the transformation of the PDE into a simpler form that can be solved using algebraic or numerical methods.
PDEs have a wide range of applications in physics, engineering, and other fields. They are used to model and understand various physical phenomena, such as heat transfer, fluid dynamics, and electromagnetic fields. PDEs are also crucial in the development of new technologies, such as predicting weather patterns and designing airplane wings.