Partial Differential Equations at university

In summary, the speaker is an Erasmus student in Vienna and is struggling with having to take Partial Differential Equations without completing the prerequisite courses, Differential Equations 1 and 2. They sought advice from their coordinator and another professor who advised them to replace Differential Equations 2 with Partial Differential Equations, but the speaker is finding it difficult to understand the subject. They are also taking other challenging courses and are questioning whether they should continue with Partial Differential Equations or focus on other aspects of their Erasmus experience. They mention the importance of gradually learning math and not jumping ahead without proper preparation.
  • #1
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Hi guys,

I am a Erasmus student in Vienna. Due to the difference between the plans in my home universtity and Vienna, I have to deal with having to take Parcial differential equations without having done Differential Equations 1 or 2.

In accordance with my university, I should take here Differential Equations 1 and 2, because we have them the same year... but here they have DE 2 in the first semester und DE 1 in the second semester.

I asked for advice to my coordinator and after having discuss with another professor they say me: "yes! the best option to replace Differential Equations 2 (without havind done 1) is Parcial differential equations, you only need some Functional Analysis..." in order take in the second semester DE 1

So, that is what I am trying to do... but I am not a specially good mathematic student... and I having a bad time trying to understand the subject (that indeed it seems to be easy). I just feel like they don't care what I do or don't do... and I am thinking it's my Erasmus year so, I have to know the country, to try to master my German... I am already taking two hard subjects (Abstract Algebra II (Category theory, Sylow theorems, Galois theory...) and Analysis 3) among other 2 (one normal and one easy)...

So my question is: Should I encourage myself to do that? (and if so, what do I need to understand it, can you give me some advice?) or I have been just badly adviced by the professor... so the best I can do is to relax and say goodbye to PDE (for this year)?


Thanks for your answers!
 
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  • #2
When I did my Bsc, in my second year I took ODE 1+2, and the next year taking alongside PDE 1 also a course in Hilbert Spaces which is basically Functional Analysis 1 if you may.

It's best to learn math gradually, and not making too big jumps with courses, unless you can learn the prequisites by yourself in time.

P.S
I haven't done your programme, but these courses in undergraduate rarley differ between universities.
 

1. What are partial differential equations?

Partial differential equations are mathematical equations that involve multiple independent variables and their partial derivatives. They are used to describe the behavior of systems that change over time and space, such as heat transfer, fluid dynamics, and quantum mechanics.

2. Why are partial differential equations important in university?

Partial differential equations play a significant role in many areas of mathematics, physics, engineering, and other sciences. They provide a powerful tool for modeling and understanding complex phenomena and are essential in many advanced courses and research projects at the university level.

3. What are some common applications of partial differential equations?

Partial differential equations have numerous applications in various fields, including physics, engineering, economics, and biology. They are used to study heat transfer, wave propagation, fluid flow, population dynamics, and many other phenomena.

4. How are partial differential equations solved?

Solving partial differential equations is a complex process that involves various techniques, such as separation of variables, Fourier transforms, and numerical methods. The specific method used depends on the type of equation and its boundary conditions.

5. Are there any real-world examples of partial differential equations?

Yes, there are many real-world examples of partial differential equations. For instance, they are used to model the spread of diseases, the behavior of stock prices, and the flow of traffic in cities. They are also crucial in engineering applications, such as designing airplanes and predicting weather patterns.

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