Partial Differential Equations at university

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SUMMARY

The discussion centers on the challenges faced by an Erasmus student in Vienna who is required to take Partial Differential Equations (PDE) without having completed Differential Equations 1 and 2. The student's academic advisor suggested that PDE could serve as a substitute for Differential Equations 2, contingent upon a foundational understanding of Functional Analysis. The student expresses concern about their mathematical proficiency and the workload of other demanding courses, such as Abstract Algebra II and Analysis 3. The consensus is that a gradual approach to learning mathematics is essential, avoiding significant leaps in course difficulty without adequate preparation.

PREREQUISITES
  • Understanding of Functional Analysis concepts
  • Familiarity with Differential Equations 1 and 2
  • Basic knowledge of Abstract Algebra, particularly Category Theory and Galois Theory
  • Proficiency in Analysis, specifically Analysis 3 topics
NEXT STEPS
  • Study Functional Analysis to build a foundation for Partial Differential Equations
  • Review Differential Equations 1 and 2 materials to fill knowledge gaps
  • Explore resources on gradual learning strategies in mathematics
  • Consider consulting additional academic advisors for alternative course options
USEFUL FOR

Mathematics students, particularly those in exchange programs, educators advising on course selections, and anyone navigating complex mathematical curricula.

Josecanto
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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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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.
 

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