Is Advanced Calculus Necessary for Success in PDE?

In summary, the conversation discusses whether taking advanced calculus is necessary for success in PDE. The speaker states that they are not required to take advanced calculus for their applied math major, but they have already taken an intro to proofs course which covered some advanced calculus topics. They are now questioning whether this is enough for success in PDE. They also mention potential drawbacks of taking an additional analysis course. Ultimately, it depends on the individual's definition of success and their future academic goals.
  • #1
lion0001
21
0
Is Advanced calculus absolutely necessary in order to succeed in PDE ?
The problem is that my school does not require me to take Adv Calculus since i am an applied math major , i am not even required to take a proof based course here's the link for the major ( http://w3.fiu.edu/math/html/urmath.htm ),
but i took intro to proofs anyways , i just finished it, the course included several proof methods, induction, strong induction, infinite sets, and then the first 2 chapters of Adv. Calculus, i covered : sequences , including cauchy sequences , and limits, using delta epsilon proofs.
after intro to proofs follows Adv. Calculus which begans with the 3rd chapter
Here is the description for MAP4401 ( PDE) http://w3.fiu.edu/math/html/ucourses.htm#MAP4401
Do you guys think this is enough ?
You probably say , take analysis , but here is the problem

1) taking analysis would delay my graduation by 1 year( since this is only offered once a year
2) i am not required to take it , but another professor told me that " having a knowledge of advanced calculus would help " by that he meant the whole course in adv. calculus or the stuff i covered in my intro to proofs class

i would like to hear your thoughts
 
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  • #2
Depends on what you mean by succeeding. Do you just want to know how to solve some basic PDEs or do you want to go to grad school?

I think the most obvious answer is that your school's graduate PDE class requires the undergraduate advanced calculus class.
 

What is the purpose of "Analysis, then PDE"?

"Analysis, then PDE" is a mathematical framework used to study partial differential equations (PDEs). It combines tools from mathematical analysis and functional analysis to solve complex PDEs that arise in various fields such as physics, engineering, and economics.

What is the difference between "Analysis, then PDE" and "PDE, then Analysis"?

The order of the words "Analysis" and "PDE" in the phrase refers to the order in which these two branches of mathematics are applied. In "Analysis, then PDE", one first uses tools from mathematical analysis to understand the behavior of functions and then applies this knowledge to solve PDEs. In "PDE, then Analysis", one first solves the PDE and then uses tools from mathematical analysis to study the solutions obtained.

What are some examples of problems that can be solved using "Analysis, then PDE"?

Some examples include heat and wave equations, fluid dynamics, and quantum mechanics. These problems are often described by PDEs, and the techniques of "Analysis, then PDE" can be used to obtain solutions and understand their behavior.

What are some common techniques used in "Analysis, then PDE"?

Some common techniques include Fourier analysis, Sobolev spaces, and variational methods. These tools allow for the rigorous study of functions and their properties, which are essential for solving PDEs.

What are the applications of "Analysis, then PDE" in real-world problems?

"Analysis, then PDE" has a wide range of applications in various fields such as physics, engineering, and economics. It can be used to model and solve problems involving heat transfer, fluid flow, and quantum mechanics, among others. These applications have significant implications in understanding and predicting real-world phenomena.

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