Partial differential equations, or Higher geometry one?

In summary, the local university offers both partial differential equations and higher geometry I, but they are only offered at the same time. As you are likely majoring in physics, you are wondering which class would be more applicable to physics. Both classes have interesting descriptions, with PDE's focusing on initial/boundary value problems and Fourier series, and higher geometry I examining axiomatic systems and non-Euclidean hyperbolic geometry. However, PDE's are more important in physics and the geometry class may be more beneficial for pure mathematics. As a prerequisite for both classes, it is important to have taken an ODE course.
  • #1
romsofia
596
309
The local university offers both partial differential equations and higher geometry I (both of which seem equally interesting to me!), but they are only offered during the same time! As I'm most likely going to major in physics when I go to college, which class would have more applications to physics?

Higher geometry I description is:
Studies the foundations of modern geometry by examining axiomatic systems for various geometrics, with an emphasis on non-Euclidean hyperbolic geometry.

Partial differential equations description is: Infrequent. Initial/Boundary value problems for first-order, wave, heat and Laplace Equations; maximum principles; Fourier Series and applications.

Thanks for the help!
 
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  • #2
Hi romsofia! :smile:

Partial Differential Equations should be of more use to you. In fact, PDE's are very important in physics!
The geometry class looks like it is a pure mathematics class, and as such will be of less use to you...
 
  • #3
micromass said:
Hi romsofia! :smile:

Partial Differential Equations should be of more use to you. In fact, PDE's are very important in physics!
The geometry class looks like it is a pure mathematics class, and as such will be of less use to you...

Thanks for the reply, I was thinking partial differential equations would be more beneficial, but I wasn't sure :x.
 
  • #4
Just to be sure, you said that you were about to enter college. Have you taken an ODE course yet? That may be a prereq.
 
  • #5
DR13 said:
Just to be sure, you said that you were about to enter college. Have you taken an ODE course yet? That may be a prereq.

Yeah, I have the prereqs for both classes :x.
 

1. What is the difference between a partial differential equation and an ordinary differential equation?

A partial differential equation involves functions of multiple variables and their partial derivatives, while an ordinary differential equation only involves functions of one variable and its derivatives.

2. How are partial differential equations used in real-world applications?

Partial differential equations are used to model and analyze a variety of physical phenomena, such as heat transfer, fluid flow, and electromagnetic fields. They can also be used in economics, finance, and other fields to solve optimization problems.

3. What is the role of higher geometry in understanding partial differential equations?

Higher geometry, particularly differential geometry, provides a mathematical framework for understanding the geometric properties of solutions to partial differential equations. It allows for the study of curvature, volume, and other geometric quantities that are important in solving and interpreting these equations.

4. Can you provide an example of a real-world problem that can be solved using partial differential equations?

A common example is the heat equation, which models the flow of heat through a material. This equation can be used to predict the temperature distribution within an object, such as a metal rod being heated at one end.

5. Are there any limitations or challenges when using partial differential equations?

Some limitations include the difficulty in finding exact solutions for certain equations and the complexity of solving equations with nonlinear terms. Additionally, the numerical methods used to solve these equations may introduce errors and may not always accurately represent the behavior of the system being studied.

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