Partial Diff. equations & Differential Geometry?

In summary, the conversation discusses the speaker's dilemma of choosing between two mathematics classes for their last semester at university, as they are pursuing a combined Mathematics & Physics major. The speaker expresses a preference for physics, but the two available classes are in mathematics. They mention that Partial Differential Equations (PDEs) are important for physics, particularly in the study of General Relativity. The speaker also considers taking other physics classes, such as electronics, atomic & nuclear physics, optics, and topology, but the other person in the conversation suggests that PDEs are essential for an undergraduate physics degree and will also be covered in a graduate course on General Relativity.
  • #1
Libohove90
41
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I have two classes that I think I can fit in on my last semester at university.

I am doing the combined Mathematics & Physics major. I am more interested in physics. However, the two classes I can fit, happen to be mathematics classes. PDE's seem like they are very useful for physics and differential geometry excites me becuz it's the first class where I will learn the mathematics of General Relativity.

What do you think? Or perhaps should I take electronics, atomic & nuclear physics, optics, topology I...etc.
 
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  • #2
I believe that Partial Differential Equations is of the most importance to learn in an Undergraduate Physics Degree, it is used throughout every subject in Physics and even General Relativity. Assuming that you are going to get a graduate degree it is necessary that you have an understanding of Partial Differential Equations for Quantum Mechanics, Quantum Field Theory and virtually every subject. Universities usually have General Relativity as a course in a graduate degree and you'll learn Differential Geometry in that course.
 

FAQ: Partial Diff. equations & Differential Geometry?

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

Partial differential equations involve multiple independent variables, whereas ordinary differential equations only involve one independent variable. Additionally, partial differential equations involve partial derivatives, while ordinary differential equations involve ordinary derivatives.

How are partial differential equations used in physics and engineering?

Partial differential equations are used to describe physical systems and phenomena that involve multiple independent variables. They are commonly used in fields such as fluid mechanics, electromagnetism, and quantum mechanics to model and predict complex behaviors and interactions.

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

Differential geometry provides the mathematical framework for studying and solving partial differential equations. It involves the study of curved surfaces and manifolds, which are often used to represent the domains of solutions to partial differential equations.

4. What is the significance of boundary conditions in solving partial differential equations?

Boundary conditions are essential in determining a unique solution to a partial differential equation. They specify the behavior of the solution at the boundaries of the domain and help to narrow down the possible solutions to the equation.

5. Can partial differential equations be solved analytically?

Some partial differential equations can be solved analytically, meaning a closed-form solution can be obtained. However, many equations are too complex and require numerical methods to approximate a solution. Additionally, some equations may not have a solution at all.

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