Where to go after Differential Equations?

[guyvsdcsniper]

I am currently pursuing a Bachelors in Physics. With my current work experience, that degree will eventually allow me to reach an engineering position in Non Destructive Testing. While I enjoy the career field I believe I could do more with my degree. I personally would like to work at LHC or something I personally feel would push all forward. I know that's vague, but with that said what should I take after DE if I want to pursue a career in physics. I have the options of:PDE, Vector Calculus, Complex Analysis, Linear Algebra, Scientific Computing, Applied Dynamical Systems. I know they all may be useful to a physicist if these are offered by my college for my degree, but just wondering what everyone thinks is most important?

 

[gwnorth]

I have the options of:PDE, Vector Calculus, Complex Analysis, Linear Algebra, Scientific Computing

Those courses aren't all mandatory for your program? How did you manage to take Differential Equations without first having taken Vector Calculus and Linear Algebra?

 

[symbolipoint]

Those courses aren't all mandatory for your program? How did you manage to take Differential Equations without first having taken Vector Calculus and Linear Algebra?

Let us further ask, was that "Differential Equations" course part of a combination 'introduction to differential equations & linear algebra', which maybe often follows the Calc1-2-3 sequence?

 

[guyvsdcsniper]

Those courses aren't all mandatory for your program? How did you manage to take Differential Equations without first having taken Vector Calculus and Linear Algebra?

Well according to my Degree Works for the school I am transferring too I only need to take two of them. I am thinking that maybe since this is a liberal arts school they are taking away from math courses and making me take social science political science etc. I am not too sure tbh.

Im not sure on your second question. I am currently at a community college and they allowed me to take Calc 3 and DE at the same time.

 

[guyvsdcsniper]

Let us further ask, was that "Differential Equations" course part of a combination 'introduction to differential equations & linear algebra', which maybe often follows the Calc1-2-3 sequence?

Im currently in the DE class, it ends in August. I have not come across linear algebra yet. I can tell you I am using the book: A First Course in Dierential Equations with Modeling Applications, Eleventh Edition. According to my syllabus this what we will cover.:

First-Order Differential Equations
Modeling with First-Order Differential Equations
Higher-Order Differential Equations
Modeling with Higher-Order Differential Equations
Series Solutions of Linear Equations (Review of Power Series/Solutions About Ordinary Points)
The Laplace Transform

I do not see any mention of Linear Algebra in this textbook.

 

[Mark44]

I can tell you I am using the book: A First Course in Dierential Equations with Modeling Applications, Eleventh Edition.

Who's the author?

First-Order Differential Equations
Modeling with First-Order Differential Equations
Higher-Order Differential Equations
Modeling with Higher-Order Differential Equations
Series Solutions of Linear Equations (Review of Power Series/Solutions About Ordinary Points)
The Laplace Transform

I do not see any mention of Linear Algebra in this textbook.

Although apparently not mentioned, there are a lot of concepts from linear algebra that are prevalent in DE. The solution set of a DE is a function space (nearly identical to a vector space) that can be one-dimensional (first-order DEs), two-dimensional (second-order DEs), and so on. When you solve a DE, you're looking for a basis for the space of solutions, from which you can generate all possible solutions.

Other linear algebra concepts can be used to solve a system of DEs, including diagonalizing matrices by the use of eigenvalues and eigenvectors.

 

[vela]

Based on the title and the syllabus topics, it looks like that book was written by Dennis Zill. If this is indeed the book, it's intended for students who have completed Calc I and II.

 

[guyvsdcsniper]

Who's the author?

Although apparently not mentioned, there are a lot of concepts from linear algebra that are prevalent in DE. The solution set of a DE is a function space (nearly identical to a vector space) that can be one-dimensional (first-order DEs), two-dimensional (second-order DEs), and so on. When you solve a DE, you're looking for a basis for the space of solutions, from which you can generate all possible solutions.

Other linear algebra concepts can be used to solve a system of DEs, including diagonalizing matrices by the use of eigenvalues and eigenvectors.

Denis Zill is the author.

Interesting I wasnt aware of that.
Unfortunately, the way it is being taught to me isn't theory heavy and its more so here is how you do it so I've been finding with myself trying to find out what the meaning what were doing. That coupled with the fact that I have no background in linear algebra has a lot of things going over my head.

 

[DaveE]

I know they all may be useful to a physicist

PDE, Vector Calculus, Complex Analysis, Linear Algebra

These aren't just useful, they are essential. No good physics program in the US will let you avoid them, IMO.

 

[MidgetDwarf]

I may add, that even taking a proof writing course (the one that math majors take) can be beneficial in the long run. Since, you would be better prepared on how to read and write math proofs.

I doubled in math/physics, and being able to read/write proofs gave me a leg up over the other physics students. In terms of having a greater skill set, and not limiting myself to only math method books...

 

[gwnorth]

I am currently at a community college and they allowed me to take Calc 3 and DE at the same time.

When you asked about if you should take Vector Calculus next I assumed you meant you hadn't taken Calculus at all yet. So the Vector Calculus you refer to is Calculus IV?

Just as a comparison at my son's school in 2nd year he also had Intro to Differential Equations concurrently with Calculus III and used the same textbook you referenced. Linear Algebra I was required by the end of 2nd year but most took it in first year and then Linear Algebra II in 2nd year. There is also a 2nd year Scientific Computing requirement. Calculus IV is not required.

For 3rd year there are 2 mandatory math courses: Mathematical Physics I and II. The first will cover a bit more Linear Algebra but mostly Partial Differential Equations. The second course is majority Complex Analysis with some additional Probability and Statistics.

 

[MidgetDwarf]

When you asked about if you should take Vector Calculus next I assumed you meant you hadn't taken Calculus at all yet. So the Vector Calculus you refer to is Calculus IV?

I believe the Vector Calculus they are referring is something akin to Mardsen and Tromba: Vector Calculus. Ie., a more general stokes theorem...