Diff. Equations or Linear Algebra

In summary, the conversation discusses whether to take Ordinary Differential Equations or Linear Algebra in summer school. It is mentioned that Linear Algebra is necessary for learning Differential Equations, but some argue that topics such as eigenvalues and linear independence can be learned without much difficulty. Both courses are important in pure math and its applications, with ODE involving integration and derivation while Linear Algebra focuses on the study of structure. It is recommended to take Linear Algebra first before ODE to gain a better perspective, intuition, and insight. However, it is noted that some teachers may incorporate linear algebra concepts into ODEs. The difficulty of both courses varies from person to person.
  • #1
calCOOLus
1
0
Hello All,

First post here. I going to be taking summer school to get some classes out of the way and am deciding whether or not to take Ordinary Diff. Eqn's or Linear Algebra.

Any help would be appreciated on the difficulty of the courses and what is covered.
Thanks in advance.
 
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  • #2
You need to know Linear Algebra in order to learn Differential Equations so take Linear Algebra first.
 
  • #3
Hercuflea said:
You need to know Linear Algebra in order to learn Differential Equations so take Linear Algebra first.

This is not true for most ODE classes (I would check with your professors). Sure, Linear Algebra is useful to know, but topics such as eigenvalues and linear independence can be picked up without much trouble.

Both are very important in pure math as well it's applications, so it really depends on your interests. ODE will feel very similar to Calculus because you are integrating and deriving, while Linear Algebra will rarely require calculus. Because Algebra is often characterized as the study of structure, you will study "larger" (in some sense) sets of vectors in Linear Algebra. ODE will develop and study specific techniques for specific functions.
 
  • #4
hsetennis said:
This is not true for most ODE classes (I would check with your professors). Sure, Linear Algebra is useful to know, but topics such as eigenvalues and linear independence can be picked up without much trouble.

Both are very important in pure math as well it's applications, so it really depends on your interests. ODE will feel very similar to Calculus because you are integrating and deriving, while Linear Algebra will rarely require calculus. Because Algebra is often characterized as the study of structure, you will study "larger" (in some sense) sets of vectors in Linear Algebra. ODE will develop and study specific techniques for specific functions.

^ This.

Pretty much sums it up; however, if I were you I'd go ahead and take ODE.
 
  • #5
I highly recommend taking linear algebra before taking multivariable calculus or ODE. I think that you will have a better perspective in this two courses by learning linear algebra first. That has been my experience. Knowing about vector spaces, spanning sets and bases, etc. before ODE can help with developing additional insight and intuition when learning ODE. Sure, you can learn ODE without linear algebra; but I think you will get more out of it knowing linear algebra than not.
 
  • #6
Hercuflea said:
You need to know Linear Algebra in order to learn Differential Equations so take Linear Algebra first.

I'm currently enrolled in Differential Equations and have never taken Linear Algebra. However, my teacher has explained all of the linear algebra tricks we'd need to know (specifically matrix math and eigenvectors and values)
 
  • #7
I'd say that while you don't need linear algebra for ODEs, I'd still take it first. That way, when you do take ODEs, you'll be ahead of the class.

In terms of difficulty, linear algebra is pretty easy. DEs vary from person to person. I found them incredibly easy, but some people think they are difficult.
 

1. What is the difference between a differential equation and a linear algebra equation?

A differential equation involves the derivative of a function, while a linear algebra equation involves a system of linear equations. Differential equations often model physical systems, while linear algebra equations involve finding solutions to a set of linear equations.

2. How are differential equations and linear algebra used in real-world applications?

Differential equations are used to model the behavior of systems in physics, engineering, and economics. Linear algebra is used to solve systems of equations and can be applied in fields such as data analysis, computer graphics, and cryptography.

3. What are the different types of differential equations?

There are several types of differential equations, including ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). ODEs involve one independent variable, while PDEs involve multiple independent variables. SDEs involve randomness and uncertainty.

4. How do you solve a system of linear equations?

To solve a system of linear equations, you can use methods such as elimination, substitution, or matrix operations. These methods involve manipulating the equations to isolate the variables and find their values.

5. What are the applications of eigenvalues and eigenvectors in linear algebra?

Eigenvalues and eigenvectors are used to analyze the behavior of linear transformations and systems of differential equations. They are also used in data analysis, image processing, and quantum mechanics.

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