Elementary differential equations

In summary, the conversation involves discussing whether it is necessary to take another math course, such as multivariable calculus or linear algebra, before taking an introductory course in elementary differential equations. It is suggested to have knowledge of linear algebra before taking differential equations as it can be useful in solving systems of linear differential equations. However, it is also mentioned that a stand-alone introductory course in diff.eq's is enough to occupy someone during the summer. Ultimately, it is decided that taking the introductory course in differential equations during the summer is the best option.
  • #1
GCT
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I plan to take the course elementary differential equations during the summer period, however I have experience up till integral calculus, which I just completed. Would anyone here advise another class should be taken before differential equations (such as multivariable calculus) or that it is too early for me to take the course? I would appreciate your comments.
 
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  • #2
At ASU and from what I've seen, to get a comprehensive view of DE's you need up to calc 3 (multivariable and vector calculus).
 
  • #3
You will typically meet only ordinary diff.eq's in an intro course, so multi-variable calculus isn't too relevant in this context (it's not useless of course, but..) .
However, if you haven't had linear algebra yet, I'd recommend you to take a course in that instead.
 
  • #4
That doesn't sound good...do you know of any introductory versions of the course (I believe ours is called elementary differential equations), perhaps your's is a more intense version for physicists and engineers.
 
  • #5
M MAT 274 Elementary Differential Equations. (3)
fall and spring or summer
Introduces ordinary differential equations, adapted to the needs of students in engineering and the sciences. Credit is allowed for only MAT 274 or 275 toward a mathematics degree. Prerequisites: MAT 271 (or its equivalent); MAT 272 (or its equivalent) recommended.

271 is calc II, 272 is calc III. It then goes on to 275 for Modern DE.
The next DE class is 400 level.
 
  • #6
You will typically meet only ordinary diff.eq's in an intro course, so multi-variable calculus isn't too relevant in this context (it's not useless of course, but..) .
However, if you haven't had linear algebra yet, I'd recommend you to take a course in that instead.

Really, so it would be fine to take linear algebra right after integral calculus? Why linear algebra before differential equations?
 
  • #7
Because, for example, to solve systems of linear differential equations, knowledge of the behaviour of matrices and vectors is very useful (for example the concept of eigenvectors/values).
You still have only one independent variable (hence, you're in ODE's and not PDE's), but your solution is a vector function.
 
  • #8
M MAT 274 Elementary Differential Equations. (3)
fall and spring or summer
Introduces ordinary differential equations, adapted to the needs of students in engineering and the sciences. Credit is allowed for only MAT 274 or 275 toward a mathematics degree. Prerequisites: MAT 271 (or its equivalent); MAT 272 (or its equivalent) recommended.

271 is calc II, 272 is calc III. It then goes on to 275 for Modern DE.
The next DE class is 400 level.

hmm...I was hoping to get acquainted with differential equations early since a lot of it seems useful towards understanding chemistry phenomenas in detail, I guess I'll have to ask the professor to be sure.

I'll have to peruse through a linear algebra text to see which is more useful, and which would be better to learn early on.
 
  • #9
I'm not saying that multi-variable calculus is useless; it's absolutely crucial later on.
However, my response was made as it was because it seemed to me that this would be your very first meeting with diff.eq's; quite soon thereafter, linear algebra techniques will be used.
 
  • #10
Because, for example, to solve systems of linear differential equations, knowledge of the behaviour of matrices and vectors is very useful (for example the concept of eigenvectors/values).
You still have only one independent variable (hence, you're in ODE's and not PDE's), but your solution is a vector function.

ahh, I see. So a lot of linear algebra has to do with vectors? Don't you think that it would be better to take linear algebra during the regular semester rather than the summer?

I had my eye on differential equations, since it seemed to involve a heavy application of calculus and integral calculus, rather than learning relatively new material associated with linear algebra.
 
  • #11
GCT said:
ahh, I see. So a lot of linear algebra has to do with vectors? Don't you think that it would be better to take linear algebra during the regular semester rather than the summer?

I had my eye on differential equations, since it seemed to involve a heavy application of calculus and integral calculus, rather than learning relatively new material associated with linear algebra.

True enough; there's a lot to cover if you were to cram everything into the summer...
In that case, I think a "stand-alone" intro course in diff.eq's is more than enough to occupy you during the summer.
 
  • #12
Im interested in learning diff eq this summer also. I'll be abroad for a month and don't think I can go that long without math :eek:
 
  • #13
True enough; there's a lot to cover if you were to cram everything into the summer...
In that case, I think a "stand-alone" intro course in diff.eq's is more than enough to occupy you during the summer.

Alright, so differential equations it is...thanks for your help.
 

1. What are elementary differential equations?

Elementary differential equations are mathematical equations that involve an unknown function and its derivatives. They are used to model various physical phenomena and are commonly used in fields such as physics, engineering, and economics.

2. What is the difference between ordinary and partial differential equations?

Ordinary differential equations involve a single independent variable, while partial differential equations involve multiple independent variables. The unknown function in ordinary differential equations depends on only one variable, while in partial differential equations, it depends on multiple variables.

3. How are differential equations solved?

Differential equations can be solved analytically or numerically. Analytical solutions involve finding the exact solution using mathematical techniques such as separation of variables or substitution. Numerical solutions involve using computational methods to approximate the solution.

4. What are the applications of differential equations?

Differential equations are used to model and understand a wide range of phenomena in various fields such as physics, engineering, biology, economics, and more. They are especially useful in predicting and analyzing the behavior of systems over time.

5. What are initial value problems and boundary value problems in differential equations?

An initial value problem is a type of differential equation where the value of the unknown function and its derivatives are known at a specific point. A boundary value problem is a type of differential equation where the values of the unknown function and its derivatives are known at multiple points. These types of problems are often used to determine the specific solution to a differential equation.

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