About taking ODE directly after taking 1 variable calculus

[E-Conservation]

This is my first time posting in this forum, I am not very familiar with the rules.

I am a year 1 physics student, and I had only taken 1 variable calculus( I also know some basic linear algebra, e.g. how to calculate eigenvector in 2x2 situation, don't know Gram–Schmidt process for orthonormalising vectors) . The syllabus is the following


Limits, derivatives, linear approximation, curve sketching, L’Hospital’s rule, techniques of integration

Because physics need a lot of knowledge of ODE, I am planning to register ODE course from the maths department. The syllabus is the following:

methods of explicit solution, linear equations and systems, series solutions, Sturm-Liouville boundary value problems, dynamical systems and stability, applications to mechanics, electrical networks and population of species.

Can you guys give me some advice that, if I have the foundation to take this course. What further mathematics I have to learn before ODE?

 

[Integral]

As long as you are familiar with integration it should not be a problem.

 

[MarneMath]

Well, if the course plans to cover series solution, then it probably would benefit you to already know it thus know calculus II already. So if you're not comfortable with integration by parts, trig sub, partial fractions, along with series, then it might be to much for you to learn at once. However, if you understand all that, then you shouldn't have an issue.

 

[HallsofIvy]

There's a lot more to differential equations than integration. First order "exact equations" require concepts form multivariable Calculus. usually covered in Calculus II or III. Linear differential equations, one of the simplest kinds of equations, require concepts from Linear Algebra. It is possible to pick up those concepts "on the fly" but you will be struggling and possibly not grasp the ideas behind the "methods".

 

[E-Conservation]

HallsofIvy: I have also learned some multivariable Calculus, only differentiation, not integration. Do I need to study multivariable integration before taking ODE?

Thank all of you for the advices.

 

[HallsofIvy]

Have you dealt with "exact differentials" and "integrating factors"? Have you dealt with integrating things like f(x,y,z)dx+ g(x,y,z)dy+ h(x,y,z)dz along a path? Those are important in rather basic first order differential equations. And, while it is possible to deal with "linear differential equations", a major topic in introductory differential equations without having taken Linear Algebra, you will miss much of the theory behind it.

 

[CosmicKitten]

You should be fine, I only brushed up a bit on calc II & III before studying ODEs on my own, having only finished calc I in college before leaving. Calc III is easy, just a three dimensional extension of calc I with a little linear algebra and vectors thrown in (I think? Not sure about the syllabus in a formal class) and calc II is mostly integration formulae that can be picked up while solving many ODE problems. I think you get a better understanding and thus better incentive to remember by reinforcing these simple concepts with harder ones as opposed to mere mindless repetition. Also, you will get a lot of algebra I quadratic formula practice just from working the solutions to second order linear diff. equations.