# About taking ODE directly after taking 1 variable calculus

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
Staff Emeritus
Gold Member
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
Homework Helper
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".

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