Differential Equations Course: What to Expect & How to Prepare

[ineedhelpnow]

Hey MHB. I'm going to be taking a course on differential equations. What can I expect? Is the course harder than Calc 3? Which of the Calc classes is it most similar to? Are there certain topics I should brush up on? I'm really scared about this class and I want to make sure I do well. Thanks

~NHN

 

[Dethrone]

Well, I'm not sure what's covered in your DE course, but from what I've learned up to second order linear differential equations and all sorts of numerical DE's, it's not harder than Calc II. There are certain rules to learn, and after that it's just algebra, but you will still need to know your calculus. Although, now that I think about it, I've only had 4 lectures on DE so I could be completely wrong :(

 

[Ackbach]

I think DE's is a little harder than Calc II, actually. You need to be very up on your integration and algebra, as Rido said. DE's is integration on steroids. The difficulty with DE's is that it doesn't come across as a course that is as unified as Calc II. In Calc II, you do one thing all semester: pick a problem apart (analyze), solve the small problem, and integrate to find the whole solution. In DE's, you have one method for one kind of DE, a completely different method for an only slightly different DE, and so it goes. The existence and uniqueness theorems are, perhaps, a unifying thread, but they do not tend to be emphasized in sophomore-level courses.

It's an extremely important course, though. It's where the rubber meets the road. You get quite a few applications in Calc I, II, and III, but DE's is by far the most applied. You can solve circuits, and mass-on-spring systems, and many other real-world problems of genuine interest (you can earn money solving these!).