I have to take diff eq this coming semester, and I just want to know if diff eq is more like calc 3 (computational) or linear algebra (abstract) in nature.
I had no trouble with calc 3, but I HATED linear algebra. Matrix computations, transformations, etc. were fine and I got those easily; it’s when we got to vector spaces and spans and dimensions that totally threw me off.
What should I expect?
When I took Diff EQ (5 years ago), it was almost all calculations. Almost no proofs. The only overlap it had with linear algebra (for me) was the two or three sections that were eigenvalues and eigenvectors. However, my department renamed the course a few years after I finished to “Differential Equations with Linear Algebra.” Not all math departments have the exact same topics for any given math course. I would recommend looking up the course description and syllabus for the course.
I had a friend taking lin alg with me and diff eq at the same time. Like @SadHippo says, it’s calculation heavy and the only overlap with lin alg was with eigenvalues/vectors.
I hear it’s not as hard as Calc 3 (multi), but it can get hard and there’s a certain ‘quirk’ to each problem; if you don’t understand how to approach the problem, you’ll be lost, but if you get how to approach it the question becomes easy work.
It all really depends on your professor. My prof had us doing stuff with spans, basis, vector spaces, and linear mappings. That being said the actual differential equations part of the class was basically just straight forward calculations.