i just finished calc 3 and really loved it and understood it. now i have to take “into to linear algebra/differential equations” and i am wondering which one is harder? do we have to think in 3-d like in calc 3? how much calculus is used? please let me know and tell me about the classes you people took. thank you
I loved Calc I, hated II, and loved both III and Linear Algebra.
I don’t even remember differential equations… but then again, I took it several decades ago.
Differential equations is the hardest math class for a typical engineering curriculum: (Calc I-III + DE’s).
I ended up with a ~91% in a class which lucky for me does not to give any pluses or minuses so I got an “A.”
I’d say differential equations is less conceptual than any of the Calculus courses and is more of a techniques based course where you get to learn the different methods to solve differential equations / systems of differential equations and apply those techniques to real life problems. The introductory level is also often single-variable for DE’s but in some cases a differential equation is modeled as a function of two variables–x and y…
Each branch of math is hard in it’s own way. I loved Calc I and Calc III. Calc II was not bad, but I liked it less than I and III. I thought linear algebra was fairly easy, but more abstract than calculus. It is more the kind of math that actual mathematicians do. Diff Eqs was not so bad either. It was similar enough to calculus that I enjoyed it.
Differential Equations, if you have a decent teacher, is pretty straightforward. If you remember integration from Cal 2, where you need to identify which technique is best to use to integrate something, differential equations is basically the same thing–try to identify/rewrite the equation to something that fits a familiar rule. There’s very few rules just like from integration, so it’s just a few things under your belt. However, occasionally things will be a page of work for just one problem, so you’ll want to buy a stack of fresh computer paper for that class, and maybe some coffee to keep you alert as you do some of the boring solving of systems of equations. A lot of times, instructors will give you tables of Laplace transforms, so the section on Laplace transforms is quite literally as easy as checking the table.
Linear Algebra–this is a tough question to answer. Are you going to be taking the proofs-based course, or an engineering applications course? If there is no distinction or only one class, you can expect it’ll be the course for math majors, so there’s going to be a few proofs in that class. The first half of the class is going to be calculation-based. So how many calculations can you do in the shortest amount of time is a good question to answer yourself. The second half, there’s no more calculations. It’s all theory-based and not very easy to visualize a lot of things. Sometimes you’ll sit there and wonder, “Why am I doing this?” There’ll probably be quite a few proofs. Not the kind of proofs from trigonometry. Proofs that involve actually writing paragraphs explaining why something is. Of course, Linear Algebra is the gateway to other math topics, so while it may seem useless at the moment, it’s actually an invaluable subject.
NOW… if you manage to get an engineering-based class, then you’re probably going to do more application than proofs, so figure out which one and you’ll be ready to prepare yourself. When I switched schools, the engineering-based class there was a joke according to some people–easy A. If it’s the proofs based course, you might want to pick up a book on proofs and read as much of it as you can before the class starts.
As a math major, I took an engineering-based course that turned into a proofs-based course mid-semester because the professor forgot his target audience I think. I was the only math major in that class, to be honest. NO ONE was prepared for the proofs that hit us. But I survived. Everyone else… Not so much.
Cal 3? I need to go and retake that. We didn’t do ANYTHING in that class, so I can’t really say for certain if those two classes are definitely harder than cal 3 since definitely for me, it was way too easy.
Taking DE’s at a community college, I had to memorize all those techniques without a cheat sheet including the Laplace table all the way through a cumulative final. Make one mistake on the problem and it becomes unsolveable / look through a bunch of work and you waste a ton of time. (professor made problem ruining mistakes writing tests too and students would have to point it out during the test).
It really depends. I loved calc I, II & III but I hated Linear algebra. I’d say look up some youtube videos or find a book and skim through it; at least for me, that helps me get an idea of what I’m about to get to (a good teacher always helps though!)
You need to talk to people at your school