Hi, I am a visiting student who plan to take MATH 54 next Summer in Berkeley. How much differential equation that we need to know beforehand to be successful in that class? In my university, I only learned first order differential equation (separable and linear) + Euler Method and Direction field + Its application.
https://math.berkeley.edu/courses/choosing/lowerdivcourses/math1B describes what is included in Math 1B, including the introductory differential equation material.
https://math.berkeley.edu/courses/choosing/ap-exams (the “please note” section at the bottom) lists the differential equation topics that students who skip Math 1B with a 5 on AP calculus BC should self-study before taking Math 54.
I didn’t take this class at UCB, but I was a Math student at other schools (with strong math departments) for a good half a dozen years, and from the course description, I wouldn’t worry about it too much, it looks like mostly linear algebra. Only some PDEs at the end. The course page says this:
“Transfer students who have taken such courses need to learn the relevant differential equations material (Stewart, Single Variable Calculus, Early Transcendentals, for UC Berkeley, Chapters 9 and 17) on their own, by approximately the 10th week of Math 54.”
I was TAing a Calculus II class a few years back and we had to cover Chapter 9 in Stewart. I hadn’t read the chapter before, hadn’t done ODEs or PDEs in many years so was quite rusty, and had never seen the Euler method. I taught myself everything in that chapter in an hour or 2. I think I also read through Chapter 17 pretty quickly.
I don’t know what sort of PDEs they cover. As long as it’s basic stuff and not multi-variable complex analysis type stuff (like the Dirichlet problem or the d-bar problem, etc.), I wouldn’t worry too much. That said, a summer course is going to be more intense.