I want to begin studying calculus III but I am unsure if I have all of the prerequisites. I took AP Calculus BC and the calculus II things I have seen make sense.
What are the prerequisites to calculus III?
If this is multi-variable calculus, the prerequisite is a semester course of single-variable calculus in parallel with a linear algebra course
“Calculus III” is a name of a course, not a description. All it tells us is that it covers things that weren’t covered in your school’s first two calculus courses. But what was covered in those first two courses, and hence what is in this course, can vary significantly from school to school.
Your best bet is to talk to a member of the math department at your school (not the counseling department; the math department knows more about what’s actually in their classes). Failing that, can you link us to to a catalog listing, syllabus, or other information about this course?
The others have given the right answer. When I passed my BC test 20 years ago my college had a special Calc 3 course for those of us skipping the first 2. The normal Calc 3 was the stuff covered by the BC test so we took Calc 2 and they called is Calc 3 honors.
In other words it’ll depend on your school.
All I did is pass a BC course. I am a high school student, so I don’t really know how the classes are named or how they work, I just looked up calculus II and saw if I could do the problems.
Is BC calculus enough to prepare you for multivariable calculus?
Here is a fairly normal second-semester calculus course for engineers:
You can click on some of the lecture notes and see if they make sense
As others have mentioned, course titles are not completely standardized. The school I just graduated from considered calculus III to be multivariable calculus, while the school I transferred from considered it to be infinite series and conic sections. Their multivariable calculus class was calculus IV.
Also as others have mentioned, reach out to the math department of whatever school you’re interested in. Syllabi are a great way to see what they’ll teach in their courses. If you already have an idea of what you want to major in, your degree program should have a listing which will spell out course requirements and (more to the point) prerequisites for said courses. Some schools also have the option of sitting for a placement exam which will help determine which math class is best for you to start at.
Did you just pass a course or did you score a 3, 4, or 5 on the test? Passing the course doesn’t mean anything to most schools and what a passing score on the test is will depend on which college you’re going to. My school required a 4 or higher before they would give you credit.
If your school will give you credit then they will know how to place you. On the other hand you don’t have to accept the credit if you don’t feel you’ve mastered the material. Many of my friends decided to take Calc 1 despite getting AB Calc credit mainly for an easy A their first semester.
Anywhere that offers a course called “Calculus III,” the prerequisite is almost certain to be “Calculus II.”
A three-course Calculus sequence is pretty standard in most colleges and universities, but there is some variation from school to school with respect to which topics are covered in which semesters.
But, looking at the page describing AP Calulus BC, I would say that, yes, if you did master the material in AP Calculus BC, you are indeed ready for Calculus III. They say that the “College Course Equivalent” is “A first-semester college calculus course and the subsequent single-variable calculus course” (i.e. something equivalent to Calculus I and Calculus II), and the list of topics covered in AP Calculus BC looks like what you would expect to learn in Calculus I and Calculus II, and have under your belt before attempting Calculus III.
For the BC exam, I didn’t get to take it yet due to some miscommunication, but I did take an old one as practice, treated as the real thing, and got a five.
Thank you all for the help, I appreciate it. 
With another clear difference arising from whether the school has semesters or quarters. The standard engineering Calculus course at my school was four parts–but we had quarters.
FWIW, I took the Calc BC exam 25 years ago, and at the university I then attended, the class I placed into was called Calculus III. But, yeah, all those things can vary. Most schools should publish which courses you’d receive credit for with a successful score on the AP exam. If the school lists Calc I and II, then you should be able to handle Calc III.
You’re almost certain to be able to find a syllabus for a calc 3 course at any college you want. It’ll list prerequisites. Rinse and repeat for any other courses.
Occasionally you can get by without the listed prerequisites, but probably don’t worry about that too much.
Are you going to be taking it eventually? Your college might not even allow you to enroll in Calc III without having the official test result.
I was on semesters and my Calc III covered diffirential equations. Which was a 200 level course at that local state school (the Ohio State University).
I got strait A’s and could speak it like a second language at the time. Now I cypher like Jethro.
Yeah, I’ll take it next year during AP exams. My test was accidentally AB this year, so that is why I have to wait.
Look at the course description for Calc II and see if all the topics covered are familiar. If they are, you should be good to go. Also, there might be some forking here. When I was a student more years ago than I care to mention, there were two sections of the course then called Advanced Calc. One, aimed to physicists and engineers was the multivariate calculus as described above. The other section was for math majors and was an introduction to mathematical analysis, which is quite different.
But does the course cover Green’s Theory in the Plane? The name of which is one of the few things I’ve retained from second year calculus over 45 years ago.
If that’s related to Green functions, then that’s something you’d see in an advanced diffEq course, far beyond second-year calculus.