What level of Calculus am I taking?

[Oriako]

Hello,
I'm currently in Grade 12 and I am taking a course called Advanced Placement Math 31. I'm using the "Calculus: Graphical, Numerical, Algebraic" textbook written by Finney, Demana, Waits and Kennedy.

We are currently in the 7th unit and thus far have covered:
-Prerequisites for Calculus
-Limits and Continuity
-Derivatives
-Applications of Derivatives
-The Definite Integral
-Differential Equations and Mathematical Modeling.

We are currently doing Applications of Definite Integrals solving questions that involve finding the area between two functions that each require integration by substitution and integration by parts simultaneously, then spinning that object around the x-axis and finding the volume of that donut or cone shaped object.

The next units we are covering are:
-L'Hopital's Rule, Improper Integrals, and Partial Fractions
-Infinite Series
-Parametric, Vector, and Polar Functions

What curriculum does this sound like? Is this Calculus I or Calculus II, what does that mean? First-year? Second-year? A little bit of each?

I just really wanted to know what exactly I'm taking right now, because I always doubted my abilities in mathematics but currently I have a 99.91% in this course and I've really had a huge confidence boost from this.

I intend on taking Honours Astrophysics Undergraduate and then eventually completing a PhD in String Theory (Just kidding, you guys must be sick of people who read the recent Brian Greene or Michio Kaku book and are now inspired to ponder to the fundamental theories of the Universe, HAHA).

On a more serious note, I'll asses my situation if I come out of undergraduate school with a solid GPA of 3.5 or above I might be able to apply to some upper-tier graduate schools and I'll take it from there. Seem like a good plan?

 

[capandbells]

This is Calc I and II, basically. The first two courses of a first year calculus series. Congratulations on doing well. Keep it up: it only gets harder. :p

 

[jtbell]

What curriculum does this sound like? Is this Calculus I or Calculus II, what does that mean? First-year? Second-year? A little bit of each?

Tip: university web sites usually have course descriptions.

 

[Oriako]

Thanks for the response, I have the opportunity to write what is called the "Advanced Placement Exam" in May and I believe I receive some sort of university credit if I receive a 4 or higher on a scale from 1 to 5. Is anyone familiar with this system? None of the other people in my class really know either; I've tried asking.

If I do receive university credit for this course, should I start first-year university in Calculus III? Or should I essentially retake both of these courses at a university level where it undoubtedly more thorough?

I know I have a lot of questions, but after all, this is the "Academic Guidance" forum! :P

Thanks again for the help, I really do appreciate it!

 

[General_Sax]

Or should I essentially retake both of these courses at a university level where it undoubtedly more thorough?

I would say so. By the time I got to Uni I had "covered" pretty much everything in the Calc I curriculum. However, the added depth and larger combined (other classes + Calc) workload made the course more difficult than I thought it would be.

 

[jtbell]

I have the opportunity to write what is called the "Advanced Placement Exam" in May and I believe I receive some sort of university credit if I receive a 4 or higher on a scale from 1 to 5.

Many universities give credit for one or more of their calculus courses if you receive a certain score on the AP Calculus exam. Some universities don't do this. Among those that do, the required score may vary. Check the web sites of universities that you are interested in, to find out what their policies are.

 

[mathwonk]

may i suggest you read at least the first three pages of the sticky thread "who wants to be a mathematician"?

 

[Oriako]

I have read the first 5 pages or so of that topic and it seemed like you just sh!t on the high school AP Calculus course and deemed it as being useless. I don't know how much free time other people have in High School but I find it extremely challenging to have high 90s in AP Math 31, Pure Math 30, and English 30 at the same time as they are all very time consuming subjects. I generally spend my time working on the actual course, not looking into more advanced topics in my leisure time... I enjoy sleeping when I have the opportunity to.

My teacher for AP Calculus has a Math undergraduate and a masters in mathematical education, so he is very qualified. He challenges the students to actually think about what is happening and understand the mechanism and proof behind the concepts and formulas. To be honest, I was very poor at math before this course and had read quite a few books on mathematics and I've found nothing more helpful for developing my mathematical thinking and logic skills than this Calculus course.

Maybe I'm not cut out for university mathematics courses, but I have done every single problem in the book thus far and generally spend 4 hours a night, every night, on math homework.