Integral Calculus Sequencing of Topics

Here is more information I have found:

1. I viewed the two leadoff videos, Introduction to integral calculus and Definite integrals intro[duction], in the first playlist, Definite integrals intro[duction], in the topic Accumulation and Riemann sums in AP Calculus AB. From a student's perspective, I definitely feel they belong in the leadoff spot in Integral Calculus.

2. After I finished the second topic in Integral Calculus, Riemann sums, I returned to the second playlist, Definite integral properties, in the first topic, Definite integrals introduction. I started with the first video, Integrating scaled version of function, which I had cut short the first time through, and continued with the rest of the material in this playlist and topic. Completing the Riemann sums topic before continuing with the rest of Definite integrals introduction was definitely a big help. From a student's perspective, Reimann sums should be done before Definite integral properties.

3. While working in the Riemann sums playlist in the Riemann sums topic, I did indeed find useful some of the additional material in the second playlist, Left & right Riemann sums, in the Accumulation and Riemann sums topic in AP Calculus AB, as preparation for the article, Riemann sums worksheet, and practice exercise, Left & right Riemann sums. In AP Calculus AB, they lead into the same practice exercise. These useful items are the video Over- and under-estimation of Riemann sums and the article Left & right Riemann sums. Again, from a student's perspective, they should be added to the Riemann sums playlist in the Riemann sums topic in Integral Calculus before the Riemann sums worksheet article and Left & right Riemann sums practice exercise.

I have more to add, but I will save this one now while I get the rest of my information ready.

This seems to be an issue at the top level, too.  The higher math courses are listed in this order:

AP Calc AB, AP Calc BC, Multivariable Calculus, Differential Equations, Linear Algebra.

But the Multivariable Calculus course presupposes knowledge of Linear Algebra.  Would be nice if it was listed earlier in the order.

Thanks for letting me know about the sequencing of Linear Algebra and Multivariable Calculus. I will keep this in mind when I am ready to take these courses.

The first time around, in college, I actually took Linear Algebra first, in 1980. I didn’t take Multivariable Calculus until after I had my degree but still wanted to take courses, about five years later.

Yeah, ditto.  I recalled enough LA to muddle through - you don't need _all_ of it, but you do need to know vector and matrix basics, and dot products and cross products and such - but for someone with no LA ever it'd be tough. 

I am learning calculus 1 and 2 and I see in diffrential and integration calculus sections are also in the 2 ap calculus sections, and in the 2 ap calculus sections are in diffrential and integration calculus so I never know what to do?

Here is some updated information. Khan Academy made major revisions to the Calculus Courses in the Summer of 2018. It appears to me that the sequencing issues with Integral Calculus have been corrected with these changes.

I’m not an educator, just someone who has been through the Khan Academy Calculus courses, but here are my recommendations with regard to what courses to take and in what sequence.

1. If you aren’t planning to take an AP exam, do Differential Calculus and then Integral Calculus. Even after you take these, you may want to look through the AP courses to see if there is any material in them that wasn’t in the courses you took.

2. If you do think you will be taking an AP exam, do either AP Calculus AB or AP Calculus BC. The latter has a little bit more material, such as polar coordinates. The individual AP courses contain both differential and integral calculus material. Even after you take one of these, you may want to look through BC if you did AB and the Differential and Integral Calculus courses regardless of which AP one you took to see if there is any material in them that wasn’t in the course you took.

3. Calculus 1 and Calculus 2 are alternate regroupings of the Differential and Integral Calculus courses. Calculus 1 goes well past the end of Differential into Integral. Calculus 2 starts with a repetition of the end of Calculus 2, leading me to think that they are meant to be a two-school-year course of study with review at the beginning of the second one as a result of students forgetting the material over the summer or other break. I believe these two may also be the revised version of Calculus, all content (2017 edition).

4. My advice is to steer clear of the 2017 editions of Differential Calculus, Integral Calculus, AP Calculus AB, AP Calculus BC, and Calculus, all content, concentrating instead on the revised courses. In particular, Integral Calculus (2017 edition) is the one in which the sequencing of topics is not done well.

5. I totally forgot about the advice I got here and began Multivariable Calculus before Linear Algebra. I finally realized, about a week after I started, that I needed more background on vectors, so I switched gears and went to Linear Algebra. I finished it o New Year’s Eve 2018 and begain Multivariable Calculus on New Year’s Day 2019. I finished the Differential part of it today (January 29, 2019) and began the Integral part today also.