So this week we started to learn about separating two different variables in different equations. We also started talking about exponential growth and decay and growth rate and bacterial colonies and what not. The exponential stuff was pretty much review for me, but it is nice to go back and learn it again in case (which I am sure it will be) it is on the AP Test. The cool thing is that in AP Chemistry we are learning different things about rates and rate constants and equations and it is quite helpful to have the calculus background to help out with that. I love seeing how the two connect because it makes me feel like what I am learning is really important.
The separation of variables problems can be pretty simple but they can also be quite difficult at times. I think the hardest part for me is when there is stuff with e^() and there are variables in the exponent. I think this can be difficult because there are a bunch of properties about things in power but I can't ever remember them. I do know that if something is being added in the exponent, you can separate the two and then multiply them together. You can also do the opposite: if two things have the same base, you can write the bases as one and add the two different powers together. Then there is the whole thing where if there is a variable in the exponent of e, you have to take the natural log of both sides. Or if a variable has a natural log in front of it, you have to raise both sides to the e power. This is also another thing that we have to do in AP Chemistry quite often which is pretty helpful.
Once again, we have problems that require prior knowledge, which is something that I quite enjoy about calculus. Since the separation of variables problems are derivatives, you have to be able to antiderive. Even though this is something we have been doing quite some time, it can still be pretty difficult. But I feel like since we do some of the same things so often, my skills improve greatly each time, which in turn makes it not so difficult. The fact that we continue to take derivatives and continue to antiderive, I am finally starting to have properties memorized and not have to look up how to do it and not struggle so much on trying to remember how to do what part of the problem, which is really nice.
The separation of variables problems can be pretty simple but they can also be quite difficult at times. I think the hardest part for me is when there is stuff with e^() and there are variables in the exponent. I think this can be difficult because there are a bunch of properties about things in power but I can't ever remember them. I do know that if something is being added in the exponent, you can separate the two and then multiply them together. You can also do the opposite: if two things have the same base, you can write the bases as one and add the two different powers together. Then there is the whole thing where if there is a variable in the exponent of e, you have to take the natural log of both sides. Or if a variable has a natural log in front of it, you have to raise both sides to the e power. This is also another thing that we have to do in AP Chemistry quite often which is pretty helpful.
Once again, we have problems that require prior knowledge, which is something that I quite enjoy about calculus. Since the separation of variables problems are derivatives, you have to be able to antiderive. Even though this is something we have been doing quite some time, it can still be pretty difficult. But I feel like since we do some of the same things so often, my skills improve greatly each time, which in turn makes it not so difficult. The fact that we continue to take derivatives and continue to antiderive, I am finally starting to have properties memorized and not have to look up how to do it and not struggle so much on trying to remember how to do what part of the problem, which is really nice.