A Simple Request

Dear Classmates,

The purpose of this blog is to help the students of this class. I was hoping to do that by making (nearly) everyone in our class an author of this blog - someone who can make posts.

If you are able to make a post, then whenever you have a question that Prof. Newberry can't answer, or one which you thing the answer to would be helpful to others, you could post your question on the blog, and at least I will be quick to try and answer it. 

(I took calculus before, got rusty on it, and am taking this class to warm up again. I would like to put my knowledge to good use immediately, and so I made this blog.)

If you feel independent, but would like to help others, there is no reason (except shortness of time) why you can't start making posts that make statements about the math - clarifying things you think others might have trouble with.

If any of you would like to make posts, please give me your name and email address in class, and I will make sure that you are sent an email inviting you to become an author of this blog.

Thank you,

David Nemati

Advice on the Word Problems

1. It might help to glance at the text of Section 3.7 to get a bit of an idea of which rates correspond to each other.

2. Make sure you read the text of 3.8

3. Pay attention to the warning on page 185 - substituting given information for variables should only be done after all the differentiation is done.

4. Remember how Prof. Newberry mentioned that differentiating equations with x and y with respect to t would be important? That will be a big thing in this section.

Implicit Differentiation

Implicit differentiation is a valuable tool. 

When y can't be isolated without turning one equation into multiple equations, you can just take the derivative of both sides, using all the rules (Chain Rule, Product Rule, Quotient Rule, etc), without worrying about isolating y, and then isolate y'. 

It will generally be easier to isolate y' than y when implicit differentiation is necessary because y prime always appears in the numerator, and to the first power. 

The cases when implicit differentiation is necessary are generally when y is put to some power other than 1, and especially (not exclusively!) when it is locked inside a root after being added to something else.

The Chain Rule

I think the Chain Rule is just so cool. 

The Leibniz notation for it is

dy/dx = dy/du du/dx

In the book it says that these shouldn't be thought of as real quotients, but that doesn't quite make sense, because dy/dx means something like "the infinitesimal change in y divided by the corrresponding infinitesimal change in x".

Any thoughts?

Welcome to Our Class's New Blog!

Hey, Classmates,

The whim popped into my head of creating a blog for our class.

It seemed good because we would be able to share questions, and help each other with difficulties.

If you want to be able to make posts, please put your name and email address as a comment on this post, and as soon as I read your comment, I'll send you an email inviting you to be an author, and then delete your comment as a measure of safety - in case some spammers stumble across our site. Or if you don't want to risk that, hand me your email address and name in class.

To become an author, someone who is able to make posts, it will be necessary to have a Google account, but if you don't have one, don't worry, because easy instructions for how to create one are included in the link in the invitation email.

I hope this works well.

- David Nemati