# First day post

This website is your “one-stop shopping” for all matters related to our class. Please check for the post of the day every time we meet!

Here is the news from the first day:

You should have received a copy of my course policies with the instructions for WeBWorK on the other side.  If you were absent or loose them ever, they are available as pages here on this blog. (Follow the links.)

Our course textbook is available at this link (which is also in the updated course policies page): there are several formats available, including interactive graphics, which might be useful!

Here are the topics of the day: to be updated when I have time. Quick run-through now.

Antiderivatives and indefinite integrals

This should be review from MAT 1475, but also take the opportunity to think more deeply about the concepts here.

An antiderivative of a function f(x) is basically another function whose derivative is f(x). We often call the antiderivative F(x), which requires distinguishing upper-case from lower-case. It’s annoying. A better notation is to subsume all the antiderivatives into one, called the indefinite integral.

A theorem of calculus tells us that once we have one antiderivative of f(x), all the others are found by adding an arbitrary constant, called the constant of integration.

So all we need to do is to find one antiderivative F(x), and the we know that the indefinite integral of f(x) is

$\int f(x) \textrm{d}x = F(x) + C$

where $C$ is any constant.

In practice, antiderivatives are used to solve differential equations, which are equations where we do not know a function but we know one of its derivatives. In order to find out the constant or constants of integration, we need some other information, which is usually called initial values or boundary values.

Homework:

Find and deal with your City Tech email: you must use this email address in WeBWorK and to join the Piazza discussion board. Also, City Tech is already sending you emails here!

• WeBWorK has been set up for this course. The WeBWorK is here.