Lesson Series
A list of figures for Calculus in 5 Hours
A sequence is a function whose domain is the natural numbers and whose range is the real numbers. This lesson defines common terms and notation for a sequence.
In this lesson we define the union and intersection of two sets. A union of two sets is another set whose elements are in either of the original two sets. An intersection of two sets is another set whose elements have to be in both of the original two sets.
In this lesson we discuss a subtle point not needed by non-mathematics majors. Because we need to know the value of $f(x)$ in the domain $(a-\delta,a)\cup (a,a+\delta)$ to prove
\[
\lim_{x\to a}\,f(x)=L,
\]
the number $a$ must be inside the domain and not just in it. We define the difference between in and inside.
In this lesson we review what a functions is, important terms related to them, and provide you with a tool to graph them.
In this lesson we review the concept of a straight line and its two main features - slope and y-intercept. We discuss polynomials and provide interactive tools to graph straight lines and polynomials.
We discuss the different ways that functions can be combined.
We briefly describe differential calculus and integral calculus. We provide pictures and basic notation of both.
In this lesson we expand the idea of continuity to be more than at a single point. A function that is uniformly continuous over some interval is continuous at every point in that interval. We also show that continuous functions are uniformly continuous.
Here we cover the four most important derivatives that you will need.
The Tangent Line is a straight line at a specific point, $x_0$, whose slope is $f\,'(x_0)$ that takes on the value $f(x_0)$ at $x_0$. In this lesson we derive the formula for the tangent line given that we know the function and its derivative.
