One of the most important mathematical object is a function, which you can think of as a machine that converts inputs into outputs. Often we study functions whose inputs and outputs are both real numbers; you would give such a function an input $x$, and it would convert that into some output $y$. Your pre-calculus mathematical life has been filled with lots of different functions: polynomials, trigonometric functions, exponential functions and more. Up to this point, the key question about a function has been to how it turns inputs into outputs, and how one can visualize this process. Calculus, on the other hand, works to understand functions even more deeply, focusing not just on where a function is at a particular point, but where the function seems to be going as it approaches a given input. In calculus we call this a limit, and its the key idea that allows us to uncover a wealth of information about the function. How much information? Well, Math 115 is the first class in a three-course calculus sequence, so suffice it to say that there's plenty to flesh out this narrative.

In Math 115 we will introduce the two key motivating problems in calculus. The first of these problems asks how we can find the equation of the line tangent to the graph of a given function. Happily, there are concrete geometric ideas that motivate the solution to this problem, and we will have the chance to use limits as a tool for answering the so-called "tangent line problem." In addition to exploring limits in a handful of contexts, we'll see how this notion of "derivative" can be used to create a new function from our original function, and we'll explore how these two functions --- a function and its derivative --- are related to each other. We then spend a number of days developing standard rules for differentiation, after which we apply the derivative to answer a handful of questions that are of real world importance. Perhaps most famously, derivatives can be used to find maximum and minimum values of functions.

The last part of the class has us asking the second major question in calculus: how does one find the area underneath the graph of a particular function? We'll come up with a way to answer this question that also requires limits. The punchline to the course is that these two seemingly disparate problems --- finding tangent lines and computing area under a curve --- are actually two sides of the same coin. This is made precise in the so-called Fundamental Theorem of Calculus, and we'll put this theory to good use at the close of the course.

Course Instructor

The professor for this class is Andy Schultz. His office is on the fourth floor of the Science Center, room W408. You are highly encouraged to attend office hours, and you never need an appointment to do so. Office hours will typically be held in or just outside my office, and are held at the following times: Mondays from 2-3; Wednesdays from 10:30-11:20; (some) Thursdays from 12:45-2:00 (see the syllabus for known exceptions) Thursdays from 8:45-9:45; and Fridays from 11:45-1:30. If these office hours don't fit with your schedule, contact the instructor so that we can set up an appointment to help you outside of office hours.

You can contact the instructor at . Though he is always happy to receive emails from you with questions or concerns about the course, he can't guarantee that he'll be able to promptly reply to emails late at night or over the weekend. If you do contact the professor by email, please be sure to follow standard email etiquette. In particular, please make sure you include a greeting and signature and avoid abbreviations. If you're contacting him to ask about a problem, please be sure to specify what the problem asks (as opposed to asking something like "I can't get problem 2 and need your help").