Calculus can be tough stuff. Calc AB was the first AP class I ever took in high school, and though I love the subject now, I certainly didn’t love it when I was first struggling with limits or with the chain rule for derivatives.

We’ve all been there: on a homework set or in an exam, you turn to the final page and, to your dismay, it’s a wall of text. The dreaded Word Problem. Some of the words are useful, some of them are meant to distract. Let’s look at a strategy for answering initial value word problems.

I’m writing this blog post because when I first came across Taylor series I found that a lot of my previous intuitions for mathematics were suddenly inadequate. It took time for me to build intuition not only for how these things work but why they are important. I hope this post will be illuminating for those just beginning to learn about Taylor series and also those who have some experience with them but haven’t quite wrapped their heads around them yet.

Taylor series can often seem a bit mysterious the first time that we learn about them. The formula for the Taylor series of a function f(x) around a point x=a is given by

One topic that seemed a bit mysterious and magic to me when I first learned calculus was implicit differentiation. In this post, we’ll start by reviewing some examples of implicit differentiation and then discuss why implicit differentiation works.

The symbol “dx” comes up everywhere in calculus. For example:

If you type √5 into your calculator, it’ll output something like 2.2360679775. But how did your calculator find that answer? Is there any way you could have found it by hand?

If you want help deciding whether to take Math 1 or Math 2 Subject Tests, there are a dozen websites that will guide you through the decision process. But once you’ve decided on Math 1, how do you know what to study? Chances are you’ve already been studying for the Math Section of the SAT, so you might want to know what topics you have to add. The College Board website lists the topics on the Math 1 Subject Test, but a cursory glance reveals that all of those topics also feature on the regular SAT. Yet, the two tests are not the same, and knowing the differences can help you master your Math 1 Subject Test and round out your college application. Fortunately, as an experienced tutor in both levels of Subject Test and the SAT Math Test, I’m here to help.

Probably the most common challenge that I see my students struggle with is understanding and writing out mathematical proofs. Although most higher level college math and computer science courses rely heavily on proofs, there aren’t many courses that really prepare students before they’re thrown off the deep end. I wanted to discuss some tips and tricks that’s helped my students become more comfortable with proofs, and some steps you can take to prepare yourself if you are planning on taking such a course.

Suppose that we have many towns spread across the country and we are trying to connect them with a network of roads. If we would like to do so by laying as little road as possible, how do we do it? In this blog post, we will use Calculus to tackle a special case of this optimization problem.