$$ \newcommand{\RR}{\mathbb{R}} \newcommand{\QQ}{\mathbb{Q}} \newcommand{\CC}{\mathbb{C}} \newcommand{\NN}{\mathbb{N}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\EE}{\mathbb{E}} \newcommand{\HH}{\mathbb{H}} \newcommand{\SO}{\operatorname{SO}} \newcommand{\dist}{\operatorname{dist}} \newcommand{\length}{\operatorname{length}} \newcommand{\uppersum}[1]{{\textstyle\sum^+_{#1}}} \newcommand{\lowersum}[1]{{\textstyle\sum^-_{#1}}} \newcommand{\upperint}[1]{{\textstyle\smallint^+_{#1}}} \newcommand{\lowerint}[1]{{\textstyle\smallint^-_{#1}}} \newcommand{\rsum}[1]{{\textstyle\sum_{#1}}} \newcommand{\partitions}[1]{\mathcal{P}_{#1}} \newcommand{\erf}{\operatorname{erf}} \newcommand{\ihat}{\hat{\imath}} \newcommand{\jhat}{\hat{\jmath}} \newcommand{\khat}{\hat{k}} \newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}} \newcommand{\smat}[1]{\left(\begin{smallmatrix}#1\end{smallmatrix}\right)} $$

HW 0

What can we learn with calculus?

Multivariable calculus is one of the essential languages we’ve developed for understanding the world around us: it underlies much of the quantitative aspects of physics and engineering, as well as biology, population dynamics (for instance, in political science), and machine learning. You’ll get the most out of a class like this if you have in mind some examples of things that you personally would like to understand someday, that may involve mathematical modeling in some way. Take this opportunity to tell me about one (or several) things you are interested in understanding someday! This will help me bring up examples that are relevant throughout the semester as well.

Lets Dust Off Our Math Brains

Its been a long summer: maybe (like me) you spent the summer doing math, but maybe you didn’t! Either way, as we jump into this next calculus course its a good opportunity to remind ourselves of some useful things we’ve learned before. Try the following problems, and feel free to read up in books / online for topics you’d like a refresher in.

Algebra

Complete the square for the quadratic \(2x^2+5x-6\) to write in the form $\(a(x-h)^2+k\)

Calculus I

What is the derivative of \(\frac{\sin(x)}{x\ln(x)}\)?

Calculus II

What is the radius of convergence of the power series below? \[\sum_{n=1}^\infty \frac{2^n x^{n}}{n}\]