These notes are a terse summary of what we’ll need from multivariable calculus. If, after reading these, some parts are still unclear, you should consult your notes or book from your multivariable calculus or ask about it at office hours. We’ve also posted a more detailed review of line integrals and Green’s theorem. You should consult that if needed. We’ve seen that complex exponentials make trigonometric functions easier to work with and give insight into many of the properties of trig functions. Similarly, we’ll eventually reformulate some mathematics into complex form. We’ll see that it’s easier to present and the main properties are more transparent in complex form.