Thankfully, I used my knowledge of chemistry to find a better way! Are you ready for directions? There are only two steps!
1). Wipe dirt off cooktop using Windex or other ammonia based window cleaner.
2). Dampen a paper towel or cleaning cloth with a little bit of vinegar (you don't need a lot) and "shine" the cooktop by rubbing in small circles until the window cleaner residue is gone.
Just a note: you can also use vinegar that has been diluted with water. Just make sure that you only use distiller water to dilute the vinegar, though. If you use tap water, there may be minerals in the tap water that will leave behind hard water stains when you try to clean.
Would you like to know how this works? It all comes down to pH. You know... acids and bases. Vinegar is an acid, which means it reacts chemically with bases. This forms the fizzy reaction you might have seen in elementary school if you ever made a model volcano and poured vinegar (an acid) over baking soda (a base) to make the volcano "erupt." Windex is also a base. Do you know what one of the main products of an acid-base reaction (called a "neutralization reaction" by chemists) is? Pure water. As in, nothing but H2O. Essentially what you are doing when you follow my directions is using the vinegar to convert the Wimdex residue into pure water, which will evaporate without a trace.