As part of one of my university courses, Multi-variable Calculus, I need to write a 5000 word essay on an a research question that is on the course. Before telling you what I have as an idea here are the key things that the essay should cover.
- The topic must be specific, yet have enough to it to have a research question, not a technique, and be in the 5000 word limit
- The topic of research must be connected to the Multi-Variable Calculus
Here are my thoughts so far:
- Researching surface areas of a 3+ dimentional function while estimating the function with taylor series. The problem is that this doesn't really fit with the first bit where it says that it should be a question rather then a technique
- Researching applications of multivariable calculus in differential geometry. For this bit I would need a topic in differential geometry but I have no idea which. (If someone has any knowledge of differential geometry please leave a suggestion)
- Furtherone investigating vector fields but I really don't have an idea of what a research question on this topic would look like that will be specific but also lenghty.
PS: I forgot to say that I will be expected to go over deffinitions, derivations on more complex topics and explaining example graphs.
Also just note that I am not asking for someone to hand me an essay, I am just looking for ideas/suggestions for a possible Research question
Any help will be greatly appriciated.