How to solve PDE efficiently, and finding functions that fail the second partial derivative test
Hello. The question I want to answers with this post is, without a good intuition of when to use techniques you've learnt, how do you solve a problem efficiently? To do this I propose a framework we'll call sequential solving, which you can see in the flowchart below. You start with the simplest technique you think will work and check if it simplifies the problem. If the check fails keep repeating those steps, each time using the next simplest technique until you find a technique that simplifies the problem. Then keep repeating that whole process with your simplified problem until you reach a solution. The main benefit of this framework is that you use the simplest techniques that works, meaning you don't have spend more time than necessaire solving the problem. O bviously if you have a good intuition for which techniques to use, use your intuition. In most topics you usually have a good intuition because there's only one maybe two good ways to solve a giv