Main Points:
Differential equations can be used to answer questions or find new information about a function when only bits and pieces of the vital information is given about the function. The solution for a differential equation is an equation that satisfies the differential equation which expresses the slope. To solve numerically a differential equation, one must be given a value for a variable in the function. Once you have this you can compute various data points and form a function that reflects that data. Finding a function for the data isn't always possible, but to check if your equation works, substitute it into both sides of the differential equation and see if they equal each other. To find the arbitrary constant of the equation you derived simply substitute in a value given to you and solve for the constant.
Challenges:
I still don't know how to find an equation that satisfies a differential equation. From what I read, it seems that we need to memorize function forms for different differential equation forms. That doesn't seem very mathematical to me. Can't we solve from scratch for the function. How did they come up with those solutions or forms for functions in the first place?
Reflections:
It seems like a great way to solve a problem when only part of the info is given, but I don't know how this can be useful when there isn't a set way to solve for an equation that works. However, I do appreciate the versatility of this method and how it can be used with different info given and in different situations.
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment