10.1 & 10.2 Intro. to differential equations, solutions to differential equations

Main points:

• Differential equation
○ Equation that is written when information about functions rate of change or its derivative is known
• Logistic differential equation
○ E.g. dP/dt = kP(L-P)
• Solution to differential equation
○ Any function that satisfies the differential equation
○ Solving numerically
○ Substituting the differential equation separately into the left and right sides of the differential equation checks the solution
○ General solution=solution that satisfies the differential equation (family of functions when C is unknown)
○ Particular solution=solution that satisfies the differential equation together with the initial condition

Challenges:

The differential equation wasn't that difficult to understand, but I am more concerned that I can myself turn worded problems into a equations. I am also not sure when the equations has a constant k. I though it would be used when the rate of change of Q (or other unit) is proportional to Q. I would like to be clarified about this point tomorrow. I am also not sure of the type of problems that require the use of a logistic differential equation, so I would like to see and example of it.

Reflection:

I found the example of net worth of a company interesting because I am planning to take accounting next semester and I am hoping there would be similar problems in the homework more. I am not sure what are all the possible application of these skills but I can imagine that for example in investing I could use this to determine the returns for different initial investments.