Hi, Class. We’ve talked quite a bit in weeks 3 and 4 here (in particular in the Lectures and Engineering Applied Exercises) about how sometimes a mathematical model is not easily solved analytically or with software. You might wonder: where do these wildly complicated differential equations come from if they’re too complicated to solve? Well–just because an equation is difficult to solve, that doesn’t mean it was difficult to create. Often we are able to create a differential equation as the starting point, or the most intuitive mathematical description of what we observe in real world phenomenon. A good very simple example of this is the exponential growth model. We might have some familiarity with
and its appearance in things like the continuously compounded interest formula or in a basic population growth model–but familiarity isn’t the same as intuition or understanding. When we look at the differential equation, things actually make much MORE sense:
If P is population, t is time, and k is a local, observable growth rate:
Check out the equation:
This equation tell us that the population grows at a rate that is proportional to the size of the population.
That’s a pretty simple and intuitive thing to write down! However, it’s not until this differential equation is solved that it’s easily useable:
For an explanation of that solution, check out this video! https://www.youtube.com/watch?v=qPzTJeCEAiU
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.Read more
Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.Read more
Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.Read more
Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.Read more
By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.Read more