differential equations?

Question

what is the point of learning differential equations? I mean all my professor does is he writes the same types of problems and does the same thing over and over and I don't understand what the purpose is. I mean i know how to do these problems but what are they for. ie: first order diff., second order diff...etc...

Answer 1

I used them in several of my design classes and I know other friends of mine used them as well in some of their later coursework. Essentially, diffy-q is just there to show you how the math works and give you a basis for understanding and possibly setting up your own system. It becomes a tool you can use later in your studies (and possibly your career). Different areas of study will require solving different types of these (however, I agree that usually you end up solving the same type over and over again).

Answer 2

Your mathematics teacher's job is how, not why. Of course, some 'why's can help with motivation.

Some examples:

If a falling object is retarded by air friction, and the drag force is proportional to the square of the velocity, then...

m d²x/dt² = mg - kv², where
v = dx/dt

Those are differential equations.

If a reactor vessel contains A which is decomposing to form C, then the rates of the reaction may be given by (say)

dC/dt = k1 A - k3 C, and
dA/dt = 2 dC/dt

That is a pair of simultaneous differential equations.

The rate at which heat is transmitted by conduction is given by

Q = k A dT/dx,

another differential equation.

There are thousands more. If you learn to solve differential equations in a math class, you don't have to learn how to solve specific instances in engineering, chemistry, physics, economics, or whatever else you are interested in.

Answer 3

Ahh... I can't do them, but I'll tell you their purposes.

There are requirements for a job science or math-related. These requirements might include differential equations and if you don't learn them properly you'll lose your chance to get a job you want.

Differential equations is just a group of rates clumped together and if you learn to solve them you can get a function instead of some dumb rates.

Sometimes it is just important to understand. Interest is all you need for the purpose of learning differential equations, so even if it isn't required for a job it'll be fun to learn. If it isn't fun... perhaps you don't want a math or science-related job. So don't learn it and be a hobo if you don't want to. =D

Answer 4

dy/dx = (x^2)(8 + y) First, we separate the variables with the aid of multiplying with the aid of dx and dividing with the aid of (8 + y): dy/(8 + y) = (x^2)dx combine the two factors, remembering the left will use a organic log and the wonderful could have a persevering with: ln(8 + y) = (a million/3)x^3 + C advance e to the capacity of the two edge: 8 + y = Ae^((a million/3)x^3) Subtract 8 and we've the final kind: y = Ae^((a million/3)x^3) - 8 Now, we've the factor (0, 3), so plug those in to locate a and the particular answer: 3 = Ae^((a million/3)(0)^3) - 8 remedy for A: 11 = Ae^((a million/3)(0)) 11 = Ae^(0) A = 11 So, the particular answer is: y = 11e^((a million/3)x^3) - 8

Answer 5

Differential Equations are useful when considering 'rates of change', in a reaction scheme, or velocity/speed in mechanics.
Also finding the volume of large irregular shapes, such as the volume of a ships' hull.

Answer 6

what is the point of learning integrals, matrix, fractions, hell for that matter history?
It's all related to what you are majoring physicas and science wont help for computer major and neither for math, and math wont help the science major.


It's part the process