In taking calculus classes geared specifically towards differential equations, what can I apply these towards? Is there practical uses outside of working as a mathematician?
2007-01-22 13:20:00 · 6 answers · asked by michaelmgkdn 2 in Science & Mathematics ➔ Mathematics
Differential equations are enormously important with broad applications across a vast array of disciplines, including engineering, chemical processes, medical science, enviromental studies, economics, physics, aerospace, military planning, communications, systems technology, even movie computer animation! Differential equations help put on a mathematical and computational footing a great variety of processes that involves changes which are best decribed by continuous functions, or manifolds, which are interdependent.
2007-01-22 13:30:58 · answer #1 · answered by Scythian1950 7 · 0⤊ 0⤋
As an engineering major, I will tell that there are some actual practical uses for differential equations. It is used in fluid mechanics for determining flow rates of a incompressible liquid. This can be used in a system where there are varying diameters of pipes, pumps, and turbines etc... It is also used in engineering dynamics for a spring,mass, and damping system for determining the oscillation, amplitude, and frequency of an object. The equation is mx''+hx'+kx=f(t) for damped, forced oscillations, where m is the mass, h is the damping coefficient, and k is the spring constant. This can be applied to the suspension system of a car. It is also used in electrical circuits for RL, RC, and RLC circuits. It is used to find the current in a circuit over time. Current changes over time in these circuits so a differential equation has to be used. I won't go into more detail and bore you with it though. This can be used in any computer circuit board or electronic device. So in other words, if you're not an engineer or a mathematician- you'll never use differential equations, but there are some actual practical uses for it.
2007-01-22 13:32:19 · answer #2 · answered by C_Rock136 3 · 0⤊ 0⤋
Yes, they are very important in a lot of practical questions like finding the change of one variable when another variable is changed. Say, finding the slope of a curve, finding the rate of a chemical reaction, and anything that has to do with "differential changes". Differential calculus is used in all natural and physical sciences and you may not readily see it but it is used in business and economics also, say the rate of inflation versus prices, goods produced, etc.
I know it seems esoteric studying it now, because you are just being instructed the BASICS. It is your job to see "beyond the blackboard" to see the usefulness of differential calculus. If you are lucky, there are some professors who concentrate in explaining calculus using actual everyday problems. OR, if you start solving WORD problems in your book, you will see the different applications.
I know also that sometimes in word problems it is not obvious what the equation is. It is your job again to formulate it as opposed to just say find the derivate given d(e^x)/dx.
This is where the robots are separated from the students who use critical thinking in analysis as opposed to just memorizing a bunch of formulas.
2007-01-22 13:37:51 · answer #3 · answered by Aldo 5 · 0⤊ 0⤋
Absolutely. Differential equations are essential for understanding anything you can imagine that involves "flow" (electrical current, fluids, even space). Also, differential equations are essential for understanding any oscillating system (pendulums, planetary orbits, certain chemical reactions, any spring-driven system (such as brakes or shocks), or even the operation of the computer chipset your PC (or mac) you are using). Another example? How about the study of vibrations in solids (structural engineering)...or the wave nature of light (electrodynamics)...or the propagation of heat...
2007-01-22 13:28:03 · answer #4 · answered by mjatthebeeb 3 · 0⤊ 0⤋
dy/dx = (x^2)(8 + y) First, we separate the variables by ability of multiplying by ability of dx and dividing by ability of (8 + y): dy/(8 + y) = (x^2)dx combine the two factors, remembering the left will use a organic log and the appropriate might have a continuing: ln(8 + y) = (a million/3)x^3 + C boost e to the potential of the two component: 8 + y = Ae^((a million/3)x^3) Subtract 8 and we've the customary type: y = Ae^((a million/3)x^3) - 8 Now, we've the component (0, 3), so plug those in to discover a and the particular answer: 3 = Ae^((a million/3)(0)^3) - 8 resolve 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
2016-11-01 01:12:42 · answer #5 · answered by ? 4 · 0⤊ 0⤋
practical use as a mathematician no
but diff. equations comes up in many engineering applications like suspension, aircraft design. I use it all the time.
2007-01-22 13:40:47 · answer #6 · answered by Anonymous · 0⤊ 1⤋