Hi! Can someone explain about Differential Equations?

[Sandra Jane]

Homework Statement

What is exactly Differential Equations?

Relevant Equations

Please use general equation examples so I can understand

So I'm new to engineering and have studied some of the calculus but until now, I still have a hard time to understand what is exactly Differential Equations, what is it for and how can I use it in the future classes as an Engineering Physics student

 

[PeroK]

This site is a good reference for all things calculus:

https://tutorial.math.lamar.edu/classes/de/de.aspx

 

[256bits]

Hi there Sandra Jane.

Have you tried some sites in the internet such as an introduction to differential equations with some neat real world applications.
https://www.mathsisfun.com/calculus/differential-equations.html

and something more in depth:
https://www.geeksforgeeks.org/maths/differential-equations/

 

[berkeman]

Welcome to PF.

Differential Equations, what is it for and how can I use it in the future classes as an Engineering Physics student

You will use Differential Equations a lot in Engineering Physics. For example, you will analyze electronic circuits that have inductors and capacitors in them using Differential Equations that describe the voltages and currents and how they vary with time.

https://en.wikipedia.org/wiki/Inductor

https://en.wikipedia.org/wiki/Capacitor

 

[FactChecker]

It's an equation where the change of a variable is involved. That is very common and there are thousands of examples. Here are a couple simple ones:
1) The population, $P$, of a country changes based on birth rate, $r_{babies}$, and death rate, $r_{deaths}$. So we get an equation like $dP/dt = r_{babies}*P -r_{deaths}*P$
2) The average air temperature, $T$, changes based on the amount of sunlight, $S$. So we get an equation like $dT/dt = \lambda S$.

 

[DaveE]

https://www.khanacademy.org/math/ap.../bc-7-1/v/differential-equation-introduction?

 

[PeroK]

It may be worth noting that Newton's second law is a differential equation, as it involves the acceleration of a particle ( which is second time derivative of displacement):
$$F = ma = m\frac{d^2x}{dt^2}$$In many cases, the force is a function of displacement. E.g. in a spring or simple pendulum we have $F =-kx$, where $k$ is a positive constant. This leads to the differential equation for simple harmonic motion:
$$\frac{d^2x}{dt^2} = -\frac k m x$$That might be the first differential equation that a lot of students encounter.