Few basic questions about differential equations....

[awholenumber]

i have a few questions to ask about differential equations ...
how many types of differential equations are there ... ?
sometimes i like to make up themes for my studies ...
few funny things went through my head ...when i saw this thread ,How is it that mathematics describe reality so well?

i also happened to read this ...

The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is also often called the Schrödinger wave equation, and is a partial differential equation that describes how the wavefunction of a physical system evolves over time.

i was also wondering that if you learn enough differential equation , you might be able to understand things like " The Schrödinger equation " , the nature of reality ... and in the end how mathematics can describe reality so well ...

i am also looking for some advice on how to start learning differential equation properly ...??

 

[Mark44]

i have a few questions to ask about differential equations ...
how many types of differential equations are there ... ?
sometimes i like to make up themes for my studies ...
few funny things went through my head ...when i saw this thread ,How is it that mathematics describe reality so well?

i also happened to read this ...
i was also wondering that if you learn enough differential equation , you might be able to understand things like " The Schrödinger equation " , the nature of reality ... and in the end how mathematics can describe reality so well ...

i am also looking for some advice on how to start learning differential equation properly ...??

Please stop filling your posts with unrelated images. I have deleted the image you posted in this thread.

 

[awholenumber]

please can i keep that image for one last time ... i won't put anymore images after this one ...

 

[Mark44]

please can i keep that image for one last time

No. The image you posted had nothing to do with differential equations or Schrodinger's equation, and that's why I deleted it.

... i won't put anymore images after this one ...

Images that are included with posts can be helpful, but most of the images you have posted are not helpful, and just clutter it up. Apparently you get a bunch of images on your computer screen, and then take a screen shot of them all. The one you posted in this thread had two of the same images in it, neither of which had anything to do with the question you're asking.

 

[awholenumber]

i am sorry , i was just beginning to delve a bit deeper into differential equation ...

 

[bigfooted]

i am also looking for some advice on how to start learning differential equation properly ...??

Start with calculus and linear algebra, then continue with a book on ordinary differential equations like Boyce and diPrima. Avoid stuff you find on internet like handouts or movies, read a real book and make all the exercises.

 

[wrobel]

I would also give an advice. It is important to understand that differential equations do not have a habit to be integrated explicitly. So do not think that the center of this science is a skill in integrating equations. It is important to be able to integrate standard types of integrable differential equations but the main thing is the qualitative analysis of DE

 

[bigfooted]

@wrobel, do you have a suggestion for a classic textbook?

 

[wrobel]

P. Hartman Ordinary Differential Equations
M Taylor Partial Differential Equations

 

[awholenumber]

thanks for the suggestions ...

anyway i happened to read this website ... and i don't know if its the complete list ... of the types of differential equations ...??

http://www.dummies.com/how-to/content/differential-equations-for-dummies-cheat-sheet.html

To confidently solve differential equations, you need to understand how the equations are classified by order, how to distinguish between linear, separable, and exact equations, and how to identify homogenous and nonhomogeneous differential equations. Learn the method of undetermined coefficients to work out nonhomogeneous differential equations

https://i.imgsafe.org/d0e81965bc.png

https://i.imgsafe.org/d0e8bba4c9.png
https://i.imgsafe.org/d0e976536b.png
https://i.imgsafe.org/d0ea314b29.png is that all ?? or is there more ??

 

[MidgetDwarf]

@wrobel, do you have a suggestion for a classic textbook?

Boyce De Prima is a run of the mill book. I do however like Morris Terrebaun. I prefer Ross: Differential Equations. Crystal clear explanation and proofs are given. Make sure to purchase the book titled Differential Equations and not Introduction to Ordinary Differential Equations. Differential Equations is the complete book, which includes some nice theory chapter.

 

[awholenumber]

Start with calculus and linear algebra, then continue with a book on ordinary differential equations like Boyce and diPrima. Avoid stuff you find on internet like handouts or movies, read a real book and make all the exercises.

thanks a lot for the book suggestion ...

i was just trying to narrow it down to a few things after reading through some materials that was available on the internet ...

this i can sort of understand ...

first order differential equations, second order differential equations , higher order differential equations ...

i am not exactly familiar with these things ...

linear differential equations ,separable differential equations ,exact differential equations ,homogeneous differential equations ,non homogeneous differential equations, using the method of undetermined coefficients ...

i am not exactly familiar with this one too ...

partial differential equations ...

anyway thanks once again , i will try to improve whenever i get time ...

 

[jackmell]

how many types of differential equations are there ... ?

We characterize them into types like we do with integrals but the list is ultimately endless.

How is it that mathematics describe reality so well?

Mathematics is a creation of the human brain; the Earth may have revolved around the sun before mankind but the mathematical constructs of gravity, in my humble opinion, did not. And of course the human brain is a product of evolution: survival and reproductive success of the organism in the environment. Organisms adapt to their environment: when in New York, act like a New Yorker. So too with the human brain. The hominid brain evolved as a survival strategy in the world early humans found themselves in. We cannot separate the human brain from the world it evolved in. The human brain and the world are cut from the same tapestry! Why should it be such a mystery the mathematics which emerges from our minds so well conforms to the reality of the world which created that mind?

was also wondering that if you learn enough differential equation , you might be able to understand things like " The Schrödinger equation " , the nature of reality ... and in the end how mathematics can describe reality so well ...

I'll tell you my own personal experience with the matter: a long time ago I use to look outside my window and wonder why about a lot of things. About 20 years ago I started studying non-linear differential equations. I no longer wonder why about a lot of things. Not saying I know, rather, I'm simply saying I no longer wonder why. :)

 

[awholenumber]

thanks a lot for the replies ...

i was reading a website and i was learning a lot from it ...

https://www.mathsisfun.com/calculus/differential-equations.html

they have nice explanations about

differential equations ...

ordinary differential equations ...
partial differential equations ...

order ...
degree ...

linear differential equation ...
separable differential equations ...

homogeneous differential equations ...

but i was unable to find definitions for ...

exact differential equations ...

non homogeneous differential equations ...

using the method of undetermined coefficients ...

can someone help me with definitions of those?