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MohammadAhmed

Ordinary Differential Equation ?

10 posts in this topic

Hello , I wanna to take this course , do you recommend this course for me ??

I am doing researches in computer graphics  ( point-based graphics ) , so what is your opinion about this course ? its gonna to help me in my research in computer graphics or not ??

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Not sure. I'd say take it if it interests you, but I don't know if it's particularly useful for computer graphics. A course in statistics with calculus (i.e. probability distribution functions, etc..) may be more relevant if you haven't taken that already. That said I'm not familiar with point-based graphics (is that point-cloud?) so take my post with a pinch of salt.

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@Bacterius ,

No I did not take probability course yet , but they told me that differential equation is very good for animation and particle effects in graphics !! , for this semmester  what is most recommended courses for computer graphics ? ( choose 2 courses smile.png

1 : Numerical methods.

 

2 : Ordinary differential equations (ODE).

 

3 : ELEMENTARY PROB. & STATISTICS .

 

4 : TOPICS IN MATHEMATICAL PHYSICS.

5 : 
ENGINEERING MATH. II .

I want to take 2 course to support me in my Computer graphics study:) 

Edited by mrmohadnan
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Differential equations are the basic language to describe mechanics. Actually Newton and Leibniz invented them precisely for that purpose.

However, I would pick 1 (numerical methods) and 3 (elementary probability and statistics) from your list. Differential equations would be my third choice.
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@Alvaro , 

It seems that I made fault :/ the course is  discrete differential geometry smile.png , so why you choose ordinary differential equation if it was for mechanics  ! ( I respect your choice by the way smile.png ). So any recommended courses more than what is  mentioned in the list !! 


any one specialized ( Master student ) in computer graphics and doing researches if you have any recommended books pls share .

Edited by mrmohadnan
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Well, if you want to render anything that moves realistically, you need mechanics. For instance, if you want to make an explosion and there will be sparkles, smoke particles and pieces of debris, you would use differential equations to describe how each of these things moves, and how the hot particles cool off. Also, if you want to have a third-person camera following the player around, you would probably use differential equations to describe how the camera moves. You can get away with a few hacks or just learning the most basic things about differential equations to get by without taking the course. That's why I made it third.
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thanks Alvaro smile.png  I will read the basic stuff about Ordinary differential equation , so any other ideas and recommended books !

Edited by mrmohadnan
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Yeah the linear algebra is the hear of computer graphics with no doubt !! , I took linear algebra course smile.png

Edited by mrmohadnan
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I also think linear algebra is very important to appreciate some of the things you'll do in course on ODEs.  I'd say the most important concept for this purpose is eigendecomposition (eigenvectors and eigenvalues) and the spectral theorem.  For instance, local equilibria of ODEs are characterized by the eigendecomposition of the Jacobian; and ODEs like the heat and wave equations are themselves solved by eigendecomposing a linear operator (the sines/cosines are its eigenvectors).

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It really depends on what kind of modeling you want to do. Like it's been said many times above, to achieve more physical realism you'll have to resort to ODEs sometime. I think taking a course on ODEs before numerical methods would probably be useful. Numerical methods are what you're going to need if you ever want to actually apply your ODE knowledge, but understanding what it is that the numerical methods are actually doing is important.

 

 

and ODEs like the heat and wave equations are themselves solved by eigendecomposing a linear operator (the sines/cosines are its eigenvectors).

Not to be too nitpicky, but as far as I remember, the heat and wave equations are second-order PDEs, not ODEs.

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