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 ??

**1**

# Ordinary Differential Equation ?

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#1
Members - Reputation: **279**

Posted 12 February 2013 - 12:44 PM

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#2
Crossbones+ - Reputation: **8945**

Posted 13 February 2013 - 01:10 AM

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.

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

- *Pessimal Algorithms and Simplexity Analysis*

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#3
Members - Reputation: **279**

Posted 13 February 2013 - 01:35 AM

@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 )

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, 13 February 2013 - 01:56 AM.**

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#4
Crossbones+ - Reputation: **13368**

Posted 13 February 2013 - 08:33 AM

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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#5
Members - Reputation: **279**

Posted 13 February 2013 - 08:44 AM

@Alvaro ,

It seems that I made fault :/ the course is discrete differential geometry , so why you choose ordinary differential equation if it was for mechanics ! ( I respect your choice by the way ). 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, 13 February 2013 - 08:45 AM.**

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#6
Crossbones+ - Reputation: **13368**

Posted 13 February 2013 - 09:37 AM

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#10
Members - Reputation: **971**

Posted 15 March 2013 - 10:26 AM

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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#11
Members - Reputation: **1301**

Posted 20 March 2013 - 10:49 AM

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.