few questions for maths related programming ... ??

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07-03-2016
delta

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few questions for maths related programming ... ??

i was trying to learn programming for differential equations ...

i was able to come up with a simple example for differential equation ...

Quote:

The (standard) calculus is broken into two pieces.

i) Differential calculus - which is looking at the instantaneous rates of change of objects with respect to some variables. We have the notion of the derivative of a function.
ii) Integral calculus - which is calculating the area under curves, calculating volumes and so on. This is all given in terms if the (indefinite or definite) integral of a function.

The two notions are tied together via the fundamental theorem of calculus. This says that the derivative and indefinite integral are basically mutual inverses (but not quite)

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Quote:

An equation containing the derivatives of one or more dependent variables, with respect to one of more independent variables, is said to be a differential equation

i have a few doubts about declaring f(x) ... theta , d^2y/dx^2 ...

then i saw this page on the internet .. i do not have this book ...

Attachment 14842

could somebody please tell me the right methods to declare

f(x) ... theta , d^2y/dx^2 ...

??
07-03-2016
CodeSlapper

Developing differential equations is going to be a very involved process. The example purposely choose a simple function to mimic.

You might have luck looking for a differential equation library out there or unless you want to code this up, you can keep searching for the source code of differential equation library.
07-03-2016
Epy

http://labs.freehackers.org/projects/symia/wiki
07-04-2016
delta

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Quote:

Originally Posted by CodeSlapper

Developing differential equations is going to be a very involved process. The example purposely choose a simple function to mimic.

You might have luck looking for a differential equation library out there or unless you want to code this up, you can keep searching for the source code of differential equation library.

thanks .. there seems to be many types of differential equations ...

Quote:

first order differential equations
second order differential equations
higher order differential equations ...
linear differential equations
separable differential equations
exact differential equations
homogeneous differential equations
non homogeneous differential equations
using the method of undetermined coefficients ...
partial differential equations ...

i am also familiar with some numerical methods associated with solving differential equations ...

Quote:

Solution by Taylor's series
Picard's method of successive approximations
Euler's method
Modified Euler's Method
Runge-Kutta method
Predictor-Corrector Methods
Adams-Moulton Method
Milne's method

and i also found this really good definition of differential equation ...

Quote:

An equation containing the derivatives of one or more dependent variables, with respect to one or more independent variables, is said to be a differential equation

but my problem right now is that i am confused with the terms like ,
dependent variables and independent variables in an equation ...

once i have a clear understanding of that i can move to solving a not so hard looking equation like this one ...

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i also have confusions about declaring

f(x) ... theta , d^2y/dx^2 , (dy/dx)^3... properly in a programming language like c ...

Quote:

Originally Posted by Epy

http://labs.freehackers.org/projects/symia/wiki

looks a bit more advanced to me ...

also looks a bit more complicated than the programming language itself that i am familiar with ...

thanks for sharing ...

but ,let me see if i can solve this with the familiar c programming language itself ...
07-04-2016
ddutch

You might have a look at Numerial Recipes in C.

It is a standard work and you have to pay for it.
You can get a free guest account and thus get limited access or you can get free access to their older editions (http://apps.nrbook.com/c/index.html).
07-04-2016
CodeSlapper

If you are having trouble understanding differential equations I would start from there. There is usually entire college courses dedicated to them and the only real world application I ever used them in was with circuits.

You can't do real differentiating on a computer but you can get a really good approximation. From what I've read on the web numerical recipes is a good book but has issues with copyright.
07-04-2016
delta

Quote:

Originally Posted by ddutch

You might have a look at Numerial Recipes in C.

It is a standard work and you have to pay for it.
You can get a free guest account and thus get limited access or you can get free access to their older editions (http://apps.nrbook.com/c/index.html).

i have gone through that book before somehow ... that was some time ago .... but the book lacks some sort of order ...

i was trying to follow these two instead ...

for some understanding of the overall mathematics , before trying to do programming ...

http://www.universityofcalicut.info/...al_methods.pdf

for programming some maths related things , i would recommend this book ...

Computer Fundamentals and Programming in C - J.B. Dixit

Quote:

Originally Posted by CodeSlapper

If you are having trouble understanding differential equations I would start from there. There is usually entire college courses dedicated to them and the only real world application I ever used them in was with circuits.

You can't do real differentiating on a computer but you can get a really good approximation. From what I've read on the web numerical recipes is a good book but has issues with copyright.

yes i should try to improve my maths a little bit more ...before i try to program .. because i have some doubts still left about some basic operations like separation of variables ...

may i ask what sort of differential equations are involved in circuits ??

when you mean circuits ... do you mean things like micro controllers ??

then is it also about things like generating waves ??
07-04-2016
Tien Nguyen

From what I remember of Calculus (I'm not sure of Differential Equation) it is like Sum to infinity, Area under a curve, etc. That is not too hard to do in Borland Turbo C 2.01. The only problem is it is going to be a close approximation like someone said. First you find the formula for the curve you need. Then you add an area of a section until it completes the curve. That is the approximation.
07-04-2016
rstanley

Quote:

Originally Posted by Tien Nguyen

... That is not too hard to do in Borland Turbo C 2.01. ...

You keep mentioning this extremely outdated C compiler first released on 11-May-1989! I doubt that it even fully implements the C Programming Standard, C89/90, let alone C99 or C11, plus it contains non-standard functions, such as those provided by conio.h, VERY Windows specific, and should NOT be used, period.

There are many more modern compilers available:

Cygwin (My Recommendation)
MinGW
Pelles

In addition to these three excellent choices, other free C compilers are listed here.

Time to move up to one of these free compilers.
07-04-2016
delta

3 Attachment(s)

Quote:

Originally Posted by Tien Nguyen

From what I remember of Calculus (I'm not sure of Differential Equation) it is like Sum to infinity, Area under a curve, etc. That is not too hard to do in Borland Turbo C 2.01. The only problem is it is going to be a close approximation like someone said. First you find the formula for the curve you need. Then you add an area of a section until it completes the curve. That is the approximation.

well its something like this ...

Quote:

for example , for a polynomial ...

a solution of a polynomial equation is also called a root of the polynomial ...

a value for the variable that makes the polynomial zero

if you can't find an exact expression, then you can use numerical methods to get approximations ...

with numerical methods you can choose how close to zero you want, and it will give you a value that's at least that close ...

i personally like Dev c++ ...

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this is where you start declaring the alphabets , variables , arrays ... etc ...

even my original question was , how to declare ...

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f(x) ... theta , d^2y/dx^2 , (dy/dx)^3... properly in a programming language like c ...
07-04-2016
CodeSlapper

5. Application of ODEs: Series RL Circuit

I've used it for RC constants.
07-05-2016
delta

thanks

i myself was after some sort of wave generating circuits , or micro controllers ...

you know these WiFi signals type , that generates electromagnetic waves...but could not find anything proper...

do you know anything about that sort of circuits or micro controllers??

i have some improvements to do on the subject of differential equations itself and the separation of variables ...

i can only touch this subject after improving that parts ...
07-05-2016
CodeSlapper

Oh man, that is a lot to this.

For a wi-fi signal you need to understand signal modulation. In a Wi-Fi signal there is likely phase and frequency modulation, but that can be taken care of for you with a wifi chip.

In order to make a board, you need to understand impedance, grounding, power, etc. and that is a huge undertaking.

I really think you need to give it some good thought on what exactly you want to do and focus in on an area.
07-05-2016
delta

thanks ...

i got interested in a bit of electronics ... after watching a video like this ...

"LEARN ROBOTICS - build microcontroller"

LEARN ROBOTICS - build microcontroller - YouTube
i find that very interesting ... i was also looking for a video where electromagnetic radio waves are generated with the help of circuits or micro controllers ... i think it would be nice to learn about some radio wave generation in the future....

anyway back to mathematics ...

after that i will try to come back with some programming questions ...