What are the applications of series and sequences

[SanjKrish]

I find every say the applications of series in calculus is ubiquitous

Can any one explain me why do we study about series... convergence , divergence of series etc...
How is geometric series or Fibonacci series related with calculus....8-O8-O8-O

Help me understand..:?::?::?:

 

[andre_luis]

That type of subject is commonly need to numerical analysis.
If you are on engineering, make sense understand, due nodal analysis is used not only at Electronic, but even at Mechanical once mechanical phenomens can ne modeled to electric components.

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[rtalcott]

A few applications from page 13 on
http://www.physics.miami.edu/~nearing/mathmethods/series.pdf

I also think you should read a calculus book...many of them have examples or problems that illustrate applications in physics and engineering.
rt




rt

 

[rtalcott]

Fourier Series is a great example....:
Fourier series - Wikipedia, the free encyclopedia

rt

 

[SanjKrish]

andre_teprom

rtalcott ,
The link was very useful for me...Thanks..
and yes, I have come across fourier series in my engineering to write a function in terms of sine and cosine which I was able to make sense of, as its tells the frequency

distribution of the function...
Even the exponential function 'e', sin(x),cos(x) can be expressed as a series... which I agree to an extend that they are someway related to physical phenomena and they

are used in calculating radioactive decay, compound interest problem etc...

But, wat about the other series like Power series, geometric series and other unnamed series like
(1/1*2) + (1/2*3) + (1/3*4) + ...
etc... Their use is not very apparent thought esp why is it so much important to calculus..
Why do we require tests like
Comparison test
D' Alembert's Ratio test
Raabe's test...
etc etc to check whether they converg or diverge...

 

[rtalcott]

Think of a dropped ball that loses a bit of energy after each collision with the ground...how far does it travel...up and down...before it stops? That's described by a series...

The tests you mention are used to determine if a series converges...sometimes you just need to know IF it converges and NOT what the series sums to.

Series are also used to solve many differential equations...

rt