I am reading Goldstein's Classical Mechanics and I've noticed there is copious use of the $\sum$ notation. He even writes the chain rule as a sum! I am having a real hard time following his arguments where this notation is used, often with differentiation and multiple indices thrown in for good measure. How do I get some working insight into how sums behave without actually saying "Now imagine n=2. What does the sum become in this case?" Is there an easier way to do this? Is there an "algebra" or "calculus" of sums, like a set of rules for manipulating them? I've seen some documents on the web but none of them seem to come close to Goldstein's usage in terms of sophistication. Where can I get my hands on practice material for this notation?
How do I get insight into equations with the $\sum$ notation without actually expanding it for a specific n every time?
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classical-mechanics
soft-question
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0...eliminate the $\Sigma$s using the Einstein summation convention ;). – 2012-07-26
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2It would be helpful, if you actually gave a reference to what book you read. Goldstein might be sufficient for some people, but not all. – 2012-07-26
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0@Joebevo You should find at least one physics subfield tag in addition to "soft-question" and attach it to your question (BTW What is the Goldstein you are reading ?) or dmckee will come and close this ... :-/ – 2012-07-26
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0Post edited to reflect suggestions. – 2012-07-27
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0I think this is actually off topic here, but it would likely be appropriate at [math.SE]. Unless anyone wants to make a case for it staying here? – 2012-07-27
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0I think it is ok here, a clarification of the notation can help students of classical mechenics who come here later too. I myself need help in notation issues sometimes when reading physics books and physicists who are familier with the context can then help better than mathematicians. – 2012-07-27
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0Where is the sophistication? Is he writing $\sum_{k=1}^{\sum_{i=1}^k i^2} {1\over k(k+1)}$? Just expand the notation until you don't need to anymore. – 2012-07-27
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1@Dilaton that doesn't make it on topic here, though. Not anything of interest to physicists is on topic for this site. I'm going to send it to math. – 2012-07-27