Where can I find videos on power series and other calculus topics?

In summary, a power series is an infinite series with a specific form, commonly used in calculus to approximate functions and solve differential equations. Convergence is important in power series as it determines its usefulness and applicability, and there are various methods to determine convergence. Power series also have numerous real-world applications, particularly in physics and engineering.
  • #1
nickto21
17
0
Hey All,
I'm learning calculus through videos. The videos that I'm watching are really good, but they are deficient in power series, taylor and mclaurin series, binomial series, and taylor polynomial applications. Anyone know where I can see video instruction for these?
Steve
 
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  • #2
KhanAcademy has eight videos at least on the subject, if that's what you're looking for...
 
  • #3
Great! Thanks for the info.
Steve.
 

1. What is a power series?

A power series is an infinite series of the form ∑n=0∞ cn(x-a)n, where cn and a are constants, and x is a variable.

2. How do power series relate to calculus?

Power series are commonly used in calculus, specifically in the study of limits, derivatives, and integrals. They allow for the approximation of functions and can be used to represent a variety of functions.

3. What is the importance of convergence in power series?

Convergence is crucial in power series as it determines whether or not the series will have a finite sum. A power series will only be useful and applicable if it converges. Different methods, such as the ratio and root tests, can be used to determine convergence.

4. Can power series be used to solve differential equations?

Yes, power series can be used to solve differential equations. By representing a function as a power series, one can find an infinite series of coefficients that satisfy the differential equation.

5. Are there any real-world applications of power series?

Yes, power series have many real-world applications, particularly in physics and engineering. They can be used to model physical phenomena, such as heat transfer and electrical circuits, and to approximate solutions to complex problems.

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