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Difference between power series and fourier power series?
A power series is a series of the form ( \sum_{n=0}^{\infty} a_n (x - c)^n ), representing a function as a sum of powers of ( (x - c) ) around a point ( c ). In contrast, a Fourier power series represents a periodic function as a sum of sine and cosine functions, typically in the form ( \sum_{n=-\infty}^{\infty} c_n e^{i n \omega_0 t} ), where ( c_n ) are Fourier coefficients and ( \omega_0 ) is the fundamental frequency. While power series are generally used for functions defined on intervals, Fourier series specifically handle periodic functions over a defined period.
Where is calculus used?
Differential calculus (commonly calculus 1) is used in optimization -- basically finding the best or most likely choice for something. For example, the best movie based on past recommendations, or the best price to sell something at), or the most likely meaning for a word. Series, especially Taylor Series, are used to approximate functions and make computation easier. For example, one can replace e^x with the approximation 1+x+x^2/2, when x is close to 0.
What comes to mind when you hear the word calculus?
The first thing that come up into my mind is numbers, calculation, integrals and derivatives
What are the applicaton of fourier series?
It can be used in function approximation, especially in physics and numerical analysis and system & signals. Actually, the essence is that the basis of series is orthorgonal.
Is the bar exam harder than the series 7?
I've never taken the Bar exam but I have taken the Series 7 Exam and passed my first try with a 94. The Series 7 is very comprehensive and contains information you are not likely to run into as a practicing financial advisor. You best prepare for 8 weeks or more if you have any hope to pass.
