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... Eric Halsey [1] has invented an ingenious method for defining the Fibonacci numbers F(x) st when x is a rational number. In addition to the r e s t r i c tion that x must be rational, his calculations yield F(4.1) = 3.155, F(3.1) = 2.1, F(l.l) = 1.1 , so that the Fibonacci identity F(x) = F ( x - 1) ...
... Eric Halsey [1] has invented an ingenious method for defining the Fibonacci numbers F(x) st when x is a rational number. In addition to the r e s t r i c tion that x must be rational, his calculations yield F(4.1) = 3.155, F(3.1) = 2.1, F(l.l) = 1.1 , so that the Fibonacci identity F(x) = F ( x - 1) ...
Passive Bandpass and Notch Filters
... Bandwidth and Q Factor • The difference between the frequencies (in Hz) where the power is ½ of the maximum output power (the -3 dB point) is the bandwidth of the filter – Maximum power to output occurs at fo =QB, where Q is the quality factor of the filter. • A high Q filter has a small bandwidth, ...
... Bandwidth and Q Factor • The difference between the frequencies (in Hz) where the power is ½ of the maximum output power (the -3 dB point) is the bandwidth of the filter – Maximum power to output occurs at fo =QB, where Q is the quality factor of the filter. • A high Q filter has a small bandwidth, ...
first quarter - Peoria Public Schools
... Divide polynomials by long division & synthetic division Remainder Theorem and Factor Theorem Evaluate polynomials using direct and synthetic division Identify all roots (real and imaginary) of a polynomial given a graph or factorable polynomial. Factor and solve polynomials Understand the ...
... Divide polynomials by long division & synthetic division Remainder Theorem and Factor Theorem Evaluate polynomials using direct and synthetic division Identify all roots (real and imaginary) of a polynomial given a graph or factorable polynomial. Factor and solve polynomials Understand the ...
Assignment #5
... (c) Find arg(1 − i) and arg(−1 + 3i). [in radians!] 3. (a) Use properties of complex conjugation to verify the identity (x2 + y 2 )(a2 + b2 ) = (xa − yb)2 + (xb + ya)2 for real numbers x, y, a, b ∈ R. [Hint: consider z1 = x + iy, z2 = a + ib.] (b) Show that if n and m ∈ Z are two integers which are ...
... (c) Find arg(1 − i) and arg(−1 + 3i). [in radians!] 3. (a) Use properties of complex conjugation to verify the identity (x2 + y 2 )(a2 + b2 ) = (xa − yb)2 + (xb + ya)2 for real numbers x, y, a, b ∈ R. [Hint: consider z1 = x + iy, z2 = a + ib.] (b) Show that if n and m ∈ Z are two integers which are ...
Situation 21: Exponential Rules
... make a list of values for m and n that made the statement true. After a few minutes, one student asked, “Can we write them all down? I keep thinking of more.” ...
... make a list of values for m and n that made the statement true. After a few minutes, one student asked, “Can we write them all down? I keep thinking of more.” ...
Mathematics of radio engineering
The mathematics of radio engineering is the mathematical description by complex analysis of the electromagnetic theory applied to radio. Waves have been studied since ancient times and many different techniques have developed of which the most useful idea is the superposition principle which apply to radio waves. The Huygen's principle, which says that each wavefront creates an infinite number of new wavefronts that can be added, is the base for this analysis.