Derivative of imaginary number
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Any function, f(x) can be written and represented as its Maclaurin Series, defined as ∑ n=0 ∞ f n 0 x n n! where f n is the nth derivative of the function. For example, f x = sin x , can be written as f x =x- x 3 3! + x 5 5! - x 7 7! … or more generally sin x= ∑ n=0 ∞ -1 n x 2n+1 2n+1 ! .Furthermore, cos x= ∑ n=1 ∞ -1 n x 2n 2n ! .The easy part about finding the Maclaurin series ...
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(d) Find the derivative of the volume V as a function of r. Show how this derivative can be used to determine how much the volume of a sphere would increase (i.e. the factor dV) if the radius of the sphere were increased from r to r + dr. Hint: Consider this increase as being the volume of a shell of thickness dr surrounding the sphere.
[DOC File]The Directional Derivative
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What is a complex number, and why do we care? The algebra of complex numbers (addition, multiplication, complex conjugation) The polar form of a complex variable, some basics about vectors. Understanding the function f(z) = zn. DeMoivre’s Theorem. Euler’s Formula and a justification for it. Basic point-set topology; connectedness, simple ...
[DOC File]Functions of Complex Variables
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4.2.4 Derivative . Definition 4.8 The derivative of a complex function f at a point written . is defined by = Provided that this limit exists. In this case, we say f is differentiable at . If we write , we also have = . Example 16 Show that f (z) = is differentiable for all complex numbers and = 2z. Solution Let be any complex number. = = .
[DOC File]California State University, Northridge
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Here i2 = -1, and M is the number of intervals on the grid. Each interval has the width, Δx = L/M. On this grid we can represent the sine-cosine waves that are equivalent to the imaginary exponential for wave numbers, βm defined as follows. [3-30] We see that βm is a real quantity; the exponent, a, that multiplies time can be complex, in ...
[DOC File]Phy 440 Lab 5: RC and RL Circuits
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where, j is the imaginary number √-1. Calculate the frequency [f = (/(2()] of the so called “half-power point.” This is simply the frequency where the output voltage amplitude is equal to the input voltage amplitude divided by √2. Calculate the phase shift at this frequency Ø = (tan-1(Im(H( )/Re(H( )).
[DOC File]Southeastern Oklahoma State University
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It must be positive or one will be trying to find the square root of a negative number. A negative discriminate is double trouble because it means the factors that are the solutions, are imaginary numbers. ... are imaginary numbers. ... Find the second derivative, set it equal to zero, and solve it for Q. You can see the solution above. There ...
[DOC File]Baselines
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Concept 1: In the time domain, if you have a derivative term, it transforms into a multiplication by the complex frequency in the frequency domain. So here is what a capacitor current transforms into: Time Domain (=====(Frequency Domain (=====(Here the i in is the imaginary number.
[PDF File]Chapter 1 Introduction
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Re is the Reynolds number, D is the diameter, L is the length, i is the imaginary number. If the maximum volume to minimum volume ratio is between 1 and 2, and the oscillation Peclet number is higher than 100, the real part and the imaginary part of the complex Nusselt number …
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Formal Fail Theory Germano Resconi. Mathematical and Physical Department, Catholic University. Via Trieste 17 Brescia . resconi@speedyposta.it Abstract—
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