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(Principal value of complex power)
z^a=? where a,z are complex numbers and z does not equal 0 |
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Definition
| Principal Value of z^a=e^(aLnz) |
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(multiple valued Complex powers)
z^a=? where a,z are complex numbers and z does not equal 0 |
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| sinz = [e^(iz) - e^(-iz)]/(2i) |
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| cosz = [e^(iz) + e^(-iz)]/2 |
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| initial and terminal point |
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| Suppose a curve C in the plane is parametrized by a set of eqns x=x(t), y=y(t), d<=t<=e, where x(t), y(t) are continuous real fns. Then the initial and terminal points of C are (x(d),y(d)) and (x(e),y(e)), denoted by the symbols D and E -- d represents a and d represents b |
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| Suppose a curve C in the plane is parametrized by a set of eqns x=x(t), y=y(t), d<=t<=e, where x(t), y(t) are continuous real fns. Then C is a simple closed curve if the curve C does not cross itself and D=E (simple and closed) |
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| Suppose a curve C in the plane is parametrized by a set of eqns x=x(t), y=y(t), d<=t<=e, where x(t), y(t) are continuous real fns. Then C is smooth if x' and y' are continuous on [d,e] and not simultaneously zero on (d,e) |
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Definition
Suppose a curve C in the plane is parametrized by a set of eqns x=x(t), y=y(t), d<=t<=e, where x(t), y(t) are continuous real fns. Then C is piecewise smooth if consists of a finite # of smooth curves C1, C2, ..., Cn joined end
to end (terminal of k coincinding with initial of k+1) |
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Definition
| Suppose a curve C in the plane is parametrized by a set of eqns x=x(t), y=y(t), d<=t<=e, where x(t), y(t) are continuous real fns. Then C is closed if D=E |
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| radius and circle of convergence for a power series |
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Definition
| make physical flashcard based on top of pg.277 |
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| Let f be a complex number that fails to be analytic at z0. Then z0 is called a signularity. |
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| antiderivative of a complex function f |
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| suppose that a fn f is continuous on a domain D. If there exists a fn F s.t. F'(z) for each z in D, then F is called an antiderivative of f. |
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