Chapter 14: Q30P (page 673)
Using the definition (2.1) of show that the following familiar formulas hold.
Short Answer
By using the definition 2.1, it is showed that the following familiar formula hold.
Chapter 14: Q30P (page 673)
Using the definition (2.1) of show that the following familiar formulas hold.
By using the definition 2.1, it is showed that the following familiar formula hold.
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Get started for freeFind the inverse Laplace transform of the following functions by using (7.16).
Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer.
at
Evaluate the following integrals by computing residues at infinity. Check your answers by computing residues at all the finite poles. (It is understood that means in the positive direction.)
around
Use the Cauchy-Riemann conditions to find out whether the functions in Problems 1.1 to 1.21 are analytic.
For each of the following functions w = f(z) = u +iv, find u and v as functions of x and y. Sketch the graph in (x,y) plane of the images of u = const. and v = const. for several values of and several values of as was done for in Figure 9.3. The curves u = const. should be orthogonal to the curves v = const.
w = ez
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