Page 269 - Numerical Analysis Using MATLAB and Excel

Chapter 6 Fourier, Taylor, and Maclaurin Series

5. Compute the first 5 components of the exponential Fourier series for the waveform below.
Assume ω = . 1

ft()
A

ωt
0

6. Compute the first 5 components of the exponential Fourier series for the waveform below.
Assume ω = . 1

ft()
A

ωt
0

−A

Figure 6.37. Waveform for Exercise 6

7. Compute the first 4 terms of the Maclaurin series for each of the following functions.

a. fx() = e – x b. fx() = sin x c. fx() = sinh x

Confirm your answers with MATLAB.
8. Compute the first 4 terms of the Taylor series for each of the following functions.

1 π
-
a. fx() = -- about a = – 1 b. fx() = sin x about a = – ---
x 4
Confirm your answers with MATLAB.
9. In a non−linear device, the voltage and current are related as

⎛
v ⎞
iv() = k1 + ---- 1.5
⎝ V ⎠
where is a constant and is the DC component of the instantaneous voltage . Expand
v
V
k
this function into a power series that can be used to compute the current , when the voltage
i
v is small, and varies about v = . 0

6−52 Numerical Analysis Using MATLAB® and Excel®, Third Edition
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