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At the junior level, I found that the students were not familiar
(enough) with the complex exponential signal, and with how to
time-shift and time-scale signals. I added a section of notes on
the complex-exponential (pp. 1–9 to 1–10) and on “function
relatives” (pp. 1–14 to 1–16). |
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The juniors also had difficulty interpreting mathematical definitions
in terms of procedures that they could use. In order to help them,
I created a series of “recipes” to help them interpret and apply
the math. In particular, refer to pages 2–4 (test for time
invariance); 2–7 (test for causality); 2–8 (test for linearity) and
2–12 (application of convolution integral). |
| |
The Fourier series was not well liked, nor was it well understood.
I created a summary table (page 3–25) to help the student distinguish
between the three flavors of Fourier series studied, and to be able
to easily convert between them. |
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The Laplace transform is key to system theory, but is not intuitive.
I added a section on dynamic interpretation of Laplace transform to
help aid intuition (pp. 6–4 to 6–6). |
| |
Linear algebra is not a prerequisite for this course, so I avoided
teaching state-variable analysis my first year. But, since
state-variable analysis is very important in systems theory, I added
a section on state-variable analysis (Section 7), including a thorough
introduction to matrix algebra. |
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I added an entire section (Section 9) reviewing the course to aid
the students studying for the final exam. |
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I typeset the lecture notes. While this
was an enormous investment of time, I believe it will make future
revisions easier, and result in even higher-quality teaching in the
future. |
