1. Lecture Set 0 – Review part 1
Some important basic materials in electrical engineering

2. ECE 3340 - Numerical Methods for Electrical and Computer Engineers
Credit Hours: 3.0 Lecture Contact Hours: 3    Lab Contact Hours: 0
Prerequisite: ECE 3331 and MATH Basic linear algebra and numerical methods with electrical engineering applications. Emphasis on use of computer-based solution techniques.
MATH 3321
Background math of numerical methods
ECE ????
What “electrical engineering applications?”
ECE 3331
Basic programming/ coding

3. ECE 3340 should not be a continuation of ECE 3331 and Math 3321
The whole point is to learn the subjects in order to apply to electrical engineering
Hence, we will not learn “numerical methods” in abstract, but in the context of electrical engineering by specific examples. IOW, apply ECE 3331 and Math 3321 to EE subjects.

4. A review of topics in electrical engineering
In preparation for background materials to apply and study ece3340

5. Topics Periodic phenomena and harmonic functions. Complex number.
Basic circuits review 1.
Laplace transform.
Circuits review 2 and introduction to filters
Fourier series and Fourier transform
Frequency analysis – power spectral density.
We will learn and put to practice “Numerical Methods” via these topical examples

6. Topic: Periodic Phenomena and Mathematical Tools to Study Them

7. Unit 1

8. Question 1
We will study periodic phenomena in time. Things that happen regularly and repeat themselves after some period of time. Give an example of periodic phenomena that you know.
Score 5

9. Discussion
here is an example of Houston average monthly temperature. It is periodic from year to year.
here is an example of day to day temperature: it goes up during the day and goes down at night. Although there is some fluctuation, the trend is periodic

10. Discussion:
Here is an example of one of the longest ecological study of predator and prey dynamic.
Note how the populations of the lynx and the hare went up and down periodically over nearly a 90-year period.
But there seems to be a time lag between them. The lynx population tended to rise a bit later than that of the hare and when the hare population dropped, it also followed. Why?

11. Discussion:
The sun has spots with 11-years cycle.

12. Circadian cycle (or rhythm) is common in many living things on earth
Circadian cycle (or rhythm) is common in many living things on earth. We have a 24-hr internal clock in our body. But it needs daylight to synchronize.
Even bacteria have it. Here is an example of a cyanobacterium species that emits light with 24-hr cycle, even in darkness.
Discussion:

13. Question 2
Now, let’s get more examples. Find what you can online or wherever.
You get points for each correct example. Find up to 3.
Score 10

14. Discussion:
Let’s test our concept. Which of the following examples do you think periodic and which is not.

15. Question 3
Human population, periodic or non-periodic
Score 12

16. Question 4
Our heart beats
Score 14

17. You must have seen the Foucault pendulum in museum
You must have seen the Foucault pendulum in museum. It appears to be periodic. But is it absolutely periodic in one fixed vertical plane? (in other words, does it swing in just one vertical plane?)
Question 5
Score 16

18. Question 6
Stock market: periodic or non-periodic
Score 18

19. Discussion:
Critical thinking: The concept of periodicity in science is not the same as that in math with rigorous definition.

20. Question 7
Now, let’s look for some periodic phenomena closer to home, like right here in this class room, right now. Find some examples here and now.

21. Question 8
Write the most general mathematical function that you can think of to describe all periodic phenomena that we have seen so far.

22. Demo:

23. Question 1
How do we describe the voltage signal as a function of time mathematically? Write a formula and plot it
Score 25

24. Discussion:
If our whistling can be recorded as a sine (or cosine) signal, can we do the reverse: can the signal we plot also be played to generate sound.
Tutorial in Mathematica

25. Another experiments. How would you plots these two signals
Question 2
Another experiments. How would you plots these two signals

26. Discussion:
𝑇= 2𝜋 
Period
𝑉=cos⁡(𝑡)
𝑇= 1 𝒇
𝑉=cos⁡(𝟐 𝝅𝒇𝑡)

27. Unit 2

28. Continued from the last time

29. Question 3

30. Discussion:
𝑉=𝐀 cos⁡(𝑡)

32. Discussion:
The answer is: G, or E, or B. But it depends on which shadow or projection that you look at.

33. Question 4
Which one is periodic and which one is not?
(a)
(b)

34. Discussion:
Use your imagination, what does this animation remind you of?
Score 50

35. Discussion:

37. Question 5
Let’s project the shadow of the planet on a wall as shown. Write a mathematical expression (function) to describe the shadow position (the red line) on the wall as a function of time?
Score 55

38. What is the relationship of the shadow frequency vs the angular (rotational) speed of the blue planet?
Question 6
𝑓= 1 𝑇 = 𝜔 2𝜋
Score 60

39. Now, let’s look at the shadow position on a different wall (the blue line). What is the function for this? You have to be specific and write out the whole expression, amplitude, frequency included).
Question 7

40. Discussion

41. Discussion
Score 65

43. Discussion:
Sine can be made into cosine and vice versa if only we can “slide” it as shown below. But how?

44. Mathematica app demo
Question 8
𝑉=𝐀 cos⁡(𝑡+)
Slide the phase back and forth to see the translation of the function.

45. 𝑉=𝐀 cos⁡(𝑡+) 𝑉=𝐀 cos⁡(2 𝜋𝑓𝑡+) Amplitude Frequency Phase
Discussion:
Just remember 3 things:
Amplitude
Frequency
Phase
𝑉=𝐀 cos⁡(𝑡+)
𝑉=𝐀 cos⁡(2 𝜋𝑓𝑡+)

46. Write expressions to describe the motions (position vs
Write expressions to describe the motions (position vs. time) of Red, Green, and Blue dots on each respective axis.
Question 9
Score 75
𝑉=𝐀 cos⁡(2 𝜋𝑓𝑡+)

47. Discussion:
Score 80

48. Discussion:
Now we look at Green, We don’t care about the absolute phase.
But this Green phase has to be correct relative to what we pick for Red. Look at the orange/purple axes. They are rotated by 2Pi/3 relative to the vertical/horizontal axes.
2𝜋 3
Score
100
Discussion:

49. Question 10
Name an application for this

50. Question 10
Name an application for this
Score
105

51. Question 11
Search online for a mechanical device that uses 3-phase AC
3-phase motor
3-cylinder engine
Score
110

52. Additional examples of phase devices

56. 2
I’m most even
Let’s get together and we can be one e