ECE3340 Numerical Methods For Electrical And Computer .

ECE3340Numerical Methods for Electrical andComputer EngineeringPROF. HAN Q. LE

If you love math & computercoding, you will very likelyenjoy the course If you hate math, or sufferdoing math & computer coding,well, are you sure you are inthe right place?

An example of “numerical math”(not pure math)

An example of pure (number theory) mathProve that: 2 2 4Or Prove that there are more irrational numbersbetween (0 1) than all integers or rational numbersOr No three integers a, b, c can satisfy theequation below for integer n 2𝑛𝑛𝑎𝑎 𝑛𝑛𝑏𝑏 𝑛𝑛𝑐𝑐

This course is about applied math for scientific, electricalengineering applications, and also general quantitativescience. Physical quantities, e. g. mass, velocity, voltage, current,frequency, temperature, pressure, flux, power, energy, andwhatnot are represented by real numbers, and related toeach other by physical laws. Why numerical methods? Data analysis of experiments and measurements.Practical scientific/engineering problems aren’t solved with abstractsymbols (v, i, ω, P ), but with numerical values for applications. Weneed numerical methods to obtain accurate & precise results.Beyond practical applications, computation – especially simulationcan give valuable insights and understanding of a problem.Numerical methods are needed for efficiency and accuracy.

Example vinvoutQ.1 What is a most common name for this circuit?Examples without inductor LQ.2 What is a most common name for these two circuits? (extra credits ifyou name each one differently based on its function and not by apermutation of letters)

Consider this circuit that has no resistors, no dissipative elements (thingsthat absorb power or energy permanently and not give back to the circuit).Assume perfect capacitor and perfect inductor.Then switch A is opened at time tA 0;simultaneously or after tA, switch B isinstantaneously closed at t 0.Switch A was connected for along time t 0 and switch Bwas open.AB -V 5 V0.3 µF 47 µHvout-Q.3 What is the voltage vout before and after the switches are activated?Sketch your guess what it looks like (only “guessing” is asked, no solvingequation or anything complicated).

A similar question but for a different circuit:Q.4 For all time t 0, input x[t] 1 Volt. Suddenly at t 0, the inputis switched to 0 V (with zero impedance at the input). Sketchyour best guess what voltage y[t] looks like as a function of timefor t 0. Extra credit if you write the correct mathematicalexpression for y[t].Numerical calculation can give us practical results (with values foractual application) as well as insight for designing, modification,and invention!

When design a circuit, we want to know how it works,what it does for the intended application. We wantnumerical simulation results such as this:inputoutputThis is what “numerical methods” is about. Theobjective: learn how to use computers to applyto ECE problems.

For those who have taken ECE2100 there are many examples ofcircuit simulation using numerical methods on the web siteExample: an op amp oscillator

For those who have taken ECE2100 there are many examples ofcircuit simulation using numerical methods on the web siteExample: harmonic responses of analog PID controller

For those who have taken ECE2100 there are many examples ofcircuit simulation using numerical methods on the web siteExample: Bode plots and harmonic responses

For those who have taken ECE2100 there are many examples ofcircuit simulation using numerical methods on the web siteExample: transient response of a second order circuit

For those who have taken ECE2100 there aremany examples of circuit simulation usingnumerical methods on the web siteExample: circuit response functions

All the above calculationsand simulations are fairlysimple and straightforward(thanks to powerful CPU andsophisticated software).Yes, you can do similarthings after this course.(hard working is required)

Although not scientific or engineering, this is an exampleof a numerical problem involving computer andprogramming (coding).Without a computer, it may take days, weeks for someoneto do by hand, which serves no useful purpose other thanknowing the company to send your resume in (if looking fora job) (“googling” it!)

A link to history of computer

TodayYesteryear

General appsStatisticsSci/eng. appsClassroom demo

Numerical methods for scientific andelectrical engineering applications This course is about concepts, methods, and algorithms. It is (and shouldbe) hardware-and-software-agnostic. Once you master the fundamentals, you can apply what you learn on anyplatform & IDE of your choice. (e. g. Python, ) That said, for convenience, there must be a single common platform forcourse materials: Wolfram Mathematica (read the syllabus).

Higher level - specialized for scientific/engineering app.Lower level implementation – general app. (web, games)

U of Houston licensed softwareThis Course lectures & HW Easy for quick & dirty demo. Convenient symbolicmanipulation.Free IDE stuffs (many )

I have tested with a focused group,consisting of students from sophomore tosenior level, also two at grad level - allwithout Mathematica & Python experience.Results showed that they learned more withless effort with Mathematica lectures thanwith Python lectures.Of course, the results could be different ifstudents were Python experts, however wecannot assume that for ECE 3340.

For those who use Anaconda, jupyter notebook is quite similarto Mathematica notebook (in concept)Mathematica has a huge list of built-in functions

Course material formats for downloadMainOthers

A tutorial in Mathematica

About of this course Review and learn some essential mathematics that havewidespread applications in scientific/engineering problems. The three most important things of the course areapplication, application, and application. “It’s all aboutAPPs!” Computer usage is of course the essential vehicle of learning.Bring your computer to do work in class as often as possible.What this course is not Learning computer programming. That’s for other courses, e.g. ECE 3331. Practice makes perfect: whether you learnedit in 3331 or you may already be an APP developer since HS,you are strongly encouraged to hone your programming skillby practicing what you learned. (Will help you to review/refresh your memory as much as possible).

If you love math AND computerprogramming, you will very likelyenjoy the course.-The more coding you do, the betteryou will be at itReinforcing your knowledge ofelectrical engineering (in this case, wepick circuit to be the example topicfor numerical math)Math knowledge at MATH 3321 level and proficiency incomputer programming at ECE 3331 level or better areprerequisite.

ECE 3340 - Numerical Methods for Electrical and Computer EngineersCredit Hours: 3.0Lecture Contact Hours: 3Lab Contact Hours: 0Prerequisite: ECE 3331 and MATH 3321.Basic linear algebra and numerical methods with electrical engineeringapplications. Emphasis on use of computer-based solution techniques.MATH 3321Background math ofnumerical methodsECE ?What “electricalengineeringapplications?”ECE 3331Basic programming/codingWe will not learn “numerical methods” in theory and abstract, but by specificexamples and applications in electrical engineering.

Expected work in this course Active lecture and class participation: you will participateto contribute to lecture and discussion in class Classwork is more important than HW: Bring paper, pensand your computer to do work in class. Turn in at the endof the class for credit.Weight40-60%Most important: take ownership of your owneducation: contribute to your own “lecture.” Homework: First, try to do on your own. Then get helpand collaborate if needed (peer learning). Submit ontime and follow policy on late HW.20-30%A good combination of personal best effort and/orpeer interactive learning can help you a great deal. Tests/exams: to be determined. No need for them if theother two categories are “good enough.”25-35% Final personalized project: to be determined.10-15%

Two reference textbooksVery easy to readand practical (usedin ECE 2331)This book is a classic!And like many otherclassics

A beautiful work – a lifetime of wisdom from theauthor, R. W. Hamming. It’s hard to absorb the wisdom of a lifetime in ashort semester. (you wouldn’t need takingthis course if you read and understand thebook) We will use it as a reference textbook: Much of things in the book are already used andimplemented in commercially available or freesoftware. Some are still relevant, some are less crucial because ofincreasing computing power and more sophisticated(intelligent) software.

In practice Rarely, if ever - do practicing scientists/engineers have to write owncodes for utility apps such as find roots, integration, differentialeqs., FDTD, FEM, special functions, linear/nonlinear systems, andmany others. There are huge libraries for those things in commercial or freesoftware, developed by dedicated professionals using well establishedor latest algorithm development, debugged, optimized for CPU speed,memory Why re-invent the wheel? Actually, in a professional world, we would insist any user to useestablished commercial software – don’t write your own except forown research: higher risk of bugs and errors. If you need a car, wouldyou rather buy one or drive a contraption built by your colleagues? This course helps you become an intelligent, informed user ofscientific/engineering software to be a professional electricalengineer – but not to develop you into a professional softwaredevelopers: this is the job for computer science major at PhD level.

price( )/unit# unitsstore A store B store C store 4.153.753.95ice .53.753.63.75storage 92.7shampoo3detergent29.559.058.657.1Pre-req for3340, ideally(array data, linear algebra)symbolic manip,anonym func“hello world”A π r2A len*wid

Learning alanguage

An example of how one can quickly adapt

An example of how one can quickly adapt

Jupyternotebookexample

Practice,practice,practice

Some math fun example

Find the first 8-20 consecutive digits in πdecimal expansion that is a prime numberwhich also contains your birth month (112), birth date (1-31), and last two digitsof your birth year (in any order & overlapOK). This is your private encryption key.Any two inthe classhave thesamebirthdate?Everyone hasthe sameanswer(”googling it”)

Check your answer with this APPIf you haven’t gota license forMathematica,download free CDFplayer and you canrun this

symbols (v, i, ω, P ), but with numerical valuesfor applications. We need numerical methods to obtain accurate & precise results. Beyond practical applications, computation – especially simulation can give valuable insights and understandi