Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected]

[email protected] • ENGR-25_MATLAB_AppMath_ProbSolve.ppt1

Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Applied MathProblem Solving



First A Note on Cheap Software All ENGR25 Students have No-Charge

Access to MATLAB software in the Rm3906 CompSci Lab

For Students who want Home-Access, the MathWorks Company Makes Available an Inexpensive MATLAB Version for Student use

Student Version Cost = $99.98 (+ Shipping)



Info From M

athWorks





Strategy for Learning ENGR25 ENGR25 is, primarily, an Engineering

PROBLEM SOLVING Class• With a Very Large SOFTWARE (MATLAB

& Excel) Component The BEST Way to Learn ANY Piece of

Software (and most Hardware):



Refined Learning Strategy1. HACK, HACK, and HACK some more2. Read The TEXTbook §-by-§3. When you come to a NEW software

Command/Tool, TRY it IMMEDIATELY4. Consult MATLAB Help

• It’s Quite Useful Actually

5. Consult with your Colleagues



ENGR25 Important??!! This Class is NOT an Academic

Exercise The PROBLEM SOLVING SKILLS and

MATLAB APPLICATION PROFICIENCY are PROFESSIONALLY IMPORTANT• That is, an Engineering STUDENT who

LEARNS these Skills we be able to USE them ON THE JOB as a PRACTICING ENGINEER



Problem Solving



Academic Honesty - Coding Students may collaborate on understanding

lectures, labs, text, problem-statements. Students may discuss the DESIGN of a

program. All Students must then write his/her OWN MATLAB® code

Students may get help from Fellow students while writing your programs only by:• Asking them to POINT OUT an error,

but NOT to FIX it • Asking Them to EXPLAIN MATLAB syntax Using

a DIFFERENT example than the program under consideration



Copy HW Code Crash&Burn Exams

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

110%

3390

2736

4795

3599

8247

3374

5407

8872

8297

0810

3187

2257

2188

0466

6829

8906

9273

0309

7511

7224

8116

8235

0606

1334

5393

Student W-No.

HW

or M

TE S

core

HW MTE

Grades_E25_Fa0909_091021.xls

HW Cheaters



Copy Code??!! Trying to Learn COMPUTER PROBLEM

SOLVING by Copying SOMEONE ELSE’S CODE is like trying to get into athletic-condition by Watching SOMEONE ELSE WORK OUT…..

There is NO Substitute for Personally STRUGGLING with the Course Material

☺☺☺



ENGR25 Bottom Line ENGR25 is NOT (only) a

MATLAB/Excel class; it's a THINKING Class...

Student should be Prepared to do LOTS of (often Frustrating) THINKING



AppMath Problem Solving Steps1. Understand the PURPOSE of the

problem.2. Collect the KNOWN information.

• Realize that some of the information might later be found UNNECESSARY.

3. Determine what information YOU must find.

4. SIMPLIFY the problem only enough to obtain the required information. State any ASSUMPTIONS you make.



Assumption Digression BMayer 2001 JVST Paper

• See ENGR45 for More Details



Assumption Digression PARTIAL Assumption List

• 100% Vapor Saturation at Bubble Edge• Gases in bubble behave as perfect gases• Bubbles are Spherical

– Radial Symmetry

• Diffusion Coefficient is Constant



Problem Solving Steps cont

5. DRAW A SKETCH and label any necessary variables.

6. Determine which FUNDAMENTAL PRINCIPLES apply to the problem.

7. Think GENERALLY about your PROPOSED SOLUTION approach and CONSIDER OTHER APPROACHES before proceeding with the details.




8. LABEL each STEP in the solution process.

9. If you solve the problem with a software program, HAND CHECK the results using a simple version of the problem.

• Checking the DIMENSIONS and UNITS and printing the results of intermediate steps in the calculation sequence can uncover mistakes.




10.Perform a “reality check” on your answer. Does it make sense? Estimate the range of the expected result and compare it with your answer. Do not state the answer with greater precision than is justified by any of the following:

a) The precision of the given information.b) The simplifying assumptions.c) The requirements of the problem.



Interpret the Mathematics If the mathematics produces multiple

answers, do not discard any of them without considering what they mean.

The mathematics might be trying to tell you something, and you might miss an opportunity to discover more about the problem.



Computer Solution Steps1. State the problem CONCISELY.2. Specify the data to be used by the

program. This is the “INPUT.”3. Specify the information to be

generated by the program. This is the “OUTPUT.”

4. Work through the solution steps by HAND or with a CALCULATOR; use a SIMPLER set of data if necessary.



Computer Solution Steps cont

5. Write and run the program.6. Check the output of the program by

comparing with your hand solution.7. Run the program with your input data

and perform a REALITY CHECK on the output.

8. If you will use the program as a general tool in the future, test it by running it for a RANGE of reasonable data values; perform a reality check on the wide-ranging results.



MATLAB History MATLAB = MATrix LABoratory Developed by Prof. Cleve Moler of New

Mexico State University Originally a user interface for numerical

Linear Algebra (LinPack) or EigenValue Problems (EisPack)

In early 1983, John Little was exposed to MATLAB During a visit made to Prof. Moler Made to Stanford University



MATLAB History In 1983 Little teamed up with Moler and

Steve Bangert to develop a second generation, professional version of MATLAB written in C and integrated with graphics.

The MathWorks, Inc. was founded in 1984 to market and continue development of MATLAB• It has become a de-facto standard for PC-

Based Hi-Perf “Math Processors”



MATLAB Construction Core functionality: compiled C-routines Most functionality is given as Stored “m”

files, grouped into “ToolBoxes” m-files contain source code, can be

copied and altered m-files are platform independent

(Windows/Intel, Unix/Linux, MAC) Simulation of dynamic systems is

performed in the SIMULINK SubEnvironment ToolBox



Next Time → use MATLAB

Covered in ENGR25

http://images.google.com/imgres?imgurl=http://www.fsa.ucl.ac.be/candis_01-02/T3/math/cd-matlab/matlab.jpg&imgrefurl=http://www.fsa.ucl.ac.be/candis_01-02/T3/math/cd-matlab/&h=431&w=513&sz=11&tbnid=LuIPwHPFo94J:&tbnh=107&tbnw=128&hl=en&start=2&prev=/images%3Fq%3Dmatlab%26hl%3Den%26lr%3D



First ENGR25 Tutorial MATLAB Video Tutorials

• http://www.mathworks.com/academia/student_center/tutorials/launchpad.html– http://www.mathworks.com/videos/matlab/

getting-started-with-matlab.html (6 min)– http://www.mathworks.com/videos/matlab/writin

g-a-matlab-program.html (6 min)

– http://www.mathworks.com/videos/matlab/using-basic-plotting-functions.html (6 min)

– http://www.mathworks.com/videos/matlab/creating-a-basic-plot-interactively.html (6 min)

http://www.mathworks.com/academia/student_center/tutorials/launchpad.html

http://www.mathworks.com/academia/student_center/tutorials/launchpad.html

http://www.mathworks.com/videos/matlab/writing-a-matlab-program.html

http://www.mathworks.com/videos/matlab/writing-a-matlab-program.html

http://www.mathworks.com/videos/matlab/creating-a-basic-plot-interactively.html

http://www.mathworks.com/videos/matlab/creating-a-basic-plot-interactively.html



First ENGR25 Tutorial– Additional Videos Useful in the future

http://www.mathworks.com/videos/matlab/importing-data-from-files.html (HW5, 7min)

http://www.mathworks.com/products/simulink/demos.html?BB=1 (Chp9, http://www.mathworks.com/videos/simulink/getting-started-with-s

imulink.html (4 min)

http://www.mathworks.com/videos/simulink/visualizing-simulation-results.html (4 min)

HW Presentation Save MATLAB work to MSWord file• Trapezoid area, 3x3 Eqn System, cosh

calculation, plot y = ln(t+.02)·sin(1.3t)

http://www.mathworks.com/videos/matlab/importing-data-from-files.html

http://www.mathworks.com/videos/matlab/importing-data-from-files.html

http://www.mathworks.com/products/simulink/demos.html?BB=1




http://www.mathworks.com/videos/simulink/getting-started-with-simulink.html

http://www.mathworks.com/videos/simulink/getting-started-with-simulink.html

http://www.mathworks.com/videos/simulink/visualizing-simulation-results.html

http://www.mathworks.com/videos/simulink/visualizing-simulation-results.html



3x3 from ENGR43 For The DC Linear Circuits We Will

need to Solve Systems Of Algebraic Equations

20642016484912

321

321

321

VVVVVVVVV2.2 kΩ 1.2 kΩ 1.5 kΩ

2.7 kΩ

1.8 kΩ

R1

R2 R3Rx

RL13V

7 mA

I1

I2 I3

IL

Documents

Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected]