Engr/Math/Physics 25
Applied Math
Problem Solving
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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)
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
Info From MathWorks
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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):
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
Refined Learning Strategy
1. HACK, HACK, and HACK some more
2. Read The TEXTbook §-by-§
3. When you come to a NEW software
Command/Tool, TRY it
IMMEDIATELY
4. Consult MATLAB Help
•
It’s Quite Useful Actually
5. Consult with your Colleagues
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
Problem Solving
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
Copy HW Code  Crash&Burn Exams
110%
HW
100%
MTE
90%
HW Cheaters
80%
70%
HW or MTE Score
60%
50%
40%
30%
20%
10%
0%
5393
1334
0606
8235
8116
7224
7511
0309
9273
8906
W-No.
6829
0466
10
2188
2257
3187
0810
8297
8872
5407
3374
8247
3599
4795
2736
3390
Engineering/Math/Physics 25: Computational Methods Student
Grades_E25_Fa0909_091021.xls
Bruce Mayer,
PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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
☺☺☺
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
AppMath Problem Solving Steps
1. 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.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
Assumption Digression
 BMayer 2001 JVST Paper
• See
ENGR45
for More
Details
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
Assumption Digression
 PARTIAL
Assumption List
• 100% Vapor
Saturation at Bubble
Edge
• Gases in bubble
behave as perfect
gases
• Bubbles are
Spherical
– Radial Symmetry
Engineering/Math/Physics 25: Computational Methods
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• Diffusion Coefficient
is Constant
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
Problem Solving Steps cont
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.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
Problem Solving Steps cont
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.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
Computer Solution Steps
1. 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.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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.
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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 PCBased Hi-Perf “Math Processors”
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
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
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
Next Time → use MATLAB
Covered in ENGR25
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
First ENGR25 Tutorial
 MATLAB Video Tutorials
• http://www.mathworks.com/academia/stud
ent_center/tutorials/launchpad.html
– http://www.mathworks.com/videos/matlab/gettin
g-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/creati
ng-a-basic-plot-interactively.html (6 min)
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
First ENGR25 Tutorial
– Additional Videos Useful in the future
 http://www.mathworks.com/videos/matlab/importingdata-from-files.html (HW5, 7min)
 http://www.mathworks.com/products/simulink/demos.
html?BB=1 (Chp9,
 http://www.mathworks.com/videos/simulink/getting-started-withsimulink.html (4 min)
 http://www.mathworks.com/videos/simulink/visualizingsimulation-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)
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt
3x3 from ENGR43
 For The DC Linear Circuits We Will
need to Solve Systems Of Algebraic
Equations
R2
2.2 kΩ
I2
R3 1.2 kΩ
1.5 kΩ
I3 Rx
R1
2.7 kΩ
7 mA
RL
13V
I1
IL
1.8 kΩ
Engineering/Math/Physics 25: Computational Methods
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12V1  9V2  4V3  8
 4V1  16V2  V3  0
 2V1  4V2  6V3  20
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_MATLAB_AppMath_ProbSolve.ppt