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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

Engr/Math/Physics 25. Applied Math Problem Solving. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. First A Note on Cheap Software. All ENGR25 Students have No-Charge Access to MATLAB software in the Rm3906 CompSci Lab

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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

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  1. Engr/Math/Physics 25 Applied MathProblem Solving Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. 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)

  3. Info From MathWorks

  4. 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): HACK at it!

  5. Refined Learning Strategy • HACK, HACK, and HACK some more • Read The TEXTbook §-by-§ • When you come to a NEW software Command/Tool, TRY it IMMEDIATELY • Consult MATLAB Help • It’s Quite Useful Actually • Consult with your Colleagues

  6. 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

  7. Problem Solving

  8. 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

  9. Copy HW Code  Crash&Burn Exams HW Cheaters

  10. 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 ☺☺☺

  11. 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

  12. AppMath Problem Solving Steps • Understand the PURPOSE of the problem. • Collect the KNOWN information. • Realize that some of the information might later be found UNNECESSARY. • Determine what information YOU must find. • SIMPLIFY the problem only enough to obtain the required information. State any ASSUMPTIONS you make.

  13. Assumption Digression • BMayer 2001 JVST Paper • See ENGR45 for More Details

  14. 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 Assumption Digression

  15. Problem Solving Steps cont • DRAW A SKETCH and label any necessary variables. • Determine which FUNDAMENTAL PRINCIPLES apply to the problem. • Think GENERALLY about your PROPOSED SOLUTION approach and CONSIDER OTHER APPROACHES before proceeding with the details.

  16. Problem Solving Steps cont • LABEL each STEP in the solution process. • 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.

  17. Problem Solving Steps cont • 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: • The precision of the given information. • The simplifying assumptions. • The requirements of the problem.

  18. 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.

  19. Computer Solution Steps • State the problem CONCISELY. • Specify the data to be used by the program. This is the “INPUT.” • Specify the information to be generated by the program. This is the “OUTPUT.” • Work through the solution steps by HAND or with a CALCULATOR; use a SIMPLER set of data if necessary.

  20. Computer Solution Steps cont • Write and run the program. • Check the output of the program by comparing with your hand solution. • Run the program with your input data and perform a REALITY CHECK on the output. • 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.

  21. 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

  22. 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”

  23. 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

  24. Next Time → use MATLAB Covered in ENGR25

  25. 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/writing-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)

  26. 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-simulink.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) Demonstrate Next Time

  27. 3x3 from ENGR43 • For The DC Linear Circuits We Will need to Solve Systems Of Algebraic Equations

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