CS123 Engineering Computation Lab Lab 2

1. CS123 Engineering Computation LabLab 2 Bruce Char Department of Computer Science Drexel University Spring 2010

2. Administrative Notes • Please contact your individual instructors with questions and problems!! • At this time, is anyone still having a MapleTA login issue?

3. Lab 2 Overview • Based on materials from Chapters 15, 16 and 17 • Chapter 15 – Using Maple’s Procedure feature • Transform the AC simulation from Lab 1 into a Maple procedure • Chapter 16 – Creating User Interfaces with Maple Components • Use of slider, button and plot area components to control the AC simulation procedure • Chapter 17 – Calculus and Optimization • Develop an objective function for the minimum surface area of a can and find optimal dimensions (radius and height) using Maple’s Optimization feature

4. Lab 2 Overview • Lab 2 outline • Part 1.1 – Converting the AC simulation to a Maple procedure • Open your AC simulation script from Lab 1 along with the model template from the course web site • Copy and paste code segments from your Lab 1 script into appropriate sections of the model template • Run the 3 tests from the scripts provided on the course web site • Part 1.2 – User interface for the AC procedure • Use the final procedure developed in part 1.1 and develop a user interface to control the high and low AC air flow settings and to invoke the simulation – see demo for user interface creation • Part 2 – Find the minimum dimensions of a can that holds a specified volume of liquid using Maple’s Optimization function • Create an expression for the can’s surface area (objective function) to hold a constant volume of liquid • Use the Maple Optimization function to find the minimum dimensions (radius and height) for the surface area

5. Lab 2 Maple Concepts:Discussion and Demo • Part 1.1 – Maple Procedure Syntax • Procedure header – 1st line of a Maple procedure • HVAC1:=proc(totaltime, dt,aFunc,fFunc,T0,Tea,lf,hf) • Local variable declaration • local N, A, L, T, U, V, c, q, rho, Zplot, EWplot, i, Time, state, Tew; • Return (will return a plot display for the temperatures vs. time) • return plots[display]([Zplot,EWplot]); • Procedure end statement • end; or end proc; • These statements appear in the model template script. Cut and paste segments of your Lab 1 script into this script in the appropriate locations.

6. Lab 2 Maple Concepts:Discussion and Demo • Part 1.2 - Demo of Maple User Interface Components • The instructor will open a Maple worksheet and develop a user interface for the plot of the sin function in which a slider is used to define the period of the sin function. • Step 1 – Identify the necessary Maple Components • Slider – set to a value between 1 and 10 to define the period • Text Area – shows the slider setting numerically • Plot Area – box into which the plot will appear • “Draw Plot” button – click to create the plot graph • Step 2 – Open the Components Palette and drag the components into the work sheet • Create a tale to organize the components – insert  table (3x2) • Slider into row 1, column 1 • Text Area into row 2, column 1 (add text “Value” to left of button) • Button into row 3, column 1 • Plot area into row 1, column 2

7. Lab 2 Maple Concepts:Discussion and Demo • Part 1.2 - Demo of Maple User Interface Components – continued • Step 3 – Configure each component (right click on the component and open “component properties”) • Slider – name=PlotSlider, range (0 to 10), ticks (major=5, minor=1), “show axis labels”, “update continually while dragging” • Text Area – name=kText, number of visible rows = 1, “not editable” (slider will determine the k value) • Plot Area – name = sinPlotter • “Draw Plot” button – Caption = “Draw Plot”

8. Lab 2 Maple Concepts:Discussion and Demo • Part 1.2 - Demo of Maple User Interface Components – continued • Step 4 – Program each component (right click on the component and open “component properties”  Edit – Action when contents change) – just before “end use;” statement at end of region • Slider • Do( %kText = %PlotSlider) • “Draw Plot” butt on • Do( %sinPlotter = plot(sin(%PlotSlider*x), x=0..10, color=red)); • Step 5 – Run the program from the user interface • Test 1 – set slider to 8 and click “Draw Plot” button • Test 2 – change slider to 1 and click “Draw Plot” button

9. Lab 2 Maple Concepts:Discussion and Demo • Part 1.2 - Demo of Maple User Interface Components – continued • Note – the “Draw Plot” button for Part 1.2 should be programmed as follows: • Do( %nameofplotarea = plots[display] (HVAC1(30, 0.01, acState, airFlowControl0, 90, 65, %lowFlowSlider, %highFlowSlider))

10. Lab 2 Maple Concepts:Discussion and Demo • Part 2 – Maple’s Optimization feature • Creating the Objective function (surface area of a can) • Surface area = lateral area + top and bottom • SA = 2*pi*r*h + 2*pi*rsquared • Since the surface area needs to be a function of a single variable (eg. radius=r), we need to find an function relating h (height) to r and substitute. Since the volume is constant at 1000: • 1000 = pi*rsquared*h  • h = 1000 / (pi*rsquared) • Substitute this equation for h into the SA equation above to obtain the objective function SA(r).

11. Lab 2 Maple Concepts:Discussion and Demo • Part 2 – Maple’s Optimization feature • Now use this objective expression SA(r) to find the minimum surface area over a range of radii that holds a volume = 1000 • minRslt:=Optimization[ Minimize](objexpression,r=1..10) • You will obtain 2 results • minRslt[1]  minimum surface area • minRslt[2]  radius that produces this minimum SA • Substitute minRslt[2] into the equation for h to obtain the associated height

12. Quiz Week (5) Activities • Quiz 1 will be released on Friday (4/23) at 6 PM • Deadline: Wednesday (4/28) at 4:30 PM • Makeup quiz – from Thursday (4/29) at 9 AM through Sunday (5/2) at 11:30 PM • 30% penalty • Pre-lab 3 quizlet • From Thursday (4/29 – noon) through Monday (5/3 – 8 AM) • Be sure to visit the CLC for quiz or general Maple assistance