CS123 Engineering Computation LabLab 2

Bruce Char

Department of Computer Science

Drexel University

Spring 2010

Administrative Notes

• Please contact your individual instructors with questions and problems!!

• At this time, is anyone still having a MapleTA login issue?

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

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

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.

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

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”

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

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))

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).

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

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