1. CS122 Engineering Computation Lab Lab 3
Bruce Char
Department of Computer Science
Drexel University
Winter 2012

2. Major Lab 2 concepts to remember
Review of Lab 2 Cycle
Major Lab 2 concepts to remember
Use of “while” versus “for” loops – when each is appropriate
“if” statement enables program to choose between execution paths
Troubleshooting / debugging
Review the “purple” error messages to understand nature of error (sometimes clear, other times not)
Syntax errors – check to see where cursor is blinking within the code edit region

3. Administrative Notes
Please contact your individual instructors with questions and problems
CLC (room 147 UC) will be staffed from Monday through Friday (odd – quiz - weeks) – 9 AM to 5 PM
In order to be eligible for a lab completion session, please see you instructor at the end of the lab period
In order to be eligible for a makeup lab session, you must contact your instructor for permission as soon as you miss your regularly scheduled lab

4. Lab 3 Overview Based on materials from Chapter 13 and 14 readings
More on user defined functions as represented by Maple proc
We define them and then invoke them to draw things.
We chain functions together to get more complicated drawings.
Using Maple tables to store a collection of data
How to initialize them
How to get a program to enter values into a table
How to use all the values you’ve put into a table in a plot
Multiple assignment
Return multiple proc results as a sequence of variables
Revisit / introduce key plotting concepts
line plots
display feature to enable multiple plots on same grid
Plotting data collected / stored in Maple tables
Plot options – titles, labels, colors

5. Lab 3 Overview – Part 0
Part 0.1 – plotting (line and display), proc function
Part 0.2 – introduction to Maple tables and multiple assignments, more on proc usage
Part 0.3 – more on plotting (plot options), procs

6. Lab 3 Overview – Part 1
Part 1 – User defined functions that draw things (boxes)
A. - proc to draw rectangular boxes anchored at origin
B. - expand proc from part A. to specify line color and an anchor point other than origin
C. – use of proc developed in B. to draw multiple boxes on same grid
Will be using proc from part B. in Lab 4 as starting point for simulation of a particle bouncing around in a box

7. Lab 3 Overview – Part 2
Use a loop and tables to simulate a “time staged” chemical reaction involving 4 chemicals
2.1 – Calculate the levels of the 4 chemicals as they change over time. Plot the levels of one of the chemicals as it changes over time
Utilizes a proc to encapsulate the simulation code and to pass in the number of time steps as an input parameter
2.2 – Extend the proc of 2.1 to :
calculate and plot the levels of all 4 chemicals on the same graph
Pass in initial concentration of all 4 reaction components as input parameters
2.3 – conduct analysis of simulation results from 2.1, 2.2

8. Lab 3 programming concepts
More about procs
The Maple proc is a user defined function in which:
You can pass parameters into the proc
You can include multiple statements
You can (optionally) return a computed value or series of values
Example
Quadratic := proc(a,b,c)
local x1, x2;
X1 := (-b + sqrt(b^2-4*a*c)) / (2*a);
X2 := (-b - sqrt(b^2-4*a*c)) / (2*a);
return X1, X2; # returns a sequence of numeric results
end proc;
X1solution, X2solution := Quadratic(1, 1, -12);
Note that this example contains a multiple assignment of results

9. Lab 3 programming concepts
Working with Maple Tables
While a Maple list can hold a series of values, it is not ideal for storing information that is being created dynamically within a loop
Maple tables contain values that all have the same variable name and are differentiated by subscripts
Tables are especially useful in conjunction with loops, where the loop counter variable can be used to represent the subscripts
Working with tables usually requires:
Declaration of the table
Storage of data in the table within a loop
Possible conversion of the table to an equivalent list for use in processes (such as plots) which require lists as input
The example on the next slide illustrates using a table to collect points for subsequent plotting – as in Part 2 of today’s lab

10. Using Maple Tables to collect data for plotting chemical reaction compositions
# Set up initial concentrations
A := A0; B := B0;
X := X0; Y := Y0;
# declare tables
indexTab := table();
Atab := table();
for i from 1 to numTimeSteps do
newA := A - k1*A*X; …
A := newA;
indexTab[i] := i;
Atab[i] := A;
end do:
# within Fplot, indexTab and Atab tables are converted to lists
display([Fplot(indexTab,Atab,"Green")], title="graph of A", labels=["time", "concentration"]);

11. Lab 3 programming concepts
A word about time staged simulations
We introduce time staged simulations in the chemical reaction exercise in today’s lab – Part 2
In a time staged simulation, the loop steps represent time slices
Each iteration of the loop calculates the next generation of values based on correlations using the present generation
In today’s chemical reaction, the concentrations the of 4 reaction components are computed for the next generation (step) from their current values and other coefficients
newA := fn(previousA, B, X, Y)
newB := fn(previousA, B, X, Y)
newX := …………..
newY := …………..

12. Lab 3 programming concepts
And finally, some Maple plot features we’ll be using today
Line plotting
Requires with(plottools);
Format  line( [x1, y1], [x2, y2] )
Display multiple plots on same grid
Requires with(plots);
Format  display( [line([x1,y1], [x2,y2]) , line([x3,y3],[x4,y4])], color=red);
Plot points contained in X and Y coordinate lists
xList := [1, 2, 3, 4, 5];
yList := [2, 4, 6, 8, 10];
Plot(xList, yList, style = point, title=“sometitle”, labels=[“x-axis”, “y-axis”]);
Converting tables to lists (plot commands require Maple lists)
xList := convert(xTab, list);
yList := convert(yTab, list);

13. Course activities for Quiz week (2/20-2/24)
Quiz 3 will be released on Friday (2/17) at 6 PM
Deadline: Thursday (2/23) at 4:30 PM
Makeup quiz – from Friday (2/24) at 9 AM through Sunday (2/26) at 11:00 PM
30% penalty
Pre-lab 3 quizlet
From Thursday (2/23 – noon) through Monday (2/27 – 8 AM)
Be sure to visit the CLC for quiz assistance