1. Course page: http://www.cse.yorku.ca/course/1560
CSE/Math 1560: Introduction to Computing for Mathematics and Statistics Winter 2011
Suprakash Datta
Office: CSEB 3043
Phone: ext 77875
Course page:
8/14/2019
Math/CSE 1560, Winter 2011 1

2. Announcements This week’s lab will also be a lightweight one.
You will work individually.
You can finish lab 1 without penalty. After this week, you will have to finish each lab within the lab hours.
It is your responsibility to know which lab section you are enrolled in and show up at the correct time.
8/14/2019
Math/CSE 1560, Winter 2011

3. Last class Basic Maple commands and syntax Today:
Some programming principles
More about solving equations and
Plotting graphs.
8/14/2019
Math/CSE 1560, Winter 2011

4. Programming principles
Programs have to be readable, for
Debugging
Extending functionality
Maintenance
Evaluation
Programming style includes directions for creating code that is easier to read.
Typical software companies spend much more effort debugging and maintaining software than in developing it.
8/14/2019
Math/CSE 1560, Winter 2011

5. Programming principle 1
Variable names
Good mnemonic value
Low ambiguity
Examples:
Bad names: i,j,x,y
Better names: iter_num, current_value, x_squared
8/14/2019
Math/CSE 1560, Winter 2011

6. Programming principle 2
Comments (“documentation”)
Meant to help the reader understand code
Tradeoff between verbosity and readability
Reader should not have to spend hours trying to figure out what the programmer wants to do
Use to
describe the problem being solved
Overall idea of the solution
Idea behind each major piece
Any segment that may not be obvious
8/14/2019
Math/CSE 1560, Winter 2011

7. Verbosity vs readability
Bad example:
x:=x+1; # add one to the current value of x
Better example:
#find the number of zeroes in n!, n<=100
8/14/2019
Math/CSE 1560, Winter 2011

8. A middle school problem
Q: How many zeroes are there at the end of 100!
8/14/2019
Math/CSE 1560, Winter 2011

9. Plotting graphs Basic command: >plot(func,x=a..b);
E.g. plot(x^2,x=0..3);
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Math/CSE 1560, Winter 2011

10. Multiple graphs > plot([func1,func2,func3],x=a..b); Example:
plot([3*x^4-5*x,10*sin(x)-10,5*cos(x)+3*exp(x)],x=-2..2);
What’s missing?
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Math/CSE 1560, Winter 2011

11. A better plot
> plot(15+cos(x),x=0..4*Pi,labels = [“day”,”price”],title = “Daily price of Maple syrup”);
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Math/CSE 1560, Winter 2011

12. More plot options color=“Red” thickness = 3 More at ?plot[options]
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Math/CSE 1560, Winter 2011

13. More on solving equations
> solve(3*x+2 = 11,x);
Check your answer:
> eval(3*x+2,x=3) OR
> evalb(eval(3*x+2=11,x=3));
8/14/2019
Math/CSE 1560, Winter 2011

14. More on solving equations - 2
> solve(x^2-2 = 0,x);
Simplify:
> evalf(%) ;
BUT
> simplify(%) does not work!
8/14/2019
Math/CSE 1560, Winter 2011

15. More on solving equations - 3
> solve({3*x-2*y = 0,4*x+5*y=10},{x,y});
Simplify:
> evalf(%) ;
Notice:
solve(x^5-x^3=1,x);
RootOf(_Z^5-_Z^3-1, index = 1), RootOf(_Z^5-_Z^3-1, index = 2), RootOf(_Z^5-_Z^3-1, index = 3), RootOf(_Z^5-_Z^3-1, index = 4), RootOf(_Z^5-_Z^3-1, index = 5)
solve(x^5-x^3=1.0,x);
, *I, *I, *I, *I
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Math/CSE 1560, Winter 2011

16. More on solving equations - 4
In general use fsolve for numerical solutions.
fsolve(x^5-x^3=1,x);
fsolve(x^5-x^3=1,x,complex,maxsols=5);
To access individual solutions:
Sols:= fsolve(x^5-x^3=1,x,complex,maxsols=5);
Sols[3];
8/14/2019
Math/CSE 1560, Winter 2011

17. Steps for solving equations
> solve(exp(x^2)-50*x^2+3*x = 0, x);
Warning, solutions may have been lost
> solve(exp(x^2)-50*x^2+3*x = 0., x);
> fsolve(exp(x^2)-50*x^2+3*x = 0, x);
8/14/2019
Math/CSE 1560, Winter 2011

18. Solutions within a range
> fsolve(sin(x)-x=0,x,-Pi..Pi);
Can do the same for solving several equations simultaneously.
8/14/2019
Math/CSE 1560, Winter 2011