Introduction to Computing for Mathematics and Statistics Winter 2011

Suprakash Datta datta@cse.yorku.ca Office: CSEB 3043 Phone: 416-736-2100 ext 77875 Course page: http://www.cse.yorku.ca/course/1560 CSE/Math 1560:Introduction to Computing for Mathematics and Statistics Winter 2011 Math/CSE 1560, Winter 2011

Math/CSE 1560, Winter 2011 Announcements No class on Wednesday Labs will start this week. This week’s lab will be a lightweight one, with very little credit attached. Next week we will commence with more challenging assignments and more associated credit. Gauss lab is in Ross S 110, not 100 as given on the web page. Please give Maple and Moodle a trial run before the lab if possible.

Math/CSE 1560, Winter 2011 Last class • Course overview • Different UI’s of Maple • Today: Basic Maple commands and syntax

Math/CSE 1560, Winter 2011 Samples of Maple at work - 5 eclipse 190 % xmaple &

Math/CSE 1560, Winter 2011 Samples of Maple at work - 6

Samples of Maple at work - 7 Math/CSE 1560, Winter 2011

Math/CSE 1560, Winter 2011 Using Maple • Starting and exiting • Getting help • Interrupting Maple • The restart command > a:=10; a := 10 > a; 10 > restart; > a; a

Math/CSE 1560, Winter 2011 Maple components • Interface • Kernel • Basic functionality • Library • Basic library • Packages

Math/CSE 1560, Winter 2011 Basic commands • > eval(Pi); • Pi • > evalf(Pi); • 3.141592654 • > evalf(Pi,30); 3.14159265358979323846264338328 • > Digits:=20; • Digits := 20 • > evalf(Pi); • 3.1415926535897932385 Specify precision What changed?

Math/CSE 1560, Winter 2011 Remember help • > ?Digits • The Digits Environment Variable • Calling Sequence • Digits := n • Parameters • n - natural number • Description • - The Digits environment variable controls the number of digits that Maple uses when calculating with software floating-point numbers. • - The default value of Digits is 10. The value of Digits is changed by using the assignment operator. • ………………………………………….

Math/CSE 1560, Winter 2011 Basic commands - 2 • > Pi_20:= evalf(Pi,20); • > evalf(sin(Pi)); • > evalf(sin(Pi_20)); • > %% - %; • -9 • 0.4102067615 10 Output suppressed to save space

Math/CSE 1560, Winter 2011 Basic commands - 3 • > solve(x^2-1=0,x); • 1, -1 • > solve(x^4-1=0,x); • -1, 1, I, -I • > solve(x^3-1=0,x); • 1/2 1/2 • 1, - 1/2 + 1/2 I 3 , - 1/2 - 1/2 I 3 • > solve(11*x^4-9*x+17=0,x); • RootOf(%1, index = 1), RootOf(%1, index = 2), RootOf(%1, index = 3), • RootOf(%1, index = 4) • 4 • %1 := 11 _Z - 9 _Z + 17

Math/CSE 1560, Winter 2011 Basic commands - 4 • > simplify(sqrt(4)+5); • 7 • > simplify((x+1)^2); • 2 • (x + 1) • > simplify((x+1)^2-1); • 2 • x + 2 x • > expand((x+1)^2); • 2 • x + 2 x + 1 • > factor((x+1)^2-1); • x (x + 2)

Math/CSE 1560, Winter 2011 Basic commands - 5 • > expand((x+1)^(10)); • 10 9 8 7 6 5 4 3 2 • x + 10 x + 45 x + 120 x + 210 x + 252 x + 210 x + 120 x + 45 x + 10 x + 1 • > sort(x+1-x^2); • 2 • -x + x + 1 • > expand(sin(2*x)); • 2 sin(x) cos(x)

Math/CSE 1560, Winter 2011 Basic operators • Arithmetic: +,-,*,/,^,mod • Logical: and,or,xor,not,implies • Relation: <,<=,>,>=,=,<> • Variable names: • Start with a letter • Letters, digits, or _ • Reserved words (e.g.: Pi, Digits,…) • Try ?reserved

Math/CSE 1560, Winter 2011 More syntax • Brackets: • () : group expressions • [] : lists, vectors, matrices,… • {} : sets := vs = > my_eqn:=2*x=2; my_eqn := 2 x = 2 > solve(my_eqn,x); 1 > y:=%: > y; 1 Note the colon

Math/CSE 1560, Winter 2011 More syntax - 2 Recall my_eqn:=2*x=2; • Manipulating equations • > rhs(my_eqn);lhs(my_eqn); • 2 • 2 x • Comments • Starts with “#” • Goes to the end of the line 2 commands on 1 line.

Math/CSE 1560, Winter 2011 Programming principles • Variable names • Good mnemonic value • Low ambiguity • Comments • 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 wanted to do

Introduction to Computing for Mathematics and Statistics Winter 2011