cs 121 engineering computation lab lab 2 bruce char department of computer science drexel university...
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CS 121 Engineering Computation Lab Lab 2
Bruce CharDepartment of Computer Science
Drexel UniversityOctober 6-10, 2008
©By the author. All rights reserved. Permission is given to CS121 Fall 2008 staff and students to use and reproduce these notes for their own use.
Your class instructor and TA
• Instructor for this section:
• Your TAs are:Note that verification sheet requires you to put
down instructor’s name.
Week 1 and 2 retrospective
• Lab 1: first week• Make up of Lab 1, Monday of second week• Quiz 1: second week• Quiz 1 (mercy version) ends 9pm Monday of
third week. Office hours in CLC all day Monday.
• If you are a latecomer and are catching up? Talk to instructor!
Lab 2
• Overview
• Part 1 Limited precision numbers(ch. 3 readings)
• Part 2 Data structures, functions (ch. 4 readings)
Limited precision arithmetic
• Limited precision arithmetic: use 10 digits (or some other fixed number such as 20).
• Perform an operation using as many decimal digits as necessary.
• Round the result to 10 decimal digits.
• Do the next limited precision arithmetic operation.
• Repeat until all the operations are done.
Adding 111.11 and 7.7777 in 5 digit limited precision arithmetic
• 111.11 + 7.7777:
111.11+ 7.7777 ________ 118.887 exact answer 118.89 rounded to five digits (final result)
Exact arithmetic is not the same as limited precision arithmetic
• Exact arithmetic always works things out to exactly.
• Operations between integers stay as exact integers.
• Operations with fractions stay as exact fractions.
Two kinds of arithmetic
• Maple does exact arithmetic with exact numbers• Maple does limited precision arithmetic with
limited precision numbers.• How does Maple know what to do with a
number? By the way it looks.– Numbers with decimal points, :”e’ exponents are
limited precision numbers– Numbers that are integers or ratios of integers without
decimal points are exact numbers.– Symbolic constants are also considered exact
numbers.
Floating Point Numbers
• Having a decimal point written with them
• Considered as limited-precision numbers in Maple
• Answers are rounded to the number of digits of accuracy
• e.g.– 1111.1, meaning the limited-precision version
with 5 digit numbers
“e” notation
• Scientific notation using “e” to indicate the exponent
• Considered as limited-precision numbers in Maple
• Do not use “e” for logarithms from the palette, but type the letter e on the keyboard normally
• e.g.: – 7e11, meaning 7*1011
– 2e-8, meaning 2*10-8
How do you convert an exact number into an approximate
number?
Clickable Approximate->20
evalf( expr) or evalf(expr,digits)
Bonus (not mentioned in chapter readings): how do you convert an approximate number into an exact
number?
Maple as a math word processor (sect 4.1, 4.4.5, 4.4.6)
• Ordinary entry is 2D Math mode• Can enter text. Once in text mode, can do
boldface, italics, center-justification as with a word processor.
• Control-T/Control-R (Command-T/Command-R) to switch between the two.
• When in doubt click cursor on position, then do Format -> Create Document Block. Switch to proper mode and start typing.
Demo of Math text entry
• Demo of word processing.
• Demo of Greek letters (section 4.4.6), math constants, subscripts in math mode.
Assignment, labels (sect 4.2)
• Hitting enter (return) gives a result a numerical label.
• Control-L (command-L) to refer to a result by its label.
• name := expression– Is similar – turns that into a label for the result
of evaluating the expression.
• Both are useful when you want to refer to results in later steps of a calculation.
Functions (Sect 4.4)
• Function name ( input )
produces an output.• Most math functions take one numerical input
and produce one numerical output.• Some math functions take two numerical inputs
and produce one numerical output.• Maple functions do this and more: sometimes
the inputs and outputs are not numbers.
Maple has “non math” functions (sect 4.4.7)
• function name( input1, input2, … )with output.
• Inputs and outputs do not have to be numbers.
Finishing up – save files
• Make sure your name/user id/section number/ date,time/instructor name are on the verification sheet.
• Get the verification sheet signed and handed in.• Save worksheet on desktop if you haven’t done
so already. You can call the file “MyLab1”. This will create a file called MyLab1.mw. Opens on any machine running Maple 12.
• Submit a copy to Blackboard site as evidence that you did the lab. This is not required but can help you later.
• Email a copy to yourself and/or your lab partners as an attachment so you can look at what you did for review purposes later.