Lecture 1 arithmetic and functions

Transcription

1 Lecture 1 arithmetic and functions MATH 190 WEBSITE: Open MATH 190 in a web browser. Read and accept the Terms of Acceptable Lab Use. Open Lecture 1. PREREQUISITE: You must have taken or be taking Calculus I concurrently. If not taken here, specify the college and course title/number. Otherwise, drop this class now. If you don t need Matlab or Fortran, maybe you shouldn t be in this class. Choose your seat carefully, it will be your seat for rest of the term. Your computer s LabPC number is on the top of its case. Locate that number in the sign-up sheet. Print and sign your name there. Record: LabPC #, login name, password. MATLAB (SCILAB) AND FORTRAN Javascript programs webpages. Perl, Python, PHP program webservers. Large team-programming projects use C++ or Java. Fortran (in engineering) and C (most other areas) are used when maximum speed (math/engineering applications). Mathematica, Maple and Matlab (in engineering) are used for symbolic math (handling formulas rather than numbers). This course teaches Matlab (easier to use but slower) and Fortran (the fastest programming language but more advanced). These languages have the biggest engineering program libraries. First five weeks are Matlab, the rest is Fortran. On your home computer (1) install a free version of Matlab (Scilab) and (2) a compiler (g95.exe or gfortran) and editor (SciTE) for Fortran. Go to the class website ( for instructions on both Scilab and Fortran. Have Scilab, Fortran and SciTE up and running by the next class (if you can t get either g95 or gfortran installed, this course might be hard). Warning: installing Fortran is hard for Macs, Windows 8. ARITHMETIC Double-click the Scilab icon (top center, black with red dots). Enter the following: (active participation is required) 3+2 3*2 3/2 3^2 3**2 In Matlab, use ^ or ** for exponentiation. In Fortran, use only ** not ^. VARIABLES a variables must be initialized a = 2 a=2 spaces don t matter a A Matlab is case sensitive, Fortran is not. b=3 a+b ab a*b must use * for products, ab is two-letter variable name it is not a*b cost=1000*(1.05)^8 cost is a variable just like x, y, z

2 ( )'S PRECEDENCE ^, then * and /, then + and -. Hence a*b^2-4*d = (a*(b^2))-(4*d) a*b/c*d =? add ( ) s to remove unambiguity. (a*b)/(c*d) a*(b/c)*d a+b-c+d =? rewrite with added ( ) s (a+b)-(c+d) a+(b-c)+d) Be able (on next time s quiz) to calculate the following values: 1* *3 2^2*3 2^(2*3) -2^2 (-2)^2 modulo(13,5) the remainder of 13/5, mod(13,5) in Fortran floor(13/5) no built-in quotient function but this works. ASSIGNMENTS AND EQUALITY TESTS. In math, x 2 means x equals 2. In MatLab, x 2 is the assignment command which sets x equal to 2 (any earlier value is lost). To test if x equals 2 in Matlab or Fortran, write x= =2. x variables must be initialized x=2 x= =2 T = "True" x= =0 F = "False" x= =x+1 is always false. x=x+1 new value on left, old value on right - increments value x+1=x wrong, need variable on the left, formula on right x=input('enter a number. > ') gets x from keyboard x<=3 test if x 3 x>=3 test if x 3 x~=3 test if x 3 (x/=3 in fortran, x!=3 in PHP, C) c1.0(3) Together. Write a function even_odd(n) which returns even if n is even, odd if not. Test it on 0, 1,..., 9. // c1.0(3) Function even_odd(n) Test it on 0, 1,..., 9. Write functions in SciNotes, not in Scilab. Click Applications/SciNotes to open SciNotes. Copy the comment line // c1.0(3)... as the first line. Write the function, Write lines which test it. Select Execute... file with echo or <ctrl-l>. Note the answers in the Scilab window. File/Save as c0.1(3), save in drive H: Once a function has been executed, you can use it in Scilab. Go back to Scilab and enter: even_odd(0)

3 CLASSWORK PROBLEM DUE NOW c1.0(3) subject line: 190 c1(3) vopen/write/compose a new message. Open a browser-based client. E.g. Gmail, Hotmail, Yahoo or click the UH Webmail link on our class website, or go to your MyUH account. vcopy/paste this classwork problem from SciNotes (never from Scilab) into the message body: highlight the lines to be copied <ctrl-a>, press <ctrl-c> or select edit/copy, put the cursor in the message, press <ctrl-v> or select edit/paste. Don t attach files (attachments get scrubbed). Do not add anything else to the , not even a problem number or your name. If you must add a comment, put // before the comment so it won t give errors in Scilab. v Copy/paste the subject line exactly. Send your . HOMEWORK 1 DUE BEFORE THE NEXT CLASS to: dale@math.hawaii.edu subject line: 190 h1(4) Don t attach files. h1.1(4) On the class website, click Fortran and follow the instructions to install Fortran and SciTE. Compile and execute (as shown in the above instructions in the section "Compiling and executing") the following file. Save it as fortran_test.f95 program fortran_test integer i character(6) xx do i = 0, 6 xx = xx(1:i) // char(i+60) enddo print *, xx end Send me the 6 characters this program gives when run. to: dale@math.hawaii.edu, subject line: 190 h0(4) Note: Fortran installation can be hard, expecially on Macs. On Macs, gfortran is more likely to install than g95. For Windows 8, try the SimplyFortran compilers at the bottom of the Windows Installation page. Or maybe try FTN95. PRINTING SUPPRESSION x=0 x=1; x To suppress printing to the monitor, end lines with ;. MULTIPLE COMMANDS PER LINE To enter several commands on the same line, separate them with ; (no printing) or, (printing). x=1, x=x+1, x=x^2 Homework prob. 2.1, 2.2 x=1; x=x+1; x=x^2 What is printed? (on the next quiz)

4 CONSTANTS AND BUILT-IN FUNCTIONS x=100 %pi = = %e = log(x) =ln(x), the natural logarithm log10(x) common base-10 logarithm sqrt(4) 4 abs(-3) absolute value -3 round(4.5) rounds to nearest integer (5 in this case). ceil(4.5) rounds up to nearest >= integer. >= means > floor(4.5) rounds down to nearest <= integer. <= means < factorial(3) = 3! = 3*2*1 sin(%pi/2) angles are in radians, not degrees The trig functions sin, cos, tan are in radians. Their inverses: sin 1,cos 1,tan 1 are also written arcsin, arcsin, arctan. In Matlab/Scilab they are written atan, asin, acos. rand() rand() rand() returns a random number between 0 and 1 COMMENTS In Scilab // indicates a comment which Scilab ignores. In Matlab % precedes comments; in Fortran it is!. One of the next two lines gives an error. log(%e) natural logarithm log(%e) //natural logarithm SAVING a=[1,2,3; 4,5,6] When you close Scilab, all values are lost. Here s how to save a and all other entered data to some file, say x1.sav with extension.sav. Select file/save environment from the top left menu. Select Drive H: in the Save in: box. Enter prob1.sav in the File name: box. a clear //clears all variables, clear a,x clears just a and x a To load the saved data, select file/load environment (not file/open...) and select the filename. HELP To get help enter: help To get help about matrices, enter help matrix ERRORS Scilab/Matlab has no mouse cursor (when a cursor is needed, use the SciNotes editor window). Fix typos, with the backspace (destructive) or back arrow key (nondestructive). Copy/paste the next line then press <enter> sin[pi*x/12) Retrieve this line using the up arrow. Use the back arrow key to correct. sin(%pi*x/12) should get

5 MATLAB VARIABLES ARE INDEPENDENT x=2 f=2*x x=3 f //changing x doesn t change f, it is a memory location. Matlab variables are independent (they don t depend on other variables). To make f a dependent variable that depends on x, define it as a function f(x). WRITE FUNCTIONS IN SCINOTES -- The mouse cursor doesn t work in SciLab but does work in SciNotes. Do all classwork and homework in SciNotes, never in the SciLab (you lose 1 point for entering homework in Scilab). DEFINING FUNCTIONS Classwork prob. 2.1, 2.2, 2.3, 2.4, hw 2.3, 2.4. Write a function vol_sphere(r) which gives the volume 4 r 3 3 of a sphere of radius r. Reminder, do this in SciNotes. Go to the SciNotes window Select File/New (or <ctrl-n>). Copy/paste the next 4 lines to SciNotes (SciNotes, not SciLab). function V=vol_sphere(r) V=4*%pi*r^3/3; endfunction vol_sphere(6) //answer = Saving: click File/Save, enter a file name, click save. Entering vol_sphere makes a file vol_sphere.sce To open this file in a later session, click File/Open, select the file name. Select Execute... file with echo or <ctrl-l> Once a function has been executed, it may be used in Scilab. Go to the Scilab window and enter vol_sphere(10) this gives the volume of a sphere of radius 10 Note: vol_sphere is the function name. V is the output variable. To call the function, use the name, not the output variable. To find the volume of a sphere of radius 10, write vol_sphere(10), not V. b For every function you define, always add at least one line after the function which tests it. List the assignment name and describe the function in an initial comment line. HOMEWORK 0 IS DUE BEFORE THE NEXT CLASS CLOSED-BOOK QUIZ AT BEGINNING OF CLASS - BE ON TIME No computer, no notes, no text. 1(3) Define a given function (e.g. Vol_sphere), 2(1) Problem like What is printed? x=1; x=x+1; x=x^2. x 3(2) Write a Scilab formula such as. Answer here x 2 e would be (sqrt(x-%pi))/(x^2-%e) A score < 50% is an F. Imperative sentences are in green. They give instructions for classwork and homework. Information is carried in the black declarative sentences. Scilab code is in monospaced font.

6 SCILAB INSTALLATION, TEXTS To install Scilab on your home computer, go to select Scilab. Follow the instructions. Also note the three Scilab online texts listed here. C students will need more explanations and examples than my one-hour lectures provide. Either read the Matlab text (which occasionally differs from Scilab) or use one of the Scilab texts listed on the class website. ERRORS The most common problems are putting lines in the text such as Problem 1 which are not Scilab code. If you must include such lines, comment them out //Problem 1. If your copied text won t paste into your , make sure plain text is selected or use paste without formatting or try <Shift-Control v> to paste without formatting. Formatted text in can cause errors in Scilab. To check that your ed answers will run in Scilab, highlight the entire message <ctrl-a>, copy <ctrl-c> then paste into Scilab. The problems should run, one after the other, without errors. Copy/paste text to your s, don t attach files. To avoid virus infections, attached files are not executed. SCILAB DISPLAY (OPTIONAL) When you change a function, you often get a function being redefined error. It also echoes the line being run. To disable this enter mode(0),warning( off ) in SciNotes. To get rid of the ans = message, use the disp(... ) function. Pressing <F2> clears Scilab s console window. To stop auto-completion in SciNotes, click Preferences and uncheck both Auto completion lines. TEXTBOOK Everything on the quizzes and exams will be from the lectures not the textbook. If you are in the upper half of the class, the lecture notes should suffice. If you are in the lower half of the class, there will be things you don t understand even after studying a lecture. In this case you will need to study the reading assignment given for that lecture. If you don t understand how programs and functions operate, you won t be able to pass the exams.