3+2 3*2 3/2 3^2 3**2 In matlab, use ^ or ** for exponentiation. In fortran, use only ** not ^ VARIABLES LECTURE 1: ARITHMETIC AND FUNCTIONS

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1 LECTURE 1: ARITHMETIC AND FUNCTIONS MATH 190 WEBSITE: gautier/190.html 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 shouldnt be in this class.choose your seat carefully, it will be your seat for rest of the term. Print and sign your name on the sign-up sheet. Record: login name, password. MATLAB (SCILAB) AND FORTRAN Fortran (in engineering) is used when maximum speed is needed in math/engineering applications. Matlab (in engineering) was originally used for numerical computations. It now has a lot of capabilities and can be used for symbolic math as well (handling formulas instead of numbers). This course teaches the basic notions of programming, using Matlab (easier to use but slower) and Fortran (the fastest programming language but harder to use). These languages have the biggest engineering program libraries, even though langages such as Python or C are very wide-spread and are also fundamental for engineers. We ll have six lectures about Matlab and then 5 lectures about Fortran. On your home computer (1) install a free version of Matlab (Scilab) and (2) a compiler (g95.exe or gfortran or FTN95 Fortran) and editor (SciTE) for Fortran. Go to the class website for instructions on both Scilab and Fortran. Try to have Scilab, Fortran and SciTE up and running by the next class. If you cant get either g95 or gfortran or FTN95 installed, you can use the online compiler compileonline ( Warning: installing Fortran may be hard *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 dont 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=8*3*5 cost is a variable just like x, y, z () s PRECEDENCE When calculating an algebraic expression, ˆ has the priority, 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) -2^2 (-2)^2 ARITHMETIC Double-click the Scilab icon (top center, black with red dots). Enter the following: 1

2 EUCLIDIAN DIVISION modulo(13,5) the remainder of 13/5, mod(13,5) in fortran floor(13/5) no builtin quotient function but this command gives the same result Can you guess what is the role played by the function floor? 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). In other words, the variable x contains the value 2. To test if x equals 2 in Matlab, that is to say to check if the variable x contains the value 2, write x == 2. x no value is assigned to the variable x x=2 the value 2 is assigned to the variable x x==2 T=True, it is true that the variable x equals 2 x==0 F=False, it is false that the variable x equals 0 x==x+1 is always false. x=input( Enter a number. > ) gets x from keyboard the value of x is entered by the user x<=3 test if x 3 x>=3 test if x 3 x =3 test if x 3 We can now use the built-in commands that we have learned so far to write our first function. A function is a little program which executes a sequence of instructions.. A function may need an argument, which is a specific input provided by the user. The codes of the functions are written in SciNotes, not in Scilab. To execute a function, follow the process: 1. Click Applications/SciNotes to open SciNotes. 2. Write the function, along with lines which test it. 3. Save it, using the extension.sci 4. Select Execute... file with echo or <ctrl-l>. (Note the answers in the Scilab window). Save as even odd. 5. Once a function has been executed, it may be used in Scilab. x=x+1 x+1=x we update the value of the variable x the new value of x (on left) is the old value of x plus 1 (on right new value of x is 2+1 so 3 doesn t work need variable on the left, formula on right c1.0 (Together). Write a function even odd(n) which returns even if n is even, odd if not. Test it on 0 (enter even odd(0) in Scilab) and 1 (enter even odd(1) in Scilab). IMPORTANT: here, the variable n is the argument of the function even odd. It can be any integer. To test the function, we replace n by 0 and 1, and the function tells us if 0 and 1 are even or odd numbers. 2

3 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 x=1; x=x+1; x=x**2 What is printed? CONSTANTS AND BUILT-IN FUNCTIONS x=100 %pi = π = %e = log(x) natural logarithm log10(x) common base-10 logarithm sqrt(4) 4 abs(-3) absolute value -3 round(4.5) rounds to nearest integer ceil(4.5) rounds up to nearest >= integer floor(4.5) rounds down to nearest <= integer factorial(3) = 3! = 3*2*1 sin(%pi/2) angles are in radians, not degrees rand() returns a random number between 0 and 1 The trig functions sin, cos, tan are in radians. Their inverses are the builtin functions atan, asin, acos. 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(2.72) natural logarithm log(2.72) //natural logarithm ERRORS, HELP Scilab 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. You must change the [ into a (. To get help enter: help To get help about matrices, enter: help matrix SAVING a=[1,2,3; 4,5,6] When you close Scilab, all values are lost. Heres how to save a and all other entered data to some file, say x1.sav: Select file/save environment from the top left menu. Select Desktop 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 To load the saved data select file/load environment (not file/open...) and select the filename. 3

4 MATLAB VARIABLES ARE INDEPENDENT x=2 f=2*x x=3 f //changing x doesnt change f, it is a memory location. Matlab variables are independent (they dont depend on other variables). To make f a dependent variable whose value changes as x changes, define it as a function f(x). For every function you define, always add at least one line after the function which tests it. To quit Scilab, enter quit WRITING CLASSWORK/HOMEWORK PROBLEMS. Classwork are the problems solved together during the class time. WRITE FUNCTIONS IN SCINOTES Do all classwork and homework in SciNotes, never in the SciLab.. The mouse cursor doesnt work in SciLab but does work in SciNotes. To turn auto completion off, select: Preferences>Auto-completion. Exemple: Write a function volsphere(r) which gives the volume 4πr3 3 of a sphere of radius r. In SciNotes, Select File/New (or <ctrl-n>). Copy/paste the next 4 lines to SciNotes (SciNotes, not SciLab). function V=volsphere(r) V=4*%pi*r**3/3; endfunction volsphere(6) Select Execute... file with echo or <ctrl-l> The answer should be Once the function has been executed, it may be used in Scilab. In the Scilab window, enter volsphere(10) This gives the volume of a sphere of radius 10. To save the function: click File/Save, enter a file name, click save. Entering volsphere, this makes a file volsphere.sce. To open this file in a later session, box click File/Open,, select the file name. To execute the function, select Execute...file with echo to put it in Scilab. DO NOT TURN IN THE CLASSWORK. For each classwork, follow the instructions : 1. Select File/New (or <ctrl-n>), 2. Paste the problems template comment into the file. 3. Select File/Save (or <ctrl-s>) and enter the file name. Make sure the directory is H: 4. Add the needed Scilab code and test lines. 5. Test using Execute/... with echo (or <ctrl-l >). 6. Save using File/Save (or <ctrl-s>). Unsaved work gets lost! c1.1. Write a function which calculates the length x 2 + y 2 + z 2 of the vector [x, y, z]. //c1.1 Function for the length of [x,y,z]. Add a line which tests it. c1.2. Write a function which calculates the surface area of a w l h box with a bottom, four sides but no top. Include a testing line. //c1.2 Function for the surface area of a w,l,h box with no top. Add a test line. 4

5 c1.3. Write a function which tosses a coin giving H or T for heads or tails. Test it by tossing the coin 20 times. //c1.3 A function which tosses a coin. //Toss it 10 times. Should get random Hs, Ts. c1.4 In SciNotes, write a Scilab formula which calculates π 5. Write just the 11 symbols of the formula (no function). //c1.4(1) Formula for the square root of pi to the 5th. Answer: c1.5. Write a Scilab function f(x) which calculates 1 + x + x2 + x3 for 2 3 any x. Add a line which tests f(x) on x = 12. Select File/New in SciNotes, copy/paste the commented template lines to SciNotes. Save. Fill in the required Scilab code. Execute...with echo. //c1.5(2) Function f(x) = 1+x+...+x**3/3. //Test f(x) on x=12. Answer: 661. Send all the problems in one to gautier@math.hawaii.edu with the subject line 190 h1(8). To do so, Copy/paste all homework problems into the message body. To copy lines from SciNotes to an message, highlight the lines to be copied and press <ctrl-c> or select edit/copy. Then put the cursor where you wish to paste the lines, and press <ctrl-v> or select edit/paste. Don t attach files Avoid formatting. Paste into with plain text set or right-click to get paste without formatting. Formatted text causes errors when run in SciLab, which may make you lose points. Do not send Scilab answers, send only SciNote lines. 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 wont give errors in Scilab. c1.6. Define (in SciNotes) a function vol can(r,h) which calculates the volume V = πr 2 h of a cylinder of radius r and height h. Add a fourth line which uses the function to find the volume of a can of radius 10 and height 4. File/New in SciNotes, copy/paste the template lines to SciNotes. Fill in the required Scilab code.. //c1.6(2) A function vol can(r,h) for the volume V of a can of radius r,height h. //Use it on a can of radius 10, height 4. Answer: Homework are the problems that you have to solve by yourselves at home. A list of homework will be assigned every week. It will be due before the first class of the following week HOMEWORK 1 IS DUE BEFORE FRIDAY JANUARY 23RD. 5 Test your . Select the entire message <ctrl-a>, copy it <ctrl-c>, paste it <ctrl-v> into Scilab. Press <enter>. All problems should run, one after the other with no errors. Ignore redefining function warnings. Copy the subject line exactly. Send your h1.1(1). Rewrite this sequence so that the b doesnt print. Make only one change. Keep it on one line. a=1,b=a+1,a=2,c=2*b**a/2+3 h1.2(1) Rewrite this sequence so that the a s dont print. Make only two changes. Keep it on one line. a=1,b=a+1,a=2,c=2*b**a/2+3 //h1.2(1) Rewrite so the a s dont print.

6 h1.3(3). Write a Scilab function (in SciNotes!) which calculates the volume of a box of height h, width w, length l. Include a following line which uses it to calculate the volume of box (should be 4 lines, all entered in SciNotes). //h1.3(3) Scilab function for the volume //of a box of dimensions wxlxh. Add a //line after the function which uses it //to find the vol. of a 1x2x3 box. Ans: 6 h1.4(3). Write a Scilab function g(x) whose value is log 10 (x). Add a line that uses this function to compute log 10 (30). //h1.4(3) 3 function lines, 1 testing line. //Answer: 1.21 SCILAB DISPLAY (OPTIONAL) When you execute a function, Scilab displays a warning that the function is being redefined. To disable this enter funcprot(0) in the Scilab window. To get rid of the ans = message, use the disp(... ) function. To turn auto completion off, select Preferences and uncheck Auto-completion. Pressing <F2> clears Scilabs console window. 6