課程名稱︰計算機程式 課程性質︰化工系必修 課程教師︰徐振哲 開課學院：工學院 開課系所︰化工系 考試日期（年月日）︰2019/11/28 考試時限（分鐘）：忘了 試題 : Problem 1 (15 points): Make the following array of plots: ┌─────────────────────────┐ │Create the following function: │ │z=x*sin(x)exp(-y^2) │ │use 3D surface plot with contour, plot the above │ │function between x=0~2pi and y=-2~2 │ ├─────────────────────────┤ │Plot the following points with black circles and │ │y=x^2 with a red solid line for x=0~5 │ │┌──┬──┬──┬──┬──┬──┐ │ ││ x │ 0 │ 1 │ 2 │ 3 │ 4 │ │ │├──┼──┼──┼──┼──┼──┤ │ ││ y │ 1 │2.5 │ 4 │9.5 │ 17 │ │ │└──┴──┴──┴──┴──┴──┘ │ ├─────────────────────────┤ │plot y=x^3*exp(x) and y=x*exp(x) on the same plot │ │using solid and dashed lines, respectively, │ │between -1 and 3. │ └─────────────────────────┘ Problem 2 (15 points): Do the following in ONE*.m file and function file and properly display results: (i) (5 points) Ask the user to input a positive integer "m". Find and display minimum "n" such that 1*2*3+2*3*4+3*4*5+...+n*(n+1)*(n+2)>m. (ii) (5 points) Solve the following equation sets: x+3y-z=3 2x-3y+3z=4 y+z=5 (iii) (5 points) Create the following function, and then plot for x=-1~5 y=|x| for x<1 y=exp(x)*sin(x) for 1<=x<3 y=log(x) for x>=3 Problem 3 (20 points): Do the following using ONE*.m file: (i) (10 points) Ask the user to input a positive even integer "n" greater than 2, if the input number is not a positive even integer, display "Invalid input", then ask the user to input it again for up to THREE TIMES. For the fourth wrong input, display "bye-bye" then exit the code. (ii) (10 points) Find show the pair of a and b, such that a and b are both prime numbers and a+b=n. Problem 4 (20 points): Fibonacci series is a series starts from a1=0 and a2=1, and each term equals the sum of the previous two terms, a_n+2_ = a_n+1_ + a_n_ such that the a1~a7 are 0,1,1,2,3,5,8, respectively. Answer the following questions (You are NOT allowed to use functions related to Fibonacci): (以底線表示下標) (i) (10 points) Ask the user to input a positive integer m, and display a_m_. (ii) (10 points) Plot the ratio of a_n+1_/a_n_ vs. n for n=1~200. Also draw a horizontal line for y=(1+sqrt5)/2. (Note: a_n+1_/a_n_ approaches (1+sqrt5)/2 when n approaches infinite) Problem 5 (15 points): In ONE*.m file, use the following methods to find and properly display approximated pi: pi_1, pi_2, pi_3 (i) (5 points) pi_1: Calculate the approximate area of the following curve: y=sqrt(1-x^2) between 0and 1 with n=150. You may use either A or B. https://i.imgur.com/Mvl0ANI.jpg (ii) (5 points) Create two arrays AA and BB, each has 1500 elements of random number between -1 and 1. C=AA.^2+BB.^2. Use "mask" to calculate the fraction of elements in C that are less than 1. Use this fraction to calculate pi_2. (iii) (5 points) Use 20 terms approximation to calculate approximated pi: pi_3 (you are NOT allowed to type in terms manually.) π 1 1 1 1 ─ = 1 - ─ + ─ - ─ + ─ ...... 4 3 5 7 9 Problem 6 (10 points): Use "rand" to generate a random positive integer N below 99999, then create a 1*M array AA with 0, 1, and 2, where AA represent N as a ternary number (三進位數). For example, N=5, AA=[1 2]; N=24, AA=[2 2 0]. Properly display AA and N (not necessarily to be in the same line.) Note: You are NOT allwed to use ANY Matlab functions for conversion between binary, decimal, and hexadecimal numbers such as "bi2de", "bin2dec", "dec2bin", "dec2hex", or "de2bi". Problem 7 (5 points, Answer on THIS exam sheet): Write down your comments and suggestionsto this course (for example: course, lecturer, exams, and teaching assistant.) -- --

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