HW 4 HINTS. 1. Chapter 6

Transcription

1 HW 4 HINTS 1. Chapter 6 ***IMPORTANT GENERAL GUIDELINE*** When running commands inside loops and conditional statements, in general ALL output should be suppressed by placing a semicolon at the of the line. Chapter 6 #6 (for/ loops and nested loops) Use 2 for/ loops: one nested inside the other. The basic structure of a for/ loop is on page of Gilat. There is a useful example on page of using nested loops to create a matrix-you just have to replace the conditional statements with the formula. Chapter 6 #12 (for/ loops and nested loops) Similar idea here, but first define a 7x7 matrix M whose elements are all zeros ( zeros, p40), then replace appropriate elements with the Pascal number (since each row of the triangle has a different number of elements, leave the rest zero). Example for #12: Create the Pascal triangle having 4 rows. X=zeros(4); for i=1:4 for j=1:4 if i>=j X(i,j)=nchoosek(i-1,j-1); X Chapter 4 #19 (for/ loops, conditional statements) Similar idea here, but with an if statement (p185) inside the loop. The pseudocode would be as follows: Given the number n, the 1

2 2 HW 4 HINTS digits can be obtained by letting H=floor(n/100), T=floor((n-H*100)/10), and O=floor(n- H*100-T*10) and if H*T*O = 6*(H+T+O), display ( disp, p101) n. See p185 for the syntax of the if statement. Example for #19: Write a MATLAB script file that finds and displays all integers between 300 and 700 whose product of digits is 2 times the sum of the digits.. for n=300:700 H=floor(n/100); T=floor((n-H*100)/10); O=floor(n-H*100-T*10); if H*T*O == 2*(H+T+O) disp(n) Chapter 6 #21 (loops, conditional statements, relational operators) Similar to #19, but using if n is prime and (p179) n+6 is prime. The isprime command makes this very easy-see the MATLAB help for details. Example for #21: Find all primes p between 100 and 500 satisfying p and p + 4 are both primes. Display them as pairs in a two-column matrix. A=[]; k=1; for n=100:500 if isprime(n) && isprime(n+4) A(k,1)=n; A(k,2)=n+4; k=k+1; disp(a) Chapter 6#23 (loops, conditional statements) Define count=0 (number of perfect numbers found) and your loop for n=1:10000 and use the divisors command (see MATLAB help) to find the divisors. Then see if the sum of the divisors = 2*n (since n will be included in the

3 HW 4 HINTS 3 divisors array). When this happens, display n, and let count=count+1 and break the loop (p202) if count=3. Chapter 7 of Gilat covers functions. Chapter 7 #1 2. Chapter 7 (anonymous functions) p of Gilat. Define the function anonymously in their M- file using notation. Read the example on p233 (especially noting the element-byelement definition needed when plotting). Note that all plots MUST have titles and axes labels (see Gilat p144, with formatting details on p ). Example for #1: Write an anonymous MATLAB function for f(x) = 5x 2 e 0.8x using elementby-element operations. (1) Calculate f (4) and f (5). (2) Use the function to make a plot of y = f(x) for 3 x 6 clc f (x) 5*(x.^2).*exp(0.8*x); f(4) f(5) t=-3:0.01:6; y=f(t); plot(t,y) Chapter 7 #11 Inputs to the anonymous function are string G and array C. Read the book to learn about strings (p53), which are arrays of characters. Each character converts to a number (using the double command): A=65, B=66, etc. So the easiest way to convert the letter grades to points is to calculate 70-G, multiply element-by-element with C, then calculate the sum of the result divided by sum of C. To get one decimal place, refer to the MATLAB help on round (specifically, round(x,n) ). Example for #11: Use the function described in problem to calculate the average of a student whose record is: Grade B A C D F Credit hours

4 4 HW 4 HINTS GPA (G,C) round(sum((70-g).*c)/sum(c),1); G=double([ B A C D F ]); C=[ ]; GPA(G,C) Chapter 7 #12 Inputs to the anonymous function are the three arrays A, B, and C. Use vectors and the dot product formula to find the angle between A-B and C-B (as done in Chapter 3 #10). Example for #12 (notice the three points A, B and C are different from the homework): Write an anonymous MATLAB function theta that determines the angle in degrees formed by the intersection of two lines. Use the function to determine the angles between the two lines determined by these noncollinear pointswhose intersection is B. A=[3, -4, 6], B=3.5, 6,-3], C=[-4.5, 3, -7] theta (A,B,C) acosd(dot(a-b,c-b)/(norm(a-b)*norm(c-b))); A=[3-4 6]; B=[ ]; C=[ ]; theta(a,b,c) The answer is , which is the angle of ABC in degree. Chapter 7 #24 Input to the anonymous function is a vector x. Use the length command (p49) to find n and divide by sum(1./x) to find H. For the other problem, create a separate function file using the function command. Refer to p , paying particular attention to the example file near the top of p229 which is used (in your M-file) midway through the page. Also emphasize that the name of the function file must agree with the name given on the first line (in this example, chp7one.m )-Matlab defaults to this name, so don t change it! If you want, you can click on New then Function under the home tab and Matlab will give the default format (you just need to replace everything with the appropriate names and variables). Chapter 7 #21 Since this function has no output, it should start with function NAME(A,B,C), where A and B are the vertices and C is the third point.

5 HW 4 HINTS 5 Here is the pseudocode to plot the ellipse: If A(2)=B(2) (vertices are points of horizontal axis) a=abs(a(1)-b(1))/2 (find horizontal axis) P=(A+B)/2 (find center) b=sqrt(a^2*(c(2)-p(2))^2/(a^2-(c(1)-p(1))^2)); Else (vertices are points of vertical axis) b=abs(a(2)-b(2))/2 (find vertical axis) P=(A+B)/2 (find center) a=sqrt(b^2*(c(1)-p(1))^2/(b^2-(c(2)-p(2))^2)); End (See p186 for syntax of an if/else statement) Once P, a, and b are calculated, use polar coordinates to plot the ellipse (define t=[0:0.01:2*pi], x=p(1)+a*cos(t), y=p(2)+a*sin(t), plot(x,y))