ENGR 1371 Computing for Engineers

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1 Homework and In-Class Assignments Do the following problems from the textbook (2 nd edition) and/or other resources. These are tentative topics/dates and the instructor can change them if and when needed. Please check this document regularly as it will be periodically updated. Most recently updated on Assignments are for practice only and are not included in the grading policy (unless specified otherwise). Students do not need to submit completed assignments for grading except if one has questions/debugging problems. Solutions to select problems will be posted upon completion of corresponding topics. However, students are expected to work through all problems covered in the assignments. Please follow the instructions given with each problem. All MATLAB programs must be completed in accordance with the Programming Assignment Format. All calculations and other work done on paper must be completed in accordance with the Engineering Problem Solving Format. Date/Week of Chapter / Topic Programming Projects / Problems Chapter 1: Introduction to Computers and Programming Chapter 2: Getting Started with MATLAB None. 1. Write a script file (*.m file) to solve this problem. You throw a ball straight up in the air with an initial speed of 25 m/s [g = 9.8 m/ s 2 ]. Compute the tp, the time it takes to reach the highest point, and hp, the highest distance the ball rises from the release point. 2. Write a script file (*.m file) to solve this problem. A jet aircraft is flying 100 feet above a level plain at 600 mph. Suddenly the ground begins to rise at a 4 degree slope. Calculate tx, the amount of time the pilot has to raise the nose before the aircraft strikes the ground. 3. Write a script file (*.m file) to solve this problem. Page 1 of 19

2 After a very hard week at work, Kirk is driving to Helen, Georgia for a tubing trip (to cool off). He drives 200 miles north from his home to Timbuktu. He then turns right and travels 400 miles east to Helen. Write a script to compute the linear distance, d, from his home to Helen Chapter 3: Vectors and Arrays: Vectors - 1D Arrays 1. Problem 1 from textbook. Write a script file (*.m file) to solve this problem. 2. Write a script file (*.m file) to solve this problem. Vector manipulation is an integral part of MATLAB. Do the following exercises using the vector shown below to practice your skills. Notes: Do not hard code any of the answers for this problem. You cannot use iteration for any of the parts of this problem. Vec = [ ]; a. Create a new vector, veca, that is the same as the vector vec except that all of the 2s have been deleted. b. Create a new vector, vecr, that is the reverse of vec. c. Create a new vector, vecb, that swaps the first and second halves of vec, so vecb will contain the second half of vec followed by the first half of vec. d. Create a new vector, vecs, that contains all of the elements in the vec that are smaller than 45. The numbers should be in the same order as they were in vec. e. Create a new vector, vect, that contains true wherever vec is greater than 10 and false everywhere else f. Create a new vector, vec2, that contains every other element of vec starting with the second element. g. Create a new vector, vec3r, that contains every third element of vec starting from the last element and going toward the first element in vec. h. Create a new vector, vecf, that contains the indices of every element in vec that is equal to 2. Page 2 of 19

3 3. Problem 3 Consider the following vector in MATLAB: vec = [ ]; Which of the following will produce an error vec(6) = 1; vec(4) = [ ]; vec(0) = 1; vec( [4 5] ) =1; vec = [[6 [5] vec]]; 4. Problem 4 from textbook. 5. Write the commands that take a vector of numbers, a, and return a new vector b, containg the cubes of the positive numbers in a. If a particular numbers is negative, the 0 is put in its place Example [ ] will produce [ ] 6. Write a MATLAB program seriesln2.m to show that the sum of the infinite series: 1 converges to ln 2. n= 0 ( 2n + 1)( 2n + 2) a. Do this by computing the sum for n=0,1,2 50. b. Do this by computing the sum for n=0,1, c. Do this by computing the sum for n=0,1, d. Do not use a loop to solve this problem. e. Use the command sum. Page 3 of 19

4 Chapter 3: Vectors and Arrays: 2D Arrays Chapter 4: Execution Control: Conditional Structures 1. Type the following array and use MATLAB commands to answer the following questions A = a. Create a vector v consisting of the elements in the second column of A b. Create a vector w consisting of the elements in the second row of A. c. Create a 4 x 3 array B consisting of all elements in the second through fourth columns of A. d. Create a 3 x 4 array C consisting of all elements in the second through fourth rows of A. e. Create a 2 x 3 array D consisting of all elements in the first two rows and the last three columns of A. f. Find the maximum and minimum values in each column of A. g. Find the maximum and minimum values in each row of A. h. Find the maximum and minimum values in A. i. Sort each column and store the result in an array E. j. Sort each row and store the result in an array F. k. Add the elements in each column and store the result in an array G. l. Add the elements in each row and store the result in an array H. 1. Write a script that calculates the variable mode, the mode of transport used to travel a certain distance according to the following definition. You are given a variable called distance that represents the distance to be covered in feet (1 mile=5,280 feet). distance <= 2miles: Walk 2 miles < distance <=10 miles: Bicycle Page 4 of 19

5 10 miles <distance <=30 miles: MARTA distance> 30 miles: Delta Airlines 2. You are given a variable named sidecount specifying the number of sides on a geometric figure. You need a string containing the name of the shape according to the value of sidecount. Write the instruction to calculate the variable ans using the following table. Value of sidecount Value of ans Less than 3 Not a shape 3 Triangle 4 Quadrilateral 5 Pentagon Greater than 5 Other 3. You need a script to compute a normalilzed class average by the following steps: Given a vector of test scores, tests, first you compute a new vector, normtests, which will contain the test scores on a linear scale from 0 to 100. A zero still corresponds to a zero, and the highest test score will correspond to a 100. Test this script with: Tests = [ ]; Add to this script the calculation of the letter grade of the class average: Average> 90 => A 80<=average<90 => B 70<=average=80 => C 60<=average<70 =>D Average<60 => F Test your script with the following grade vectors: [ ] -> B [ ] -> C [ ] -> F Page 5 of 19

6 tests Hint: normtests = * 100. max(tests) Use MATLAB command mean to calculate average. 4. Suppose the legal drinking age is 21 in your state. Write and test a MATLAB program to determine whether a person is old enough to drink. Use the command input to create a user-input interface. 5. When a part is manufactured, the dimensions are usually specified with a tolerance. Assume that a certain part needs to be 5.4 cm long, plus or minus 0.1 cm. Write a MATLAB program to determine whether a part is within these specifications. 6. Many solid rocket motors consist of three stages. Once the 1 st stage burns out, it separates from the missile and the 2 nd stage lights. Then the 2 nd stage burns out and separates and the 3 rd stage lights. Finally, once the 3 rd stage burns out, it also separates from the missile. Assume that the following data approximately represent the times during which each stage burns: Stage 1: seconds; stage 2: seconds and stage 3: seconds. Write a MATLAB program to determine whether the missile is in stage 1, stage 2, stage3 or free flight Chapter 4: Execution Control: Iteration 1. Complete the following exercises in iteration. Although you will probably see ways to solve these problems without iteration, you must use it for all these solutions. a. Iterate through the following vector, a, using a for loop, and cdreate a new vector, b, of the same size containing Boolean values. The item in b should be true if the corresponding item in a is positive, and false for all other values. a = [ ] b. Iterate through the vector, a, using a while loop, and create a new vector, c, containing Boolean values by the same criteria as in exercise a. Page 6 of 19

7 c. Iterate through the following string array, d, using for loop, and create a new vector, f. The item in f should be the character A wherever the corresponding item in d is G, and T wherever the item in d is B. All other characters should not be changed. d = GBBBBBGGBGBABGBFBBGGGTGBGBGGBBGGJGGBGKBBLGBGTGG GB d. Iterate through the string array, d, using a while loop and create a new vector, g, under the same rules as exercise c. e. Iterate through the following logical array, n, using a for loop, and create a new vector, m, whose item should be 2 wherever the corresponding item in n is ture and -1 otherwise. N = [ ture false false true true true false true false true false false false false true false true false false true true false true true false] f. Iterate through th following array, z, using a while loop. Replace every element with the number 3 until you reach a number larger than 50. Leave the rest unchanged. z = [ ] 2. Write a script that transforms a vector v by raising each element in the vector to the power of its index and then reversing the order of the elements Example: V = [ ] -> [ ] Write two programs to do this problem: o using a for loop and o using vector operations only. 3. Write a MATLAB program to plot the following function: Page 7 of 19

8 15 4x + 10 x 9 y = 10x x 9 for 5 x x < 0 Use a for loop Use if elseif end statements 4. Write a MATLAB program to compute the sum of the first 15 terms in the series: f = 15 5k k = 1,2,3, k Use a for loop Use vectors only 5. Write a MATLAB program to determine how many terms (N) are required for the sum of the series: f = N 5 k k = 1,2,3, k to exceed 10,000. What is the sum for this many terms? Use a while loop. 6. Determine how long it will take to accumulate at least $10,000 in a bank account if you deposit $500 initially and $500 at the end of each year, if the account pays 5% annual interest. o Write a MATLAB program to solve this problem. Page 8 of 19

9 Chapter 11: Plotting 1. We need to plot a hyperbolic paraboloid. This is special in mathematics due to the existence of a saddle point or minimax that exists at the origin. This function can be created from the equation Z= (x^2/4)-(y^2/4). Write a MATLAB script to plot this function with following restrictions: a. Vary x and y between -3 and 3, incremented in steps of.1 b. Draw the picture as a wire frame with the lines colored to indicate the y value c. Put a color bar on the plot identifying the colors to values of y Make sure the plot is labeled and titled. 2. Problem 3 from textbook Write a MATLAB program to do this problem. Show your results for the interval: [ 0,4π ] only. Use the command linspace. 3. Problem 6 from textbook. 4. Problem 7 from textbook Chapter 5: Functions 1. Write a function circle.m that consumes the radius r of a circle, calculates the 2 circumference and area of the circle: c = 2πr and a = πr, and gives the outputs as c and a. Write a program problem1.m that calls the function circle.m in order to calculate the circumference and area of a circle with radius 10 mm. 2. Write a function quadroots.m that consumes the three coefficients: a, b, c ; 2 calculates the two roots of the quadratic equation: ax + bx + c = 0 and gives the Page 9 of 19

10 Chapter 12: Matrices 1. Problem 1 from textbook. 2 2 b + b 4ac b b 4ac outputs as x1 = ; x2 =. 2a 2a Write a program problem2.m to test your function quadroots.m for the 2 equation: x x 6 = 0. The program should call the function quadroots.m to calculate the roots of the given equation. 3. Write a function polynomialvalue.m that consumes a vector: a [ a a ] = n n 1...a 0, and a scalar value x, calculates the polynomial value: n n 1 f ( x) = an x + an 1 x a1x + a0 and gives the outputs: n, the order of the polynomial and f, the value of the polynomial at x. Write a program polynomialvaluetest.m that calls the above function in 2 order to calculate the value of the polynomial: x x 6 at x = 3. Read the help pages on MATLAB s command: polyval; but do not use polyval to do this problem. 2. Write a short script to solve the system of linear equations: 2x+5y+7z=0 3x+2y+3z=2 X+3y+2z=5 3. Problem 2 from textbook. Write a script to compute and print the value of the dollar in eullars. For example, your script might print 1 dollar = 4.64 eullars. Use the fprintf command Chapter 6: Character Strings 1. We need to count the vowels in a character string. Follow these directions: a. Write a function called isconsonant that takes in a letter of the alphabet. Page 10 of 19

11 It returns true if the letter is a consonant, and false if it is a vowel. You can assume that only lowercase letters will be passed into the function, but you should not need to write out all the consonants! b. Write an iterative function called countvowels that takes in a character string and returns the number of vowels in the array. You must use isconsonant in this function Do not use switch statements. The following is an example of an output >> b=isconsonant('a') b = 0 >> b=isconsonant('b') b = 1 >> n=countvowels('engineering') n = 5 2. Coding & Decoding Write a function mycoding.m, which takes in a string array as an input, creates a coded string array using your coding scheme and displays the coded string as the output. Write a function mydecoding.m, which takes in the coded string as an input, decodes it using your decoding scheme and displays the original string as the output. Write a main or test program mycodetest.m to test your functions for various cases. The following is an example of an output. Your coding scheme may be different from the one shown. >> a=mycoding('matlab is cool') Page 11 of 19

12 a = WK^VKL*s}*myyv >> b=mydecoding(a) b = MATLAB is cool Chapter 7: Cell Arrays and Structures 1. Calculate your GPA this semester Write a function makesemester.m that creates the structure mysemester with the following fields: lastname, firstname, class, credit and grade. Write a program mysemester.m that uses the function makesemester.m to create a structure array myfall2008 with the fields mentioned above. The 1 st element in the array includes your 1 st class with current grade, 2 nd element includes your 2 nd class with current grade and so on. For example for the 1 st element: myfall2008(1) =makesemester('jones','david','engr1371',3,'b'); Include in your program the commands to calculate your GPA for this semester. 2. Suppose we have a car structure that has the following fields: baseprice: a number representing the starting price of the car trim: the style of the car, represented as a string cc: a Boolean variable indicating that the car has cruise control dualab: a Boolean variable indicating that the car has dual air bags o Write a function makecar.m that creates the structure car with the fields mentioned in the problem. o Write a program examplecar.m that uses the function makecar.m to create a structure car with a base price of $10,000.00, trim LS, no cruise control and no dual air bags. o Write a function caroptions.m that takes in a car structure and returns its final price from the base price and options: The standard trim of the car is s Page 12 of 19

13 Chapter 9: Recursion 1. Problem 2 from textbook. If the trim is LS add $600 If the trim is LE, add $1200 If the car has cruise control, add $150 If the car had dual air bags, add $300 o Include in the program examplecar.m a command to calculate the final price of the car using the function caroptions.m. o Write a function carinventory.m that consumes an array of car structures and calculates the total value (sum of the final prices of all the cars) of the vehicles. o Include in the program examplecar.m a command to calculate the total value of an inventory with N cars. Test your program for N=3 using: a base price of $10,000.00, trim LS, no cruise control and no dual air bags. a base price of $10,000.00, trim LS, cruise control and no dual air bags. a base price of $10,000.00, trim LS, cruise control and dual air bags. o Use the function caroptions.m for the above calculation. 2. Write a function myrecursive.m that takes in a positive integer N and displays the following message N times: I am going to work very hard to become a highly qualified engineer!. Your function must utilize recursion. Test your function for N=100. Use the disp command to display the statement. Chapter 8: File I/O Chapter 15: Numerical Methods 1. Problem 6, Chapter 11 from textbook. Download relevant Excel files from the class website. Download relevant Excel files from the class website. Page 13 of 19

14 1. The subject of thermodynamics makes extensive use of tables. Although many properties can be described by fairly simple equations, others are poorly understood, or the equations describing their behavior are very complicated. It is much easier just to tabulate the data. For example, consider the data for steam at 0.1 MPa (approximately 1 atm), given in the following table. Temperature, C Internal Energy, kj/kg^ a. Use a linear interpolation to determine the internal energy at 215C b. Use linear interpolation to determine the temperature if the internal energy is 2600 kj/kg. 2. Determining how much water will flow through a culvert is not as easy as it might seem at first. The channel could have a non-uniform shape, obstructions might influence the flow, friction is important, and so forth. A numerical approach allows us to fold all of the concerns into a model of how the water actually behaves. Consider the following data collected from an actual culvert: Height, ft Flow, ft3/sec Page 14 of 19

15 a. Compute a best-fit linear, quadratic, and cubic fit for the data, and plot the information on the same graph. b. Which model best represents the data? (Linear is first order, quadratic is second order, and cubic is third order.) 3. Generate f(x)=x 2 for x = [ ], a. Compute and plot the linear and cubic-spline interpolation of the data points over the range [-3:0.05:6]. b. Compute the value of f(4) using the linear interpolation and cubic-spline interpolation. c. What are the respective errors when the answer is compared with the actual value of f(4)? 4. Assume that the following set of temperature measurements is taken from the cylinder head in a new engine that is being tested for possible use in a race car: Time, sec Temperature, F a. Compare plots of these data, assuming linear interpolation and assuming cubic-spline interpolation for values between the data points, using time values from 0 to 5 in increments of 0.1 s. b. Using the data from part (a), find the time value for which there is the largest difference between its linear interpolated temperature and its cubic interpolated temperature. Page 15 of 19

16 5. Assume that we measure temperatures at three points around the cylinder head in the engine from Programming Project 6, instead of at just one point. The set of data is then the following. Time, sec Temp1 Temp2 Temp a. Assume that these data have been stored in a matrix with six rows and four columns. Determine interpolated values of temperature at the three points in the engine at 2.6 seconds using linear interpolation. b. Using the information from part (a), determine the time when the temperature reached 75 at each of the three points in the cylinder head. 6. The following data set represents the time and altitude values for a sounding rocket that is performing high-altitude atmospheric research on the ionosphere. a. Determine the equation that best represents the data, using the interactive curve-fitting tools available in MATLAB. Plot the altitude data. b. The velocity function is the derivative of the altitude function. Using numerical differentiation, compute the velocity values form the data.. Plot the velocity data. (Note that the rocked is a two-stage rocket.) c. The acceleration function is the derivative of the velocity function. Using the velocity data determined from part (b), compute the acceleration data. Plot the acceleration data. Time Altitude 0 60 Page 16 of 19

17 10 2, , , , , , , , , , , , , , , , , , , , , , , , , Although the MATLAB makes it easy to find the roots of a function, sometimes all that is needed is a quick estimate. This can bed done by plotting a function and zooming in very close to see where the function equals zero. Since MATLAB draws straight lines between data points on a plot, it is good to draw Page 17 of 19

18 circles or stars at each data point, in addition to straight lines connecting the points. Plot the following function and zoom in to find the roots. >>n = 5; >>x = linspace (1, 2*pi, n); >>y =x.* sin(x) + cos (1/2*x). ^2-1./(x-7); >>plot(x,y, =o ) 8. The function f(x) is defined by f(x) =4e^-x. a. Plot this function over the interval [0, 1] with a suitable number of points. b. Use numerical integration techniques to estimate the integral of f(x) over [0, 0.5] and [0, 1]. c. Compare these results to the theoretical answer Chapter 13: Images 1. Write a MATLAB program which does the following: Reads three images (use jpg format) Creates a collage with the three images Creates a border of equal width around all three images Displays the final collage as an image Writes a new image file collage.jpg. Select three images which are of similar size, format and relevant to engineering. Chapter 14: Processing Sound (FYI only) 1. Write a MATLAB program which does the following: Reads an audio file (*.wav) Plots the sound data in the time domain. Plays the sound data. Performs an FFT on the sound data. Plots the data in the frequency domain Chapter 16: Sorting 1. Sort the following array using the algorithms listed below. Show all of the Page 18 of 19

19 vectors excluding the empty ones created at each step. [ ] Using insertion sort Using merge sort Using quick sort You do not need MATLAB for this problem. Clearly show all steps. Chapter 17: Searching Graphs TBD Page 19 of 19