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# Math Math 015

UMD

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This 2 page Class Notes was uploaded by Sindhu Furtari on Monday September 19, 2016. The Class Notes belongs to Math 015 at University of Maryland taught by Ben Bezejouh in Fall 2016. Since its upload, it has received 37 views.

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Date Created: 09/19/16

Math 206 Fall 2016 Project 2 Generated For: bmao12 Covers: This project covers up through and including some easy problems from Chapter 15 of the tutorial. What to Submit: For this project you will need to create and upload a single script m-▯le called matlab2.m (all lower case!). This ▯le should do all of the things requested in the problems below in the order speci▯ed. Grading Method: Grading for this course is via an automated grading system which checks both that your answers are correct and that you used the correct method of obtaining them. This is why it is important to assign your answers to the correct variable names and use the methods speci▯ed. Use of comments (if you know how to use them) is ▯ne - comments are ignored by the grading system. If there are any unexpected errors or the ▯le is incorrectly named (hence can’t be found) then the project will automatically earn a grade of 0 so make sure you run your m-▯le through Matlab and check the output before submitting! Be very careful about making sure that any necessary symbolic variables are de▯ned in your code. The assumption should be that we will run your m-▯le through a clear matlab process. Final Warning: When you test your script m-▯le, type the following in Matlab: >> clear all >> matlab2 Alternatively type clear all in Matlab and then use the run button in the project editor. Whatever you do, don’t put clear all inside the actual m-▯le though, it will be removed before grading because it trashes the grading software. This will make sure that you’ve cleared out any residual de▯ned variables and it will make sure that your code is not going to error. You have been warned! 1. This problem is here to remind you to make sure you syms any variables you need. You can do it ▯rst, or later when you need them, but don’t forget! ▯ ▯ 2. Find d 1 + 2x + 4x ▯ 9x . Assign to p2. [3 pts] dx 2 3. Find dx2 [cos(2x + 3)]. Assign to p3. [4 pts] ▯p ▯▯ 4. Find d 3 1 + 3x + 2x + 3x 4 ▯ . Assign to p4. [4 pts] dx ▯ x=34 h▯ ▯ ▯ ▯▯▯i ▯ d2 6 ▯ 5. Find dt2 2 4 ▯ (4+t) ▯ . Assign to p5. [4 pts] t=41 R 2 6. Find (5x + 8x + 2)cos(8x + 3) dx. Assign to p6. [4 pts] R22 7. Find 7 cos(7x + 6) dx. Assign to p7. [4 pts] 8. The following problem spans several questions. First de▯ne f(x) = 8x + 5 + 3 symbolically. Assign [3 pts] 3+x to f(x). 9. Evaluate f(4). Assign to p9. [3 pts] 00 10. Evaluate f (▯34). Assign to p10. [4 pts] 11. Evaluate dx [(3x + 6)f(x)]. Assign to p11. [4 pts] R 12. Evaluate and simplify 8x + 3 + (3x + 7)f(x) dx. Assign to p12. [4 pts] 13. The following problem spans several questions. First de▯ne g(x) = 1+5x +7x +8x with a function handle (not symbolically!) Assign to g. [3 pts] ▯ ▯ 14. Evaluate and simplify (wrap in simplify) g 5 . Assign to p14. [3 pts] 2+x ▯ p ▯00 15. Evaluate 6 g(cosx) (6). Note that the 6 is plugged in, not multiplied. Assign to p15. [4 pts] R 0:20 16. Evaluate 0:03xg(4x + 4) dx. Assign to p16. [4 pts] 17. Solve the di▯erential equation y +0 yt= 6t + 2 + sint. Assign to p17. [6 pts] 0 18. Suppose a symbolically de▯ned h(t) satis▯es the initial value problem h (t)+9sint = h(t) with h(4) = 0. [7 pts] Use dsolve wrapped in subs to ▯nd h(0). Assign to p18. 19. Plot y = 6x +9x+2 using ezplot. Assigning this to p19 is just a way of the grading software checking [4 pts] it. Assign to p19. 20. The goal of this for loop is to add the numbers 1;2;:::;117. Set the variable p20 equal to 0. Then run [6 pts] a for loop which goes through all those numbers, adding them each in turn to p20, changing p20 each time. 21. The goal of this while loop is to ▯nd the ▯rst number whose factorial has 28 digits (meaning it’s at [6 pts] least equal to 10 ). Set the variable p21 equal to 1. Then, while p21! is less than 10 , increase p21 by 1, changing p21 each time. Note that Matlab has a command for factorial. 22. Set the variable p22 equal to 46. Then run a for loop which goes through the numbers [8 pts] 1 2 31 8 ; 8 ;:::; 8 12 2 123 1231+1 and adds them in turn to p22, changing p22 each time. 23. Set the variable p23 equal to 5. Then run a while loop which, while p23 is less than 153068008, squares [8 pts] it and adds 4, changing p23 each time.

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