MATH 3421 Maple Assignment 1 Due February 13, 2019 Maple is a Computer Algebra System that is able to do some of the algebraic calculations of mathematics. Maple also allows you to present nicely-formatted mathematics! The purpose of this assignment is to remind you of Maples capabilities. Ground Rules 1. Your assignment must have a properly-formatted title identifying the assignment number and course. There must be an author. There must be other text with properly-formatted math included. 2. Your assignment must be as a Worksheet, not a Document, and commands must be in Maple notation, not 2-D Display. 3. Load all packages at the top of the worksheet, just below the title. 4. Lines whose output you do not want to see must end with a : 5. Object names must be descriptive. f1 is a very bad choice for an object name, especially if you dene many functions. 6. When naming an object, := has a space before and a space after. Commas must be followed by a space. 7. Comment your code! If you are commenting the code itself, use an inline code comment, (command line starting with a #), but if it is a comment on your math, it must be in Text Mode. 8. Late assignments lose 10% per day. 9. All graphs must be black-and-white. If they have more than one plot, dierent line styles must be used to distinguish the plots, and there must be a legend. 10. Eliminate unnecessary blank lines (Ctrl-Delete). Assignment 1.

question1: The function f(x) ={x^2 sin(1/x) if x is not equal to zero and 0 if x is zero} has an interesting feature at 0. (a) Plot f(x) over some reasonably small interval that contains 0. (b) Find the derivative of x^2 sin( 1 /x) , and nd the limit of the derivative as x 0. Remember that a limit must be a single value, not a range of values. (c) Plot the derivative. Is the result of the previous part surprising? (d) Use the denition of derivative to nd the derivative of f at 0, that is, take the limit of the dierence quotient using Maple. (e) Comment on what you have found.

question 2. We will solve two dierential equations that look similar but lead to very dierent-looking solutions. We will then plot those solutions. (a) Use dsolve to solve dy /dx = (1y)^2, y(0) = 0.8, and dy /dx = (1.01y)(1y), y(0) = 0.8. All Maple DE commands like the dependence of dependent variables made explicit in the DE (y(x), not y). (b) Plot both solutions on the same graph. The solutions from the previous part will be equations, which Maple will refuse to plot. Use rhs to extract the right-hand side of each equation. Make sure they have either dierent colours or dierent linestyles, and make sure your graph has a legend and title. (c) Comment on the two solutions and their graphs, and make sure your conclusion includes properly formatted math.