Question

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 Maple’s 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 define 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, different 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 find 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 definition of derivative to find the derivative of f at 0, that is, take the limit of the difference quotient using Maple. (e) Comment on what you have found.

question 2. We will solve two differential equations that look similar but lead to very different-looking solutions. We will then plot those solutions. (a) Use dsolve to solve dy /dx = (1−y)^2, y(0) = 0.8, and dy /dx = (1.01−y)(1−y), 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 different colours or different 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.

Answer 1

Here is the completed code for this problem. Comments are included, go through it, learn how things work and let me know if you have any doubts. Also a word of advice: in future, when posting another question, please split these kinds of problems into multiple questions. They are big enough to be single questions. Also there is difficulty while submitting answers. Thanks

Answer for part 1 (a2a)

// PartA.java

import java.io.File;

import java.io.FileNotFoundException;

import java.io.PrintWriter;

import java.util.HashMap;

import java.util.Iterator;

import java.util.Map;

import java.util.Scanner;

public class PartA {

                static HashMap<String, Integer> medalsbyCountries;

                static HashMap<String, Integer> medalsbyEvents;

                /**

                * method to read the input file and fill the hashmaps

                * @param filename- input file name

                * @throws FileNotFoundException - if file not found

                */

                static void readFile(String filename) throws FileNotFoundException {

                                medalsbyCountries = new HashMap<String, Integer>();

                                medalsbyEvents = new HashMap<String, Integer>();

                                Scanner scanner = new Scanner(new File(filename));

                                /**

                                * looping through the file

                                */

                                while (scanner.hasNext()) {

                                                /**

                                                * getting country and event names

                                                */

                                                String country = scanner.nextLine();

                                                String eventType = scanner.nextLine();

                                                String specificEvent = scanner.nextLine();

                                                /**

                                                * Adding to the maps of countries and medals, if not already exists

                                                */

                                                if (!medalsbyCountries.containsKey(country)) {

                                                                medalsbyCountries.put(country, 1);

                                                } else {

                                                                /**

                                                                * updating the medals if country exists

                                                                */

                                                                int medals = medalsbyCountries.get(country);

                                                                medals++;

                                                                medalsbyCountries.put(country, medals);

                                                }

                                                /**

                                                * Adding to the maps of event types and medals, if not already exists

                                                */

                                                if (!medalsbyEvents.containsKey(eventType)) {

                                                                medalsbyEvents.put(eventType, 1);

                                                } else {

                                                                /**

                                                                * updating the medals if event type exists

                                                                */

                                                                int medals = medalsbyEvents.get(eventType);

                                                                medals++;

                                                                medalsbyEvents.put(eventType, medals);

                                                }

                                }

                }

                /**

                * method to display and save the results from the hashmaps

                * @throws FileNotFoundException- if output file cannot be created

                */

                static void displayAndSave() throws FileNotFoundException {

                                /**

                                * Defining a PrintWriter for writing to a2q1out.txt file

                                */

                                PrintWriter writer = new PrintWriter(new File("a2q1out.txt"));

                                System.out.println("Count of gold medallists by country:");

                                writer.println("Count of gold medallists by country:");

                                /**

                                * looping through the hashmap

                                */

                                for (Map.Entry<String, Integer> entry : medalsbyCountries.entrySet()) {

                                                System.out.println(entry.getKey() + " - " + entry.getValue());

                                                writer.println(entry.getKey() + " - " + entry.getValue());

                                }

                               

                                System.out.println("Count of gold medallists by event type:");

                                writer.println("Count of gold medallists by event type:");

                                /**

                                * looping through the hashmap

                                */

                                for (Map.Entry<String, Integer> entry : medalsbyEvents.entrySet()) {

                                                System.out.println(entry.getKey() + " - " + entry.getValue());

                                                writer.println(entry.getKey() + " - " + entry.getValue());

                                }

                               

                                writer.close();//closing the writer and saving the file

                }

                public static void main(String[] args) {

                                try {

                                                /**

                                                * Reading the file and displaying the results

                                                */

                                                readFile("a2a.txt");

                                                displayAndSave();

                                } catch (FileNotFoundException e) {

                                                e.printStackTrace();

                                }

                }

}

Answer for part2 (a2b)

// PartB.java

import java.io.File;

import java.io.FileNotFoundException;

import java.util.ArrayList;

import java.util.Scanner;

public class PartB {

                static ArrayList<Sentence> sentences;//array list of sentences

                /**

                * method to read the input file, and fill the sentences array list

                */

                static void readFile(String filename) throws FileNotFoundException {

                                sentences = new ArrayList<Sentence>();

                                Scanner scanner = new Scanner(new File(filename));

                                Sentence sentence = new Sentence();

                                while (scanner.hasNext()) {

                                                String word = scanner.next();

                                                sentence.add(word);

                                                char ending = word.charAt(word.length() - 1);

                                                if (ending == '.' || ending == '!' || ending == '?'

                                                                                || ending == ':' || ending == ';' || !scanner.hasNext()) {

                                                                sentences.add(sentence);

                                                                sentence = new Sentence();

                                                }

                                }

                }

                /**

                * method to print the first and last five sentences

                */

                static void printFirstAndLastFive() {

                                if (sentences != null && sentences.size() >= 5) {

                                                System.out.println("First five sentences: ");

                                                for (int i = 0; i < 5; i++) {

                                                                System.out.println(sentences.get(i).getText());

                                                }

                                                System.out.println(" Last five sentences: ");

                                                for (int i = sentences.size() - 1; i >= sentences.size() - 5; i--) {

                                                                System.out.println(sentences.get(i).getText());

                                                }

                                }

                }

                /**

                * method to analyze and print the stats

                */

                static void analyzeStats() {

                                int totalWords = 0, totalLetters = 0;

                                int totalSentences = sentences.size();

                                for (Sentence s : sentences) {

                                                //finding total words and letters

                                                totalWords += s.getWordCount();

                                                totalLetters += s.getLettersCount();

                                }

                                System.out.println(" Summary statistics");

                                System.out.println("Letters: " + totalLetters);

                                System.out.println("Words: " + totalWords);

                                System.out.println("Sentences: " + totalSentences);

                                double lettersByWords = (double) totalLetters / totalWords;

                                double wordsBySentences = (double) totalWords / totalSentences;

                                double ARI = 4.71 * lettersByWords + 0.5 * wordsBySentences - 21.43;

                                System.out.println("Readability: "+ARI);

                }

               

                public static void main(String[] args) {

                                try {

                                                /**

                                                * reading and displaying the stats

                                                */

                                                readFile("a2b.txt");

                                                printFirstAndLastFive();

                                                analyzeStats();

                                } catch (FileNotFoundException e) {

                                                e.printStackTrace();

                                }

                               

                }

}

//Sentence.java

public class Sentence {

                private String text;

                private int wordCount;

                private int lettersCount;

               

                public Sentence() {

                                text="";

                                wordCount=0;

                                lettersCount=0;

                }

                public void add(String word){

                                text+=word+" ";

                                wordCount++;

                                /**

                                * Reading letters count

                                */

                                for(int i=0;i<word.length();i++){

                                                if(Character.isLetter(word.charAt(i))){

                                                                lettersCount++;

                                                }

                                }

                }

                public String getText() {

                                return text;

                }

                public int getLettersCount() {

                                return lettersCount;

                }

                public int getWordCount() {

                                return wordCount;

                }

}

/*OUTPUT part 1 (partial)*/

/*OUTPUT part 2 (partial)*/