帮写MATH1062: Mathematics 1B Semester 1, 2024 Assignment 1代写R语言

日期：2024-03-17 12:34

School of Mathematics and Statistics

Assignment 1

MATH1062: Mathematics 1B

Semester 1, 2024

This individual assignment is due by 11:59pm Sunday 17 March 2024, via Can-vas. Late assignments will receive a penalty of 5% per day until the closing date. Your answers must be compiled in two separate documents, and uploaded in Can-vas to different submission boxes, as outlined in the submission instructions below. Both documents should include your SID. Please make sure you review your submis-sions carefully. What you see is exactly how the marker will see your assignment. Submissions can be overwritten until the due date. To ensure compliance with our anonymous marking obligations, please do not under any circumstances include your name in any area of your assignment; only your SID should be present. The School of Mathematics and Statistics encourages some collaboration between students when working on problems, but students must write up and submit their own version of the solutions. If you have technical difficulties with your submission, see the University of Sydney Canvas Guide, available from the Help section of Canvas.

This assignment is worth 2.5% + 2.5% = 5% of your final assessment for this course. Your answers should be neat, thoughtful, and a pleasure to read. Cite any resources used and show all working. Present your arguments clearly using words of explanation and diagrams where relevant. The marker will allocate an overall mark of at most 5 points for each part (calcu-lus and statistics) of the assignment. That is, in total, the assignment will be marked out of 5+5=10 points using two copies of the following marking rubric.

Submission instructions

Solutions to Part A must be prepared in written form, and uploaded as a single pdf file to https://canvas.sydney.edu.au/courses/57267/assignments/520092.

Solutions to Part B must be prepared as a single html file and submitted to https://canvas.sydney.edu.au/courses/57267/assignments/520093.

Part A: Calculus questions

1. For both of the first-order differential equations in standard form. below, sketch a direction field at the 16 points (x, y), x, y ∈ {0, 1, 2, 3}.

For both differential equations, trace the particular solution through point (0, 1).

Your sketch needs to be hand-written, your axes need to be labelled, and coordinates need to be clearly visible.

2. Given is the following first-order differential equation in standard form.

(a) Solve this differential equation using the method of separation of variables, as learned in lectures.

(b) For the general solution of the previous part, determine the particular solution defined by initial condition (x0, y0) = (0, 2).

3. The direction field below models the population growth of goannas on a large island near Australia. According to this model, if the initial population at time t = 0 is two goannas, how many goannas exist at times t = 6, t = 12, and t = 18? Show all your working and justify your answers.

Part B: Statistics questions

You need the following files to complete Part B.

• An R Markdown worksheet Assignment1Worksheet.Rmd at https://canvas.sydney.edu.au/courses/57267/files/35848926. You need to write your solutions as either embedded R code or text answers in this worksheet. Then use the Knit button in R Studio to generate an html file for the submission. We can only mark this html file.

• A data file A1math1005.csv at https://canvas.sydney.edu.au/courses/57267/files/35856850. This data file is needed to knit the worksheet and complete your assignment questions.