The University of Sydney
School of Mathematics and Statistics
Assignment 1
MATH1062: Mathematics 1B Semester 1, 2024
Lecturers: Joseph Baine, Tiangang Cui, Jonathan Spreer, and Michael Stewart
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.
Copyright © 2024 The University of Sydney 1
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.
(a) dy
dx
= x
2
y+1
(b) dy
dx
= 1
3
(x− y)
2. Given is the following first-order differential equation in standard form
dy
dx
=
3x2
y
(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.
2
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.