MATH1023代写、代写Python/C++编程

日期：2023-03-17 08:26

Assignment 1

MATH1023: Multivariable Calculus and Modelling Semester 1, 2023

Lecturer: Clio Cresswell

This individual assignment is due by 11:59pm Wednesday 15 March 2023, via

Canvas. Late assignments will receive a penalty of 5% per day until the closing date.

A single PDF copy of your answers must be uploaded in Canvas at https://canvas.

sydney.edu.au/courses/48841. It should include your SID. Please make sure you

review your submission 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 5% of your final assessment for this course. Your answers should be

well written, neat, thoughtful, mathematically concise, and a pleasure to read. Please cite any

resources used and show all working. Present your arguments clearly using words of explanation

and diagrams where relevant. After all, mathematics is about communicating your ideas. This

is a worthwhile skill which takes time and effort to master. The marker will give you feedback

and allocate an overall mark to your assignment using the following criteria:

Copyright c? 2023 The University of Sydney 1

A researcher has conducted an experiment concerning the placement of an object, given as y

in centimetres, at time t in hours, after an initial force on 22/02/2023 at 9:00 a.m. disturbed

the object from rest. It is a particularly delicate experiment and only the following data is

gathered successfully.

Date Time y Y, the rate of change of y The rate of change of Y

22/02/2023 11:00 a.m. 0.1 ?0.2 0.5

22/02/2023 3:09 p.m. 10?5 2× 10?6 ?6× 10?5

Even with such limited data, to advance on the project the researcher considers, separately,

the following three possible models for the experiment. Each model consists of a differential

equation.

1. Find the general solution y(t) to model (1). Then give the particular solution that satisfies

y being 3.2 cm from an initial reference point at the very start of the experiment.

2. The solutions y(t) = Ae?2t and y(t) = e?2t(A cos(t) + 5 sin(t)) (where A is an arbitrary

constant) solve models (2) and (3), but the researcher cannot remember which one solves

which.

(a) Find which solution solves which model, clearly showing your working.

(b) Give the particular solution for each model that satisfies y being 3.2 cm from an

initial reference point at the very start of the experiment.

3. Accepting that y is 3.2 cm from an initial reference point at the very start of the experi-

ment, construct a table mirroring the one above, where the values for y, Y and its rate of

change, are the values given by model (2). Then, produce the same table that fits model

(3). Give results to 2 significant figures.

4. Construct a table of the differences in the recorded and predicted y values and the

recorded and predicted rates of change of the y values for both model (2) and (3). Give

results to a single significant figure. Does a particular model appear to fit the data better

and if so, which one and why? Your explanation should be short, simply showing your

understanding. A single sentence of around 10-20 words is all that is required for clarity.

5. Feeling curious, the researcher then considers the following model for the experiment,

accepting y as 3.2 cm from an initial reference point at the very start of the experiment:

dy

dt= 2y + sin(t). (4)

Using the Direction Field Grapher available on the MATH1023 Canvas site, give the

predicted value of this model for 8 p.m. 23/02/2023.