MATH2021代写、c++，Java程序代写

日期：2023-04-14 08:04

The University of Sydney

School of Mathematics and Statistics

Assignment 1

MATH2021: Vector Calculus and Differential Equations Semester 1, 2023

Lecturer: Eduardo G. Altmann and Fernando Viera

This individual assignment is due by 11:59pm Thursday 6 April 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. Please make sure you review your

submission carefully. What you see is exactly how the marker will see your assignment.

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.

This assignment is worth 10% 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 or explanations 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 letter grade and mark to your assignment

using the following criteria:

Mark Grade Criterion

16 A Outstanding and scholarly work, answering all parts correctly, with clear accurate expla-

nations and all relevant diagrams and working. There are at most only minor or trivial

errors or omissions.

14 B Very good work, making excellent progress, but with one or two substantial errors, mis-

understandings or omissions throughout the assignment.

12 C Good work, making good progress, but making more than two distinct substantial errors,

misunderstandings or omissions throughout the assignment.

10 D A reasonable attempt, but making more than three distinct substantial errors, misunder-

standings or omissions throughout the assignment.

6 E Some attempt, with limited progress made.

2 F Extremely limited attempt.

0 Z No credit awarded.

Copyright ? 2023 The University of Sydney 1

Imagine that during the exam period of the year 2027, an alien spaceship lands at the centre of the

Quadrangle Building (A14) at the Camperdown Campus of the University of Sydney. Using unknown

technology, it creates a force field ? = ? at the surface (, ) of the Campus given by the potential

(, ) = ?

√

2+2 ,

where (, ) = (0, 0) is the location of the ship.

Academics and students interested in investigating the phenomenon grouped in two locations

: The Business School Building (H70)

: The Fisher Library (F03)

When answering the questions below, neglect the vertical variation and treat the problem in

(, ) ∈ R2 (surface of the Campus). You may want to check the locations above using the map of the

Campus at https://maps.sydney.edu.au/.

1. (a) Calculate the force field ? = ? at an arbitrary point (, ).

(b) Calculate the strength of the force | | ? (, ) | | at an arbitrary point (, ) and determine

which loaction ( or ) experiences the strongest force. Explain why.

(c) Calculate the curl of ? at an arbitrary point (, ) and determine which location ( or

) experiences the strongest curl of ?. Explain why.

2. As part of their investigation, the groups prepared identical drones at the locations and

specified above. The work done by the force field when transporting the drones across the

Campus according to a curve is given by.

(a) Consider that each group transports their drone from their location (specified above) to

the spaceship at the Quadrangle Building (, ) = (0, 0). Which group ( or ) will

experience the smallest work ? Explain why.

(b) Consider that a drone will be transported from location to the location . Which curve

should be chosen to minimize the work ? Explain why.

3. The groups program the drones to follow curves in (, ) parametrised by

(a) Calculate the line integral

∫

where is the curve described by ? () in ∈ [0, ].

(b) Calculate the line integral

∫

where is the curve described by ? () in ∈ [0, /4].

(c) Calculate

(, ) where is the area enclosed by ? () in ∈ [0, 2].

(d) Calculate the area enclosed by ? () in ∈ [0, /2]. A sketch of the curve in (, ) is

shown below.