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MATH2021: Vector Calculus and Differential Equations (2019 - Semester 1)

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Unit: MATH2021: Vector Calculus and Differential Equations (6 CP)
Mode: Normal-Day
On Offer: Yes
Level: Intermediate
Faculty/School: School of Mathematics and Statistics
Unit Coordinator/s:
Session options: Semester 1
Versions for this Unit:
Campus: Camperdown/Darlington
Pre-Requisites: (MATH1021 OR MATH1921 OR MATH1931 OR MATH1001 OR MATH1901) AND (MATH1002 OR MATH1902) AND (MATH1023 OR MATH1923 OR MATH1933 OR MATH1003 OR MATH1903).
Prohibitions: MATH2921 OR MATH2065 OR MATH2965 OR MATH2061 OR MATH2961 OR MATH2067.
Brief Handbook Description: MATH2021 opens with topics from vector calculus, including vector-valued functions (parametrised curves and surfaces; vector fields; div, grad and curl; gradient fields and potential functions), line integrals (arc length; work; path-independent integrals and conservative fields; flux across a curve), iterated integrals (double and triple integrals, polar, cylindrical and spherical coordinates; areas, volumes and mass; Green's Theorem), flux integrals (flow through a surface; flux integrals through a surface defined by a function of two variables, through cylinders, spheres and other parametrised surfaces), Gauss' and Stokes' theorems.

The unit then moves to topics in solution techniques for ordinary and partial differential equations (ODEs and PDEs) with applications. It provides a basic grounding in these techniques to enable students to build on the concepts in their subsequent courses. The main topics are: second order ODEs (including inhomogeneous equations), higher order ODEs and systems of first order equations, solution methods (variation of parameters, undetermined coefficients) the Laplace and Fourier Transform, an introduction to PDEs, and first methods of solutions (including separation of variables, and Fourier Series).
Assumed Knowledge: None.
Timetable: MATH2021 Timetable
Time Commitment:
# Activity Name Hours per Week Sessions per Week Weeks per Semester
1 Lecture 3.00 1 13
2 Tutorial 1.00 1 13
3 Practice class 1.00 1 13

Learning outcomes are the key abilities and knowledge that will be assessed in this unit. They are listed according to the course goal supported by each. See Assessment Tab for details how each outcome is assessed.

(1) Maths/ Science Methods and Tools (Level 2)
1. Explain what a vector function and a vector field are, and qualitatively sketch attributes of a vector field dependent on two variables.
2. Calculate the divergence, curl and gradient of a vector field and apply these to practical problems.
3. Evaluate line integrals and double and triple integrals of functions of two or more variables and path integrals of a vector function and sketch regions of integration and other geometric and physical aspects relating to these integrals.
4. Recall and explain Green’s, Gauss’ and Stokes theorems and apply these theorems to simple three-dimensional examples.
5. Transform coordinate frames between Cartesian and polar coordinates and apply these transformations to solve problems with spherical and cylindrical symmetry.
6. Solve systems of linear first order ODEs and interpret these in the framework of practical problems
7. Solve second order differential equations using a range of appropriate methods and use these ideas to solve second order linear PDEs.
8. Calculate Fourier and Laplace transforms and use these to solve differential equations.
9. Explain the use of Fourier series in approximating periodic functions and calculate coefficients of these series in a variety of situations.
Assessment Methods:
# Name Group Weight Due Week Outcomes
1 Exam No 60.00 Exam Period
2 Quiz 1 No 15.00 Multiple Weeks
3 Quiz 2 No 15.00 Multiple Weeks
4 Assignment 1 No 5.00 Multiple Weeks
5 Assignment 2 No 5.00 Multiple Weeks
Grading:
Grade Type Description
Standards Based Assessment Final grades in this unit are awarded at levels of HD for High Distinction, DI (previously D) for Distinction, CR for Credit, PS (previously P) for Pass and FA (previously F) for Fail as defined by University of Sydney Assessment Policy. Details of the Assessment Policy are available on the Policies website at http://sydney.edu.au/policies . Standards for grades in individual assessment tasks and the summative method for obtaining a final mark in the unit will be set out in a marking guide supplied by the unit coordinator.

Note that the "Weeks" referred to in this Schedule are those of the official university semester calendar https://web.timetable.usyd.edu.au/calendar.jsp

Week Description
Exam Period Assessment Due: Exam

Course Relations

The following is a list of courses which have added this Unit to their structure.

Course Year(s) Offered
Aeronautical Mid-Year 2017, 2018, 2019, 2020, 2016
Aeronautical 2017, 2018, 2019, 2020, 2016
Mechatronic Mid-Year 2017, 2018, 2019, 2020, 2016
Mechatronic 2017, 2018, 2019, 2020, 2016
Mechanical Mid-Year 2016, 2017, 2018, 2019, 2020
Mechanical 2016, 2017, 2018, 2019, 2020
Mechanical / Science 2018, 2019, 2020
Mechanical/Science(Health) 2018, 2019, 2020
Mechanical / Law 2018, 2019, 2020
Bachelor of Project Management (Built Environment) 2018
Bachelor of Project Management (Civil Engineering Science) 2018
Bachelor of Project Management (Software) 2018
Bachelor of Project Management (Built Environment) Mid-Year 2018
Bachelor of Project Management (Civil Engineering Science) Mid-Year 2018
Bachelor of Project Management (Software) Mid-Year 2018

Course Goals

This unit contributes to the achievement of the following course goals:

Attribute Practiced Assessed
(1) Maths/ Science Methods and Tools (Level 2) No 0%

These goals are selected from Engineering & IT Graduate Outcomes Table 2018 which defines overall goals for courses where this unit is primarily offered. See Engineering & IT Graduate Outcomes Table 2018 for details of the attributes and levels to be developed in the course as a whole. Percentage figures alongside each course goal provide a rough indication of their relative weighting in assessment for this unit. Note that not all goals are necessarily part of assessment. Some may be more about practice activity. See Learning outcomes for details of what is assessed in relation to each goal and Assessment for details of how the outcome is assessed. See Attributes for details of practice provided for each goal.