Note: This unit version is currently under review and is subject to change!
MATH2021: Vector Calculus and Differential Equations (2019  Semester 1)
Unit:  MATH2021: Vector Calculus and Differential Equations (6 CP) 
Mode:  NormalDay 
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 
PreRequisites:  (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 vectorvalued functions (parametrised curves and surfaces; vector fields; div, grad and curl; gradient fields and potential functions), line integrals (arc length; work; pathindependent 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: 

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)Assessment Methods: 


Grading: 

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 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.