Note: This unit version is currently being edited and is subject to change!
MATH1923: Multivariable Calculus and Modelling (Adv) (2019 - Semester 2)
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| Unit: | MATH1923: Multivariable Calculus and Modelling (Adv) (3 CP) |
| Mode: | Normal-Day |
| On Offer: | Yes |
| Level: | Junior |
| Faculty/School: | School of Mathematics and Statistics |
| Unit Coordinator/s: | |
| Session options: | Semester 2 |
| Versions for this Unit: |
| Campus: | Camperdown/Darlington |
| Pre-Requisites: | None. |
| Prohibitions: | MATH1003 OR MATH1013 OR MATH1907 OR MATH1903 OR MATH1023 OR MATH1933. |
| Brief Handbook Description: | Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates multivariable differential calculus and modelling. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include mathematical modelling, first order differential equations, second order differential equations, systems of linear equations, visualisation in 2 and 3 dimensions, partial derivatives, directional derivatives, the gradient vector, and optimisation for functions of more than one variable. Additional topics covered in this advanced unit of study include the use of diagonalisation of matrices to study systems of linear equation and optimisation problems, limits of functions of two or more variables, and the derivative of a function of two or more variables. |
| Assumed Knowledge: | (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. |
| Department Permission | Department permission is required for enrollment in this session. |
| Timetable: | MATH1923 Timetable | |||||||||||||||
| Time Commitment: |
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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 1)| Assessment Methods: |
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| Grading: |
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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 |
| Week 1 | Introduction to models |
| Week 2 | First order differential equations |
| Week 3 | Integrating factors and direction fields |
| Week 4 | Second order differential equations, boundary conditions |
| Week 5 | Systems of linear differential equations, interpretation through diagonalisation, intro to phase plane analysis |
| Week 6 | Functions of more than one real variable |
| Week 7 | Limits of functions of more than one real variable. |
| Week 8 | Partial derivatives, tangent planes, linear approximation |
| Week 9 | Directional derivatives, gradient vector, and applications |
| Week 10 | Chain rule, implicit differentiation |
| Week 11 | Optimising functions of two or more variables |
| Week 12 | Further optimisation and interpretation using diagonalisation |
| Week 13 | Revision/further applications |
| 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 1) | No | 99.98% |
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.
