Note: This unit is an archived version! See Overview tab for delivered versions.
MATH1023: Multivariable Calculus and Modelling (2018 - Semester 2)
| Unit: | MATH1023: Multivariable Calculus and Modelling (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: | MATH1013 OR MATH1903 OR MATH1907 OR MATH1003 OR MATH1923 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. |
| Assumed Knowledge: | HSC Mathematics Extension 1. Students who have not completed HSC Extension 1 Mathematics (or equivalent) are strongly advised to take the Extension 1 Mathematics Bridging Course (offered in February). |
| Timetable: | MATH1023 Timetable | |||||||||||||||
| Time Commitment: |
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Attributes listed here represent the key course goals (see Course Map tab) designated for this unit. The list below describes how these attributes are developed through practice in the unit. See Learning Outcomes and Assessment tabs for details of how these attributes are assessed.
| Attribute Development Method | Attribute Developed |
| Disciplinary Expertise: The unit will develop disciplinary expertise by delving deeper into the structure of Calculus and its applications. | Depth of Disciplinary Expertise |
| Critical thinking and problem solving through the tutorial exercises and assessment tasks | Critical thinking and problem solving |
| Communication through the ``flipped`` tutorial structure to enhance verbal communication. | Communication (oral and written) |
| Interdisciplinary competence: Through the broad and contextualised applications of the Calculus. | Interdisciplinary effectiveness |
For explanation of attributes and levels see Engineering & IT Graduate Outcomes Table 2018.
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.
Interdisciplinary effectiveness| 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 | Integration techniques for differential equations |
| Week 4 | Integrating factors, direction fields |
| Week 5 | Second order differential equations, boundary conditions |
| Week 6 | Systems of differential equations, introduction to phase plane analysis |
| Week 7 | Functions of more than one 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 |
| 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 |
| Interdisciplinary effectiveness | Yes | 33.3% |
| Communication (oral and written) | Yes | 0% |
| Critical thinking and problem solving | Yes | 33.3% |
| Depth of Disciplinary Expertise | Yes | 33.4% |
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.
