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MATH1023: Multivariable Calculus and Modelling (2019 - Semester 1)

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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 1
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:
# Activity Name Hours per Week Sessions per Week Weeks per Semester
1 Lecture 2.00 2 13
2 Tutorial 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 1)
1. Applying mathematical logic and rigour to solving problems; expressing mathematical ideas and arguments coherently in written form; setting up differential equations which arise from mathematical models of interest to scientists and engineers; understand the relationship between a first order differential equation, its direction field, and its solution curves; solve separable and first order linear differential equations; solve second order homogeneous linear differential equations with constant coefficients; calculate partial derivatives and understand their geometric significance; finding equations of tangent planes to surfaces; optimisation of functions of two or more variables; calculating the direction derivative and gradient vector, and understanding their physical significance.
2. Applying mathematical logic and rigour to solving problems
3. Expressing mathematical ideas and arguments coherently in written form
4. Interdisciplinary effectiveness: setting up differential equations which arise from mathematical models of interest to scientists and engineers
Assessment Methods:
# Name Group Weight Due Week Outcomes
1 Exam No 65.00 Exam Period 1, 2, 3, 4,
2 Assignment No 10.00 Multiple Weeks 1, 2, 4,
3 Quiz No 15.00 Multiple Weeks 1, 2, 4,
4 Computer/Online task No 10.00 Multiple Weeks 1, 2, 4,
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
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 Year(s) Offered
Aeronautical / Science (Medical Science Stream) 2018, 2019, 2020
Aeronautical Mid-Year 2018, 2019, 2020
Aeronautical/ Project Management 2019, 2020
Aeronautical 2018, 2019, 2020
Aeronautical / Arts 2018, 2019, 2020
Aeronautical / Commerce 2018, 2019, 2020
Aeronautical / Project Management 2018
Aeronautical / Science 2018, 2019, 2020
Aeronautical/Science (Health) 2018, 2019, 2020
Aeronautical / Law 2018, 2019, 2020
Biomedical Mid-Year 2018, 2019, 2020
Biomedical/ Project Management 2019, 2020
Biomedical 2018, 2019, 2020, 2016, 2017
Biomedical / Arts 2018, 2019, 2020
Biomedical / Commerce 2018, 2019, 2020
Biomedical / Project Management 2018
Biomedical /Science 2018, 2019, 2020
Biomedical/Science (Health) 2018, 2019, 2020
Biomedical / Law 2018, 2019, 2020
Chemical & Biomolecular 2018, 2019, 2020
Chemical & Biomolecular / Arts 2018, 2019, 2020
Chemical & Biomolecular / Commerce 2018, 2019, 2020
Chemical & Biomolecular / Project Management 2018
Chemical & Biomolecular / Science 2018, 2019, 2020
Chemical & Biomolecular/Science (Health) 2018, 2019, 2020
Chemical & Biomolecular / Law 2018, 2019, 2020
Chemical & Biomolecular Mid-Year 2018, 2019, 2020
Chemical & Biomolecular/ Project Management 2019, 2020
Civil/ Project Management 2019, 2020
Civil 2018, 2019, 2020
Civil / Arts 2018, 2019, 2020
Civil / Commerce 2018, 2019, 2020
Civil / Design in Architecture 2018, 2019, 2020
Civil / Project Management 2018
Civil / Science 2018, 2019, 2020
Civil/Science (Health) 2018, 2019, 2020
Civil / Law 2018, 2019, 2020
Civil Mid-Year 2018, 2019, 2020
Electrical Mid-Year 2018, 2019, 2020
Electrical/ Project Management 2019, 2020
Electrical 2018, 2019, 2020
Electrical / Arts 2018, 2019, 2020
Electrical / Commerce 2018, 2019, 2020
Electrical / Project Management 2018, 2020
Electrical / Science 2018, 2019, 2020
Electrical/Science (Health) 2018, 2019, 2020
Electrical / Law 2018, 2019, 2020
Mechanical Mid-Year 2018, 2019, 2020
Mechanical/ Project Management 2019, 2020
Mechanical 2018, 2019, 2020
Mechanical / Arts 2018, 2019, 2020
Mechanical / Commerce 2018, 2019, 2020
Mechanical / Project Management 2018
Mechanical / Science 2018, 2019, 2020
Mechanical/Science(Health) 2018, 2019, 2020
Mechanical / Law 2018, 2019, 2020
Mechatronic Mid-Year 2018, 2019, 2020
Mechatronic/ Project Management 2019, 2020
Mechatronic 2018, 2019, 2020
Mechatronic / Arts 2018, 2019, 2020
Mechatronic / Commerce 2018, 2019, 2020
Mechatronic / Project Management 2018
Mechatronic / Science 2018, 2019, 2020
Mechatronic/Science (Health) 2018, 2019, 2020
Mechatronic / Law 2018, 2019, 2020
Software Mid-Year 2018, 2019, 2020
Software/ Project Management 2019, 2020
Software 2018, 2019, 2020
Software / Arts 2018, 2019, 2020
Software / Commerce 2018, 2019, 2020
Software / Project Management 2018
Software / Science 2018, 2019, 2020
Software/Science (Health) 2018, 2019, 2020
Software / Law 2018, 2019, 2020
Biomedical/Science (Medical Science Stream) 2018, 2019, 2020
Bachelor of Project Management (Built Environment) 2018
Bachelor of Project Management (Built Environment) Mid-Year 2018
Bachelor of Project Management (Civil Engineering Science) 2018
Bachelor of Project Management (Civil Engineering Science) Mid-Year 2018
Bachelor of Project Management (Software) Mid-Year 2018
Bachelor of Project Management (Software) 2018
Chemical & Biomolecular/Science (Medical Science Stream) 2018, 2019, 2020
Civil/Science (Medical Science Stream) 2018, 2019, 2020
Electrical/Science (Medical Science Stream) 2018, 2019, 2020
Flexible First Year (2016+) 2018, 2019, 2020
Flexible First Year 2016+ / Arts 2018, 2019, 2020
Flexible First Year 2016+ / Commerce 2018, 2019, 2020
Flexible First Year 2016+ / Project Management 2018
Flexible First Year 2016+ / Science 2018, 2019, 2020
Flexible First Year 2016+ / Science (Health) 2019, 2020
Flexible First Year 2016+ / Science (Medical Science Stream) 2018, 2019, 2020
Flexible First Year 2016+ / Law 2018, 2019, 2020
Flexible First Year 2019+ /Project Management 2019, 2020
Mechanical/Science (Medical Science Stream) 2018, 2019, 2020
Mechatronic/Science (Medical Science Stream) 2018, 2019, 2020
Software/Science (Medical Science Stream) 2018, 2019, 2020
Bachelor of Computer Science and Technology 2016, 2017
Bachelor of Computer Science and Technology (Advanced) 2016, 2017
Bachelor of Computer Science & Tech. Mid-Year 2016, 2017
Bachelor of Information Technology 2015, 2016, 2017
Bachelor of Information Technology/Bachelor of Arts 2015, 2016, 2017
Bachelor of Information Technology/Bachelor of Commerce 2015, 2016, 2017
Bachelor of Information Technology/Bachelor of Medical Science 2016, 2017
Bachelor of Information Technology/Bachelor of Science 2015, 2016, 2017
Bachelor of Information Technology/Bachelor of Laws 2015, 2016, 2017

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 100%

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.