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MATH1921: Calculus of One Variable (Adv) (2019 - Semester 1)

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Unit: MATH1921: Calculus of One Variable (Adv) (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: MATH1001 OR MATH1011 OR MATH1906 OR MATH1111 OR ENVX1001 OR MATH1901 OR MATH1021 OR MATH1931.
Brief Handbook Description: Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates differential calculus and integral calculus of one variable and the diverse applications of this theory. 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 complex numbers, functions of a single variable, limits and continuity, differentiation, optimisation, Taylor polynomials, Taylor's Theorem, Taylor series, Riemann sums, and Riemann integrals. Additional theoretical topics included in this advanced unit include the Intermediate Value Theorem, Rolle's Theorem, and the Mean Value Theorem.
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: MATH1921 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; fluency in basic set notation; perform arithmetic operations with complex numbers; applying de Moivre’s Theorem to find roots and powers of complex numbers; understanding the concept and definition of limits, and applying limit laws to calculate limits; apply l’Hopital’s rule to compute limits; calculating derivatives; using calculus to solve practical problems; calculating Taylor polynomials and Taylor series; applying Taylor’s Theorem to approximate functions and integrals; using integration to find areas and volumes; understanding the Fundamental Theorem of Calculus and its applications; understand and apply the main theorems of differential calculus (Intermediate Value Theorem, Mean Value Theorem, and Rolle’s Theorem).
2. Applying mathematical logic and rigour to solving problems; using calculus to solve practical problems
3. Expressing mathematical ideas and arguments coherently in written form; fluency in basic set notation
4. Interdisciplinary effectiveness
Assessment Methods:
# Name Group Weight Due Week Outcomes
1 Exam No 65.00 Exam Period 1, 2, 4,
2 Quiz No 15.00 Multiple Weeks 1, 2, 4,
3 Computer/Online task No 10.00 Multiple Weeks 1, 2, 4,
4 Assignment No 10.00 Multiple Weeks 1, 3, 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 Sets, numbers, and complex numbers revision
Week 2 Functions (injective, surjective, inverse)
Week 3 Heuristic and definition of limits, and limit laws
Week 4 One sided limits, limits to infinity, continuity
Week 5 Intermediate Value Theorem, differentiation
Week 6 Extreme values, Rolle’s Theorem, Mean Value Theorem
Week 7 l’Hopital’s Rule, Taylor polynomials
Week 8 Taylor’s Theorem, higher derivative tests
Week 9 Taylor series, complex exponential function
Week 10 Riemann sums and Riemann integral
Week 11 Fundamental Theorem of Calculus
Week 12 Arc length, volume, and area
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
Bachelor of Computer Science and Technology 2016, 2017
Bachelor of Computer Science and Technology (Advanced) 2016, 2017
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 2016, 2017, 2018, 2019, 2020
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 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
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

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.