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MATH1021: Calculus of One Variable (2019 - Semester 1)

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Unit: MATH1021: Calculus of One Variable (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: MATH1011 OR MATH1901 OR MATH1906 OR MATH1111 OR ENVX1001 OR MATH1001 OR MATH1921 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.
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: MATH1021 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; 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; calculating Taylor polynomials and Taylor series; applying Taylor’s Theorem to approximate functions and integrals; using integration to find areas and volumes;
2. Using calculus to solve practical problems;
3. Expressing mathematical ideas and arguments coherently in written form; fluency in basic set notation
4. Understanding the Fundamental Theorem of Calculus and its applications
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 Sets, numbers, and complex numbers
Week 2 The complex plane, polar form
Week 3 Roots of complex numbers, review of functions
Week 4 Heuristic and intuition of limits, definition of limits
Week 5 Limit laws and continuity
Week 6 Differentiation, extreme values, L'Hopital's rule
Week 7 Taylor polynomials and approximation
Week 8 The remainder term, basic Taylor series
Week 9 Riemann sums and the Riemann integral
Week 10 The Fundamental Theorem of Calculus
Week 11 Approximating integrals with Taylor polynomials, volumes
Week 12 Further integration techniques
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
Bachelor of Advanced Computing/Bachelor of Commerce 2018, 2019
Bachelor of Advanced Computing/Bachelor of Science 2018, 2019
Bachelor of Advanced Computing/Bachelor of Science (Health) 2018, 2019
Bachelor of Advanced Computing/Bachelor of Science (Medical Science) 2018, 2019
Bachelor of Advanced Computing (Computational Data Science) 2018, 2019
Bachelor of Advanced Computing (Computer Science Major) 2018, 2019
Bachelor of Advanced Computing (Information Systems Major) 2018, 2019
Bachelor of Advanced Computing (Software Development) 2018, 2019
Aeronautical Mid-Year 2018, 2019
Aeronautical/ Project Management 2019
Aeronautical 2018, 2019
Aeronautical / Arts 2018, 2019
Aeronautical / Commerce 2018, 2019
Aeronautical / Project Management 2018
Aeronautical / Science 2018, 2019
Aeronautical/Science (Health) 2018, 2019
Aeronautical / Law 2018, 2019
Biomedical Mid-Year 2018, 2019
Biomedical/ Project Management 2019
Biomedical 2018, 2019, 2016, 2017
Biomedical / Arts 2018, 2019
Biomedical / Commerce 2018, 2019
Biomedical / Project Management 2018
Biomedical /Science 2018, 2019
Biomedical/Science (Health) 2018, 2019
Biomedical / Law 2018, 2019
Chemical & Biomolecular 2018, 2019
Chemical & Biomolecular / Arts 2018, 2019
Chemical & Biomolecular / Commerce 2018, 2019
Chemical & Biomolecular / Project Management 2018
Chemical & Biomolecular / Science 2018, 2019
Chemical & Biomolecular/Science (Health) 2018, 2019
Chemical & Biomolecular / Law 2018, 2019
Chemical & Biomolecular Mid-Year 2018, 2019
Chemical & Biomolecular/ Project Management 2019
Civil/ Project Management 2019
Civil 2018, 2019
Civil / Arts 2018, 2019
Civil / Commerce 2018, 2019
Civil / Design in Architecture 2018, 2019
Civil / Project Management 2018
Civil / Science 2018, 2019
Civil/Science (Health) 2018, 2019
Civil / Law 2018, 2019
Civil Mid-Year 2018, 2019
Electrical Mid-Year 2018, 2019
Electrical/ Project Management 2019
Electrical 2018, 2019
Electrical / Arts 2018, 2019
Electrical / Commerce 2018, 2019
Electrical / Project Management 2018
Electrical / Science 2018, 2019
Electrical/Science (Health) 2018, 2019
Electrical / Law 2018, 2019
Mechanical Mid-Year 2018, 2019
Mechanical/ Project Management 2019
Mechanical 2018, 2019
Mechanical / Arts 2018, 2019
Mechanical / Commerce 2018, 2019
Mechanical / Project Management 2018
Mechanical / Science 2018, 2019
Mechanical/Science(Health) 2018, 2019
Mechanical / Law 2018, 2019
Mechatronic Mid-Year 2018, 2019
Mechatronic/ Project Management 2019
Mechatronic 2018, 2019
Mechatronic / Arts 2018, 2019
Mechatronic / Commerce 2018, 2019
Mechatronic / Project Management 2018
Mechatronic / Science 2018, 2019
Mechatronic/Science (Health) 2018, 2019
Mechatronic / Law 2018, 2019
Software Mid-Year 2018, 2019
Software/ Project Management 2019
Software 2018, 2019
Software / Arts 2018, 2019
Software / Commerce 2018, 2019
Software / Project Management 2018
Software / Science 2018, 2019
Software/Science (Health) 2018, 2019
Software / Law 2018, 2019
Biomedical/Science (Medical Science Stream) 2018, 2019
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
Civil/Science (Medical Science Stream) 2018, 2019
Electrical/Science (Medical Science Stream) 2018, 2019
Flexible First Year (2016+) 2018, 2019
Flexible First Year 2016+ / Arts 2018, 2019
Flexible First Year 2016+ / Commerce 2018, 2019
Flexible First Year 2016+ / Project Management 2018
Flexible First Year 2016+ / Science 2018, 2019
Flexible First Year 2016+ / Science (Health) 2019
Flexible First Year 2016+ / Science (Medical Science Stream) 2018, 2019
Flexible First Year 2016+ / Law 2018, 2019
Flexible First Year 2019+ /Project Management 2019
Mechanical/Science (Medical Science Stream) 2018, 2019
Mechatronic/Science (Medical Science Stream) 2018, 2019
Software/Science (Medical Science Stream) 2018, 2019
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.