Note: This unit version is currently being edited and is subject to change!
MATH1921: Calculus of One Variable (Adv) (2019  Semester 1)
Unit:  MATH1921: Calculus of One Variable (Adv) (3 CP) 
Mode:  NormalDay 
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 
PreRequisites:  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: 

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: 


Grading: 

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 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.