Program Overview

---

Overview

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.

Unit Details and Rules

• Academic unit: Mathematics and Statistics Academic Operations
• Credit points: 3
• Prerequisites: None
• Corequisites: None
• Prohibitions: MATH1011 or MATH1901 or MATH1906 or ENVX1001 or MATH1001 or MATH1921 or MATH1931
• Assumed knowledge: HSC Mathematics Extension 1 or equivalent
• Available to study abroad and exchange students: Yes

Teaching Staff

• Coordinator: Daniel Daners
• Lecturer(s): Fernando Viera, Brad Roberts

Assessment

• Type: Final exam (Open book), Assignment, Online task
• Description:
  • Final exam: multiple choice and written calculations, 65% of total mark
  • Assignment 1: written calculations, 4% of total mark
  • Quiz: multiple choice or written calculations, 15% of total mark
  • Assignment 2: written calculations, 8% of total mark
  • Webwork Online Quizzes: online task, 8% of total mark
• Weight:
  • Final exam: 65%
  • Assignment 1: 4%
  • Quiz: 15%
  • Assignment 2: 8%
  • Webwork Online Quizzes: 8%
• Due:
  • Final exam: Formal exam period
  • Assignment 1: Week 04, due date: 14 Sep 2020 at 23:59, closing date: 24 Sep 2020
  • Quiz: Week 08, due date: 20 Oct 2020 at 23:59, closing date: 20 Oct 2020
  • Assignment 2: Week 11, due date: 09 Nov 2020 at 23:59, closing date: 19 Nov 2020
  • Webwork Online Quizzes: Weekly, Weeks 2-7, 9-12
• Length:
  • Final exam: 1.5 hours
  • Assignment 1: 10 days
  • Quiz: 40 minutes
  • Assignment 2: 10 days
  • Webwork Online Quizzes: varies

Assessment Summary

• Assignments: There are two assignments, each must be submitted electronically as one single typeset or scanned PDF file only, via Canvas by the deadline.
• Quiz: One quiz will be held online through Canvas, 40 minutes, due date and closing time specified on Canvas.
• Webwork Online Quizzes: Ten weekly online quizzes, each consists of a set of randomized questions, best 8 of 10 quizzes will count, making each worth 1%.
• Final Exam: One examination during the examination period at the end of Semester, further information will be made available at a later date on Canvas.

Assessment Criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

• Result name:
  • High distinction: 85-100, representing complete or close to complete mastery of the material
  • Distinction: 75-84, representing excellence, but substantially less than complete mastery
  • Credit: 65-74, representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence
  • Pass: 50-64, representing at least routine knowledge and understanding over a spectrum of topics and important ideas in the course
  • Fail: 0-49, when you don’t meet the learning outcomes of the unit to a satisfactory standard

Late Submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

• Deduction of 5% of the maximum mark for each calendar day after the due date
• After ten calendar days late, a mark of zero will be awarded

Academic Integrity

The Current Student website provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

Learning Support

• Simple extensions: If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.
• Special consideration: If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Weekly Schedule

Week	Topic	Learning Activity	Learning Outcomes
Week 01	1. Set notation, the real number line; 2. Complex numbers in Cartesian form; 3. Complex plane, modulus	Lecture (2 hr)	LO2, LO3
Week 02	1. Complex numbers in polar form; 2. De Moivre’s theorem; 3. Complex powers and nth roots	Lecture and tutorial (3 hr)	LO3, LO4, LO5
Week 03	1. Definition of e^iθ and e^z for z complex; 2. Applications to trigonometry; 3. Revision of domain and range of a function	Lecture and tutorial (3 hr)	LO5
Week 04	1. Limits and continuity; 2. Vertical and horizontal asymptotes	Lecture and tutorial (3 hr)	LO6
Week 05	1. Differentiation and the chain rule; 2. Implicit differentiation; 3. Hyperbolic and inverse functions	Lecture and tutorial (3 hr)	LO8
Week 06	1. Optimising and sketching functions of one variable; 2. Linear approximations and differentials; 3. L’Hopital’s rule	Lecture and tutorial (3 hr)	LO7, LO9
Week 07	1. Taylor polynomials; 2. The remainder term	Lecture and tutorial (3 hr)	LO10
Week 08	Taylor series	Lecture and tutorial (3 hr)	LO10
Week 09	1. Riemann sums; 2. Definition of definite integral; 3. Non-positive functions	Lecture and tutorial (3 hr)	LO11, LO12
Week 10	1. Fundamental theorem of calculus (parts 1 and 2); 2. Functions defined by integrals; 3. Natural logarithm and exponential functions	Lecture and tutorial (3 hr)	LO14
Week 11	1. Integration by substitution; 2. Integration by parts; 3. Trigonometric substitutions	Lecture and tutorial (3 hr)	LO13
Week 12	1. Areas and volumes by slicing; 2. The disk and shell methods	Lecture and tutorial (3 hr)	LO12

Learning Outcomes

At the completion of this unit, you should be able to:

• LO1: apply mathematical logic and rigour to solve problems
• LO2: read and write basic set notation
• LO3: demonstrate competency in arithmetic operations with complex numbers in Cartesian, polar, and exponential form
• LO4: use de Moivre’s theorem to find powers and roots of complex numbers
• LO5: solve simple polynomial equations involving complex numbers
• LO6: apply an intuitive understanding of a limit and knowledge of basic limit laws to calculate the limits of functions
• LO7: use the differential of a function to calculate critical points and apply them to optimise functions of one variable
• LO8: find inverse functions
• LO9: use L’Hopital’s rule to find limits of indeterminate forms
• LO10: find Taylor polynomials and the Taylor series expansion of a function
• LO11: approximate definite integrals by finite sums and vice versa
• LO12: express areas, and volumes of revolution, as definite integrals
• LO13: apply standard integration techniques to find anti-derivatives and definite integrals
• LO14: determine properties of a function defined by an integral using the graph of its integrand
• LO15: express mathematical ideas and arguments coherently in written form

Graduate Qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course.

• GQ1: Depth of disciplinary expertise
• GQ2: Critical thinking and problem solving
• GQ3: Oral and written communication
• GQ4: Information and digital literacy
• GQ5: Inventiveness
• GQ6: Cultural competence
• GQ7: Interdisciplinary effectiveness
• GQ8: Integrated professional, ethical, and personal identity
• GQ9: Influence

Outcome Map

Learning outcomes are aligned with the University's graduate qualities.

Responding to Student Feedback

This section outlines changes made to this unit following staff and student reviews.

No changes have been made since this unit was last offered.

Additional Information

• Science student portal
• Mathematics and Statistics student portal

Work, Health and Safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work.

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

This unit of study outline was last modified on 15 Dec 2020.