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MATH1021: Calculus Of One Variable

The University of Sydney
Sydney , Australia
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Degree
Bachelors
Major
Applied Mathematics | Mathematics | Statistics
Area of study
Mathematics and Statistics
Course Language
English
About Program

Program Overview

Overview

The MATH1021: Calculus Of One Variable unit 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.


Unit Details and Rules

  • Academic unit: Mathematics and Statistics Academic Operations
  • Credit points: 3
  • Prerequisites: None
  • Corequisites: None
  • Prohibitions: 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: Florica-Corina Cirstea
  • Lecturer(s): Florica-Corina Cirstea, Dingxuan Zhou

Assessment

  • Type: Supervised exam, Assignment, Online task, Small test, Participation
  • Weight:
    • Supervised exam: 60%
    • Assignment 1: 5%
    • Online task: 15%
    • Assignment 2: 10%
    • Small test: 8%
    • Participation: 2%
  • Due dates and lengths:
    • Supervised exam: Formal exam period, 1.5 hours
    • Assignment 1: Week 04, 2-4 pages
    • Online task: Week 08, 40 minutes
    • Assignment 2: Week 11, 6-8 pages
    • Small test: Weekly, Weeks 2-7, 9-12
    • Participation: Weekly, 50 minutes/week

Assessment Summary

  • Assignments: Two assignments, each submitted electronically as a single typeset or scanned PDF file via Canvas
  • Quiz: One online quiz through Canvas, 40 minutes, submitted by the closing time of 23:59 on the due date
  • Webwork Online Quizzes: Ten weekly online quizzes, equally weighted, marks for the best eight count
  • Tutorial Participation: Satisfactory
    on-satisfactory mark assessing participation in class activities during tutorials

Late Submission

  • 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 University expects students and staff to act ethically and honestly
  • Similarity detection software is used to detect potential instances of plagiarism or other forms of academic integrity breach

Learning Support

  • Simple extensions: Application process for a five-calendar-day extension
  • Special consideration: Application process for a longer period of time or for essential commitments that impact performance in an assessment
  • Using AI responsibly: Guidance on the use of generative AI tools to support learning

Weekly Schedule

Week Topic Learning Activity Learning Outcomes
Week 01 Set notation, real number line, complex numbers in Cartesian form Lecture (2 hr) LO2, LO3
Week 02 Complex numbers in polar form, De Moivre’s theorem, complex powers and nth roots Lecture and tutorial (3 hr) LO1, LO3, LO4, LO5
Week 03 Definition, domain and range of a function, composite and inverse functions Lecture and tutorial (3 hr) LO5
Week 04 Definition of a limit, vertical and horizontal asymptotes, The Squeeze Law, continuity Lecture and tutorial (3 hr) LO1, LO6, LO15
Week 05 The derivative as a rate of change, formal definition of the derivative, The Chain Rule Lecture and tutorial (3 hr) LO1, LO6, LO15
Week 06 Optimising and sketching functions of one variable, concavity, curve sketching, L’Hopital’s rule Lecture and tutorial (3 hr) LO1, LO7, LO9, LO15
Week 07 Taylor polynomials, the remainder term Lecture and tutorial (3 hr) LO10
Week 08 Taylor series Lecture and tutorial (3 hr) LO10
Week 09 The integral as a measure of accumulation, Riemann sums, definition of definite integral Lecture and tutorial (3 hr) LO1, LO11, LO12, LO15
Week 10 Fundamental theorem of calculus, functions defined by integrals, natural logarithm and exponential functions Lecture and tutorial (3 hr) LO14
Week 11 Integration by substitution, partial fraction decomposition, integration by parts Lecture and tutorial (3 hr) LO1, LO13
Week 12 Areas and volumes by slicing, the disk and shell methods, using incremental lengths to find the arc length of a function Lecture and tutorial (3 hr) LO12, LO15
Week 13 Revision/further applications Lecture and tutorial (3 hr) LO1, LO2, LO3, LO4, LO5, LO6, LO7, LO8, LO9, LO10, LO11, LO12, LO13, LO14

Learning Outcomes

At the completion of this unit, students 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. These include:


  • 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

Additional Information

  • Lectures: Face-to-face and streamed live with online access from Canvas
  • Tutorials: Small classes in which students work through questions from the tutorial sheet in small groups on the white board
  • Tutorial and exercise sheets: Available on the MATH1021 Canvas page
  • Ed Discussion forum: Available for discussion and support
  • Science student portal and Mathematics and Statistics student portal: Available for resources and support
  • Work, health and safety: The University is governed by the Work Health and Safety Act 2011 and Work Health and Safety Regulation 2011
  • Disclaimer: The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.
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