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: Caroline Wormell
• Lecturer(s): Caroline Wormell, Christopher Lustri

Assessment

The census date for this unit availability is 31 March 2025

• Type: Supervised exam, Online task, Short release assignment, Small test, Participation
• Description:
  • Supervised exam: Final exam, Multiple choice and written calculations, 60%, Formal exam period, 1 hour
  • Online task: Weekly online quizzes 3-10, Weekly online quizzes, 6%, Multiple weeks, 1 hour per week
  • Online task: Weekly online quizzes 1-2, #earlyfeedbacktask, 2%, Week 03, 1 hour per quiz
  • Short release assignment: Assignment 1, Written calculations, 5%, Week 04, 1-2 pages
  • Small test: Quiz, Multiple choice, 15%, Week 08, 20 minutes
  • Short release assignment: Assignment 2, Written calculations, 10%, Week 11, 3-4 pages
  • Participation: Tutorials, Participation in tutorials, 2%, Weekly, 50 minutes per week

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

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 Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
• GQ2: Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
• GQ3: Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
• GQ4: Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
• GQ5: Inventiveness Generating novel ideas and solutions.
• GQ6: Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures.
• GQ7: Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
• GQ8: Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
• GQ9: Influence Engaging others in a process, idea or vision.