This course covers single-variable calculus and introductory linear algebra. The emphasis is on understanding the material such that it both can be applied across a range of fields including the physical and biological sciences, engineering and information technologies, economics and commerce, and can also serve as a base for future mathematics courses. Many applications and connections with other fields will be discussed although not developed in detail. Not all the material will be developed in a rigorous theorem-proof style, although students will see some examples of this and may work some examples themselves. Students interested in a deeper understanding of mathematics and more mathematical/theoretical aspects of topics (including those students who are interested in the more theoretical aspects from engineering, computing, science, and economics) should enrol in MATH1115.
Topics to be covered include:
Calculus - Limits, including infinite limits and limits at infinity. Continuity and global properties of continuous functions. Differentiation, including mean value theorem, chain rule, implicit differentiation, inverse functions, antiderivatives and basic ideas about differential equations. Transcendental functions: exponential and logarithmic functions and their connection with integration, growth and decay, hyperbolic functions. Local and absolute extrema, concavity and inflection points. L'Hopital's rule. Riemann integration and the Fundamental Theorem of Calculus. Techniques of integration including the method of substitution and integration by parts. Volumes.
Linear Algebra - Solution of linear systems of equations. Matrix algebra including matrix inverses, linear transformations, matrix factorisation and subspaces. Determinants. Example applications including computer graphics, the Leontief Input-Output Model, and various linear models in science and engineering. Complex numbers.
Learning Outcomes
Upon successful completion, students will have the knowledge and skills to:
- Explain the fundamental concepts of calculus and linear algebra and their role in modern mathematics and applied contexts. These concepts include the solution of linear systems, matrix algebra, linear transformations and determinants in Linear Algebra; and limits, continuity, differentiation, local and absolute extrema, Riemann integration and the fundamental theorem of calculus in Calculus.
- Demonstrate accurate and efficient use of calculus and linear algebra techniques as they relate to the concepts listed above.
- Demonstrate capacity for mathematical reasoning through explaining concepts from calculus and linear algebra and reproducing familiar proofs.
- Apply problem-solving using calculus and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.
Other Information
Secondary School Prerequisite: A satisfactory result in ACT Specialist Mathematics Major-Minor or NSW HSC Mathematics Extension 1 or equivalent is recommended. Students who took ACT Specialist Mathematics Major or NSW HSC Mathematics Advanced or equivalent and are confident with that material may be ready for MATH1013. Students who took ACT Specialist Mathematics Major or NSW HSC Mathematics Advanced or equivalent and are not confident with that material, and students with a level of mathematics equivalent to ACT Mathematical Methods, should take MATH1003 before taking MATH1013.
Students who are concerned about their level of preparation for MATH1013 should contact the MSI first-year coordinator for advice.
Indicative Assessment
- Workshop contributions (7) [LO 1,2,3,4]
- Online quizzes (7) [LO 1,2,3,4]
- Assignments (two) (18) [LO 1,2,3,4]
- Mastery Hurdle Examinations (20) [LO 1,2,4]
- Final examination (48) [LO 1,2,3,4]
The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.
Workload
The expected workload will consist of approximately 130 hours throughout the semester including:
- Lecture component which is typically: in weeks 1, 2, 3, 4, 6, 7, 8, 10, 11 and 12, 4x1 hour in-person lectures and 2 x 0.5 hours of pre-recorded online lectures; in weeks 5 and 9, 2 x 1 hour in-person lectures; for a total of 54 hours over the 12 weeks of teaching.
- Workshop component which is typically 9 x 1.5 hour workshops, with one 1.5 hour workshop in each of the weeks 2, 3, 4, 6, 7, 8, 10, 11 and 12.
- Approximately 62.5 hours of self-directed study per semester which will include preparation for lectures, quizzes and other assessment tasks.
Inherent Requirements
No specific inherent requirements have been identified for this course.
Requisite and Incompatibility
Prescribed Texts
• Linear Algebra (4th edition or later) by David Lay.
• Essential Calculus (2nd edition) by James Stewart.
Fees
Tuition fees are for the academic year indicated at the top of the page.
Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees.
- Student Contribution Band:
- 1
- Unit value:
- 6 units
If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
Where there is a unit range displayed for this course, not all unit options below may be available.
| Units | EFTSL |
|---|---|
| 6.00 | 0.12500 |
Course fees
- Domestic fee paying students
| Year | Fee |
|---|---|
| 2025 | $4680 |
- International fee paying students
| Year | Fee |
|---|---|
| 2025 | $6720 |
Offerings, Dates and Class Summary Links
ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
First Semester
| Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|
| 3555 | 17 Feb 2025 | 24 Feb 2025 | 31 Mar 2025 | 23 May 2025 | In Person | View |
Second Semester
| Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|
| 8562 | 21 Jul 2025 | 28 Jul 2025 | 31 Aug 2025 | 24 Oct 2025 | In Person | N/A |