This course covers single-variable calculus and introductory linear algebra. The emphasis will be on understanding the material so 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. The material will not be developed in a rigorous theorem-proof style. Students interested in a deeper understanding of mathematics or more mathematical/theoretical aspects of topics including engineering, 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, partitioned matrices, linear transformations, matrix factorisation and subspaces. Determinants. Example applications including graphics, the Leontief Input-Output Model and various linear models in science and engineering. Complex numbers. Emphasis is on understanding and on using algorithms.

## 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.
- 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. Students with a good pass in ACT Specialist Mathematics Major or NSW HSC Mathematics Advanced or equivalent will be considered. Students with a level of mathematics equivalent to ACT Mathematical Methods should enrol in the bridging course MATH1003.

Students who are concerned about their level of preparation for MATH1013 should contact the MSI first-year coordinator for advice.

## Indicative Assessment

- Workshop assessment (completed during workshops) (10) [LO 1,2,3,4]
- Online quizzes (10) [LO 1,2,3,4]
- Assignments (10) [LO 1,2,3,4]
- Midsemester examination (20) [LO 1,2,4]
- Final examination (50) [LO 1,2,4]

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:

• Face-to face component which may consist of 4 x 1 hour lectures per week (48 hours) as well as a total of 15 hours of workshop time.

• Approximately 67 hours of self-study per semester which will include preparation for lectures, quizzes and other assessment tasks.

## Inherent Requirements

There are no course-specific inherent requirements.

## Requisite and Incompatibility

## Prescribed Texts

• Linear Algebra (3rd edition or later) by David Lay.

• Essential Calculus (2nd edition) by James Stewart.

## Minors

## 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 |

**Note:**Please note that fee information is for current year only.

## 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 | N/A |

### 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 |