This course provides a study of the fundamental concepts of calculus and linear algebra. The use and understanding of proof and abstract ideas, will allow students to develop analytical skills which will form a foundation for further study in the quantitative areas of actuarial studies.

Calculus topics to be covered include: limits, continuity, differentiation, inverse functions, transcendental functions, extrema, concavity and inflections, applications of derivatives, Taylor Polynomials, integration, differential equations, functions of several variables, partial derivatives, optimality, gradient and the second derivative test in two variables, double integrals.

Linear Algebra topics to be covered include: complex numbers, solving linear equations, matrix equations, linear independence, linear transformations, matrix operations, matrix inverses, subspaces, dimension and rank, determinants, Cramer's rule, volumes, eigenvalues, eigenvectors.

## 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.
- Demonstrate accurate and efficient use of calculus and linear algebra techniques.
- Demonstrate capacity for mathematical reasoning through analysing, proving and explaining concepts from calculus and linear algebra.
- Apply problem-solving using calculus and linear algebra techniques applied to situations in statistics, 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 or equivalent will be considered. For students with a level of maths equivalent to ACT Mathematical Methods, MATH1003 is required to be completed before enrolling.

## Indicative Assessment

- Exam 1 (35) [LO 1,2,3,4]
- Exam 2 (35) [LO 1,2,3,4]
- Workshop activities (10) [LO 1,2,3,4]
- Assignments (10) [LO 1,2,3,4]
- Online quizzes (10) [LO 1,2]

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 approximately 48 hours of lecture activities (usually four one-hour lectures each week), and twenty hours of workshop activities (one two-hour workshop per week in ten weeks of the semester).
- Approximately 62 hours of self-study which will include preparation for lectures and workshops, completion of regular formative assessment items, and study of the course materials.

## Inherent Requirements

To be determined

## Requisite and Incompatibility

## Prescribed Texts

Essential Calculus (2nd edition) by James Stewart.

## Preliminary Reading

Some students may find it helpful to refer to a text book for an alternative exposition of certain topics and extra practice problems in Linear Algebra. The following texts are recommended for this purpose:

- Linear Algebra and its applications (5th edition, although earlier additions are fine too) by David Lay.
- Linear Algebra (fourth edition) by Jim Hefferon. Available for free (by express permission of the author) at https://hefferon.net/linearalgebra/

## Assumed Knowledge

Students are assumed to have achieved a satisfactory result in ACT Specialist Mathematics Major-Minor or NSW HSC Mathematics Extension 1. Other students should have equivalent background knowledge.

## 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.

### Second Semester

Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
---|---|---|---|---|---|---|

5936 | 24 Jul 2023 | 31 Jul 2023 | 31 Aug 2023 | 27 Oct 2023 | In Person | N/A |