• Offered by Mathematical Sciences Institute
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Course convener
• Mr Neil Montgomery
• Prof Lilia Ferrario
• Prof Murray Batchelor
• Mode of delivery In Person
• Offered in First Semester 2018
Second Semester 2018
Mathematics and Applications 1 (MATH1013)

The emphasis will be on understanding the material so that it can both 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. However, the material will not be developed in a rigorous theorem-proof style. Students interested in continuing with mathematics subjects beyond second year should initially enrol in MATH1115. This includes students interested in more mathematical/theoretical aspects of engineering, science and economics.

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, Newton's method, Taylor polynomials, L'Hopital's rules. Riemann integration and the Fundamental Theorem of Calculus. Techniques of integration including the method of substitution and integration by parts.
Linear Algebra - Complex numbers. Solution of linear system 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. Emphasis is on understanding and on using algorithms.

## Learning Outcomes

Upon successful completion of this course, students will have the knowledge and skills to:

1. 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.
2. Demonstrate accurate and efficient use of calculus and linear algebra techniques as they relate to the concepts listed above.
3. Demonstrate capacity for mathematical reasoning through explaining concepts from calculus and linear algebra.
4. 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 or equivalent will be considered. Students with a level of mathematics equivalent to ACT Mathematical Methods should enrol in the bridging course MATH1003.

## Indicative Assessment

Tutorials 25% (LO 1-4)
Tests - 25% in total (LO 1-4)
Final examination 50 (LO 1-4)

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.

Four lectures per week and regular tutorials.

## Requisite and Incompatibility

You are not able to enrol in this course if you have previously completed MATH1113 or MATH1115.

## Prescribed Texts

Linear Algebra (3rd edition or 3rd edition update, or 4th edition) by David Lay, Essential Calculus (second edition) by James Stewart.

## Fees

Tuition fees are for the academic year indicated at the top of the page.

If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Student Contribution Band:
Band 2
Unit value:
6 units

If you are an undergraduate student and 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). You can find your student contribution amount for each course 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
2018 \$3660
International fee paying students
Year Fee
2018 \$5160
Note: Please note that fee information is for current year only.

## Offerings and Dates

The list of offerings for future years is indicative only

### First Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery
2664 19 Feb 2018 27 Feb 2018 31 Mar 2018 25 May 2018 In Person

### Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery
7640 23 Jul 2018 30 Jul 2018 31 Aug 2018 26 Oct 2018 In Person