• Offered by Department of Mathematics
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Academic career UGRD
• Course convener
• Dr Griffith Ware
• Mode of delivery In Person
• Offered in Second Semester 2015
Advanced Mathematics and Applications 2 (MATH1116)

This course continues on from MATH1115, providing an in-depth development of fundamental concepts of calculus and linear algebra, with a particular emphasis on the underlying foundations of mathematics. The use and understanding of proof and abstract ideas, will allow students to develop analytical skills which will form a base for further study in fundamental mathematics as well as providing a foundation for a wide range of quantitative areas such as computer science, engineering, economics, statistics and physics.

Topics to be covered include:

Analysis - Functions of several variables, partial derivatives, double integrals; infinite series, convergence tests, power series, Taylor series, binomial series, complex power series, vectors, dot product, cross product, planes and lines in 3-space, vector functions, curves and parametrization, Kepler’s laws, functions of several variables, chain rule, gradients and directional derivatives, Quadratic forms, extreme values, Lagrange multipliers;

Algebra – induction, theory and application of Euclidean vector spaces, vector spaces, linear independence, bases and dimension, eigenvalues and eigenvectors, orthogonality and least squares.

Note: This is an Honours Pathway Course. It involves extra material and emphasizes the use and understanding of proof and abstract ideas to a deeper conceptual level than MATH1014.

## Learning Outcomes

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

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of analysis and linear algebra and their role in modern mathematics and applied contexts.
2. Demonstrate accurate and efficient use of analysis and linear algebra techniques.
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from analysis and linear algebra.
4. Apply problem-solving using analysis and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.

## Indicative Assessment

Assessment will be based on:

• Tutorials (5%; LO 1-4)
• Five assignments (25% in total: LO 1-4)
• Mid-semester test (25%; LO 1-4)
• Final examination (45%; 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.

48 lectures and 10 hours of laboratory and tutorial sessions

## Requisite and Incompatibility

To enrol in this course you must have completed MATH1115 with a mark of 60 or above. You are not able to enrol in this course if you have previously completed MATH1014

## Prescribed Texts

Linear Algebra by David Lay

Calculus: A Complete Course, seventh Edition by Robert A. Adams

## 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:
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
2015 \$3096
International fee paying students
Year Fee
2015 \$4146
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

The list of offerings for future years is indicative only.
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
1782 20 Jul 2015 07 Aug 2015 31 Aug 2015 30 Oct 2015 In Person N/A

Responsible Officer: Registrar, Student Administration / Page Contact: Website Administrator / Frequently Asked Questions