This course provides an in depth exposition of the theory of differential equations and vector calculus. Applications will be related to problems mainly from the Physical Sciences.

Topics to be covered include:

Ordinary Differential Equations - Linear and non-linear first and second order differential equations; existence and uniqueness of solutions; solution methods; the use of Green’s functions; power series solutions; Bessel and Legendre equations; the gamma function; systems of first and second order equations; equilibrium points and stability; phase portraits; elementary bifurcation theory; the van der Pol equation; normal modes of oscillation; boundary value problems; regular and singular Sturm-Liouville systems and eigenvalue problems; generalized Fourier series.

Advanced Vector Calculus - Curves and surfaces in three dimensions; parametric representations; curvilinear coordinate systems; surface and volume integrals; use of Jacobians; scalar and vector fields; gradient, divergence and curl in orthogonal curvilinear coordinates. identities involving vector differential operators; the Laplacian; Green’s theorem in the plane; Divergence and Stoke’s theorems; scalar and vector potentials.

Note: This is an HPC, taught at a level requiring greater conceptual understanding than MATH2305.

## 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 differential equations and vector calculus and their role in modern mathematics and applied contexts.

2. Demonstrate accurate and efficient use of techniques involved in solving differential equations and applying vector differential operators.

3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from the theory of differential equations.

4. Apply problem-solving using techniques in differential equations and vector calculus in diverse situations in physics, engineering and other mathematical contexts.

## Indicative Assessment

Assessment will be based on:

- Eight assignments (25% in total; LO 1-4)
- Mid-semester test (25%; 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.

## Workload

48 lectures and 10 tutorials

## Requisite and Incompatibility

## Majors

## Minors

## Specialisations

## 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. Students continuing in their current program of study will have their tuition fees indexed annually from the year in which you commenced your program. 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 |
---|---|

1994-2003 | $1650 |

2004 | $1926 |

2005 | $2298 |

2006 | $2520 |

2007 | $2520 |

2008 | $2916 |

2009 | $2916 |

2010 | $2916 |

2011 | $2946 |

2012 | $2946 |

2013 | $2946 |

2014 | $2946 |

- International fee paying students

Year | Fee |
---|---|

1994-2003 | $3390 |

2004 | $3450 |

2005 | $3450 |

2006 | $3618 |

2007 | $3618 |

2008 | $3618 |

2009 | $3618 |

2010 | $3750 |

2011 | $3756 |

2012 | $3756 |

2013 | $3756 |

2014 | $3762 |

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

## Offerings, Dates and Class Summary Links

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 |
---|---|---|---|---|---|---|

3326 | 17 Feb 2014 | 07 Mar 2014 | 31 Mar 2014 | 30 May 2014 | In Person | N/A |