Contact
24 hours of lectures and tutorials

Subject Description
The objective of this subject is to apply theories gained in earlier mathematical studies to fundamental problems associated with practice in Geomatics. Topics covered include: Spherical Trigonometry: properties of spherical triangles, development of fundamental formulae relating elements, area and spherical excess, application in navigation, map projections and positional astronomy.

• Vector geometry for Geomatics: vector representation of spatial relationships between points, line and planes, applications in positioning, mining surveying, solid modelling, reference frames and spatial analysis representations of curves on the ellipsoid as vector chains.
  
• Spherical Trigonometry: properties of spherical triangles, development of fundamental formulae relating elements, area and spherical excess, application in navigation, map projections and positional astronomy.
  
• Geometry of the ellipsoid, the ellipsoid as a geodetic reference surface, coordinate systems - geocentric cartesian, curvilinear and universal transverse mercator (UTM), plane curves, loxodromes and geodesics computations on the UTM map grid.
  
• Transformations between reference frames, rotation matrices for moving vectors between reference frames, properties of orthogonal matrices, conformal transformations in 2 and 3-dimensions.
  
• Algorithms for solving simultaneous linear equations, algorithms for general and symmetric matrix inversion, conditioning matrices for inversion, solutions for redundant linear equations, solutions for non-linear simultaneous equations, applications to curve fitting by least squares methods.
  

Assessment
Not more than three hours of written examinations and tests and not more than the equivalent of 60 pages of written assignments and reports on practical work. The
relative weighting of the assessment components will be published at the commencement of the subject.

One 3-hour written examination: 60%
Two assignments: 24%
Eight short exercises: 16%

References:

(1) Subject Webpage(here): http://www.sli.unimelb.edu.au/fjleahy/comp_methods/index.html
(2) Any 1st year university maths text which includes vector geometry
(3) Web address on spherical trigonometry:
http://www.shef.ac.uk/physics/people/vdhillon/teaching/phy105/phy105_syllabus.htm
(4) Linear Algebra, Geodesy & GPS, Strang & Borre, Wellesley-Cambridge Press (see library)
(5) Australian Government Web address for Geodesy: http://www.ga.gov.au/nmd/geodesy/