451-208 Mathematics 2 (Geomatics)

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Objectives:

At the conclusion of this subject the student should have developed skills in the use of vector and matrix algebra that will support further studies in measurement science. These include:

• computational procedures associated with mining surveying;

• the solution of solid modelling problems;

• the theory and application of least squares;

• foundation mathematics for the study of photogrammetry;

• development of computational procedures for geodetic surveying;

• establishing relationships between reference frames used in geodetic surveying;

• the depiction of precision of correlated measurements; and

• the development of testing procedures in survey network adjustment.

Content:

Vector Algebra: Review of vector operations; applications to determination of angles between vectors and planes, intersection of vectors and planes, location of circles and spheres, development of spherical trigonometry formulae.

Matrix Algebra: Review of matrix operations, multiplication, transposition, inversion, partitioning, orthogonal and rotation matrices; applications to solution of linear equations, curve fitting by least squares, coordinate transformation, determination of variance-covariance matrices. Matrix diagonalisation by elementary and orthogonal matrices; application to establishing rank of matrices, solution of linear equations, eigenvalues. Symmetric matrices, idempotency, positive definiteness; application in least squares estimating.

Mathematical methods: Solution of non-linear equations.

Assessment: