BASIC SUBJECTS Topic/Element Content Learning outcomes Module and Content T P SG B1: Mathematics, statistics, theory of observations B1.1 Geometry and Linear Algebra B1.1a Geometry Conic Sections, geometry of Express curves and surfaces in parametric the ellipse and of the ellipsoid. form. Parametric equations of curves (B) and surfaces. Compute lengths and coordinates on an ellipse. B1.1b Linear Vector and affine spaces, Derive and compute 2D and 3D Algebra vector and inner products, transformations, as typically involved in norms. geodesy, surveying and survey data Linear operators, matrix referencing. (I) representation, composition, transpose. Translations, rotations, coordinate transformations, similitudes, orthogonal projection. B1.1c Systems of linear equations, Solve linear equations by numerical Numerical Gauss elimination. methods in a scientific computing methods for Matrix decomposition, and environment and analyze error bounds. linear systems factorization. of equations Condition number of a matrix. (I) B1.2 Differential calculus and differential equations B1.2a Real and vector valued Apply differential calculus to real and Differential and functions. vector valued functions from a integral calculus Series, Taylor expansions vector space. Gradient of a real-valued functions. Calculate integral of classical functions (B) Jacobian matrix and approximate numerical values.
BASIC SUBJECTS Topic/Element Content Learning outcomes Module and Content T P SG B1: Mathematics, statistics, theory of observations B1.1 Geometry and Linear Algebra B1.1a Geometry (B) Conic Sections, geometry of the ellipse and of the ellipsoid. Parametric equations of curves and surfaces. Express curves and surfaces in parametric form. Compute lengths and coordinates on an ellipse. B1.1b Linear Algebra (I) Vector and affine spaces, vector and inner products, norms. Linear operators, matrix representation, composition, transpose. Translations, rotations, coordinate transformations, similitudes, orthogonal projection. Derive and compute 2D and 3D transformations, as typically involved in geodesy, surveying and survey data B1.1c Numerical methods for linear systems of equations (I) Systems of linear equations, Gauss elimination. Matrix decomposition, and factorization. Condition number of a matrix. Solve linear equations by numerical methods in a scientific computing environment and analyze error bounds. B1.2 Differential calculus and differential equations B1.2a Differential and integral calculus (B) Real and vector valued functions. Series, Taylor expansions Gradient of a real-valued functions. Jacobian matrix Apply differential calculus to real and vector valued functions from a vector space. Calculate integral of classical functions and approximate numerical values. referencing.
S-5A_Ed1.0.2-template.docx