BASIC SUBJECTS Hours Topic/Element Content Learning outcomes Module and Content T P SG B1: Mathematics, Statistics, Theory of Errors B1.1 Linear Vector and affine spaces, Describe and apply 2D transformations Algebra vector and inner products, involved in surveying and mapping. norms. (E4.1c) Linear equations, Solve linear equations using matrix (B) determinants. methods. Analytical geometry, line and plane equations. Linear operators, matrix representation, composition, inverse, transpose. Translations, rotations, coordinate transformations. B1.2 Real and vector valued Compute the gradient of a vector valued Differential functions. function. Define a function as a series. calculus Gradient of real-valued Calculate explicit integrals of classical functions and their discrete functions. approximations. (B) Series and integrals. B1.3 Basic trigonometry Apply plane and spherical trigonometry to Trigonometry surveying problems. Sphere, great circle, rhumb lines, sphere angles, spherical (B) triangles and spherical excess. B1.4 Statistics Random variables, mean, Explain what is meant by a random variance, standard deviation variable, estimate the mean, variance and Covariance and correlation standard deviation for a random variable (I) Estimation of mean, variance, and also the covariance between random covariance variables. Normal distribution B1.5 Theory of Linear observation equations Apply the variance propagation law to a errors Covariance propagation law linear observation equation, and derive a
BASIC SUBJECTS Topic/Element Content Learning outcomes Module and Content Hours T P SG B1: Mathematics, Statistics, Theory of Errors B1.1 Linear Algebra (B) Vector and affine spaces, vector and inner products, norms. Linear equations, determinants. Analytical geometry, line and plane equations. Linear operators, matrix representation, composition, inverse, transpose. Translations, rotations, coordinate transformations. Describe and apply 2D transformations involved in surveying and mapping. (E4.1c) Solve linear equations using matrix methods. B1.2 Differential calculus (B) Real and vector valued functions. Gradient of real-valued functions and their discrete approximations. Series and integrals. Compute the gradient of a vector valued function. Define a function as a series. Calculate explicit integrals of classical functions. B1.3 Trigonometry (B) Basic trigonometry Sphere, great circle, rhumb lines, sphere angles, spherical triangles and spherical excess. Apply plane and spherical trigonometry to surveying problems. B1.4 Statistics (I) Random variables, mean, variance, standard deviation Covariance and correlation Estimation of mean, variance, covariance Normal distribution Explain what is meant by a random variable, estimate the mean, variance and standard deviation for a random variable and also the covariance between random variables. B1.5 Theory of errors Linear observation equations Covariance propagation law Apply the variance propagation law to a linear observation equation, and derive a
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