Mathematics for the natural sciences - programme subject in programmes for Specialization in General Studies (MAT3-01)

Mathematics R2

Geometry

The aims of the training are to enable the apprentice to
  • perform calculations with three-dimensional vectors that are represented both geometrically and in co-ordinate form
  • use and interpret the scalar and vector product in the calculation of distances, angles, area and volume
  • use vector calculus to find equation and parameter presentations for lines, plane and spherical surfaces
  • calculate longitudinals, angles and areas in bodies limited by plane and spherical surfaces

Algebra

The aims of the training are to enable the apprentice to
  • find and analyze recursive and explicit formulae for numerical patterns with or without digital means, and implement and present simple proofs linked to these formulae
  • implement and give an account of proof by induction
  • sum finite series with or without digital means, derive and use the formulae to the sum of the first n members in arithmetic and geometric series, and use this to solve practical problems
  • calculate with infinite geometric series with a constant and variable quotients, determine the area of convergence for these series and present the results

Functions

The aims of the training are to enable the apprentice to
  • simplify and solve linear and quadratic equations in trigonometric expressions by using relations between the trigonometric functions
  • derive central functions and use first and second derivatives to elaborate on and discuss such functions
  • transform trigonometric expressions of the type a sin kx + b cos kx , and use these to model periodic phenomena
  • give an account of the definition of a definite integral as a limit of a sum and an indefinite integral as an anti-derivative
  • calculate integrals of the central functions by anti-derivation, substitution, partial fraction decomposition with linear denominators and integration by parts
  • interpret the definite integral in models of practical situations and use it to compute plane areas and volumes of rotating bodies
  • formulate a mathematical model with the help of central functions on the basis of observed data, process the model and elaborate on and discuss the result and method

Differential equations

The aims of the training are to enable the apprentice to
  • model practical situations by converting the problem to a differential equation, solving it and interpreting the result
  • solve the first order linear and separable differential equations by calculation and give an account of some important areas of application
  • solve homogenous second order differential equations and use Newton’s second law to describe free oscillations by periodic functions
  • solve differential equations and draw vector diagrams and integral curves, and interpret them using digital tools

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