Læreplan i matematikk for realfag - programfag i utdanningsprogram for studiespesialisering (MAT3-01)
Utgått
Denne læreplanen har utgått.
Mathematics R2
Geometry
- 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
- 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
- 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
- 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
8 av 9