Course Description REA1041 - Mathematics 10 - Functions with One Variable. (2003/2004)

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The students shall be able to show skill in algebraic manipulations, transforming of function expressions, differentiation and integration.The students shall be able to show a good understanding of central concepts in the subjects of the course.The students shall be able to apply functions, differentiation and integration on simple practical problems (modelling).The students shall have knowledge on plotting of function graphs, numerical solving of equations and numerical integration with calculator and computer programmes.There will also be an extra part covering fundamental subjects for the ”three terms students”, following a programme not requiring maximum amount of mathematics and physics from upper secondary school.

Numbers:
Integers, rational, irrational, real and complex numbers.
Functions:
Explicitly and implicitly defined functions, inverse functions, limits, continuity.Parameterised curves, vector valued functions, position, velocity and acceleration. Modelling of functions.Polynomials, rational functions, root functions. Trigonometric and inverse trigonometric functions, exponential and logarithmic functions.
Differentiation:
Definition and differentiation rules, differential and linear approximation, implicit differentiation. Modelling.
The integral:
Riemann sums, integration by substitution and by parts, partial fraction, arc length, area, volumes, mass centre, momentum.