Prerequisites:
wi1256/57/58mt |
Follow
up: wi212 |
Detailed
description of topics:
Vectorfunctions, continuity and limits of functions
of two variables, partial differentials of the 1st and higher orders, total differential,
direction differential, implicite differentiation, Taylor's theorem for more variables,
differential forms, tangent plane, extreme values of a function of two variables on a open
or closed area, determinant of Hesse. Line integrals, arc length, surfaces and surface
area, particular cases of this, Gauss theorem, Stokes theorem
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Course
material:
Lecture notes: Calculus by R. Adams, Analyse 1988,
Almering (DUM)
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References
from literature:
Finney and Thomas: Calculus ISBN 0-201-54977-8
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Remarks
(specific information about assesment, entry requirements, etc.):
Admissionrequirement: passed for the Propaedeutic
exam.
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Goals:
Can work abstract on basis of definitions. This
applied on functions of n-variables with the definitions of continuity, partial
differentiable, differentiable in a certain direction, total differentiable and
continuesly differentiable. Further applied via the definition of a extreem and the
theorem of a continuesly function on a closed and bounded area to can find the extreems on
areas with or without a boundary. The solving of two equations (not linear) with previous
as application. Can calculating with Taylor's theorem for functions of two variables, can
differentiating in implicit falls with n-variables as well as can determinate
differentialforms after coördinate transformations, gradiënt, divergence and rotation.
To know how to use the integraltheorems of Gauss and Stokes in simple cases. To know how
to make a choise in complicated circumstances between directly calculation, Stokes and/or
Gauss, so that the calculation is as simple as possible.
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Computer
use:
MAPLE-exercise
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Laboratory
project(s):
as before
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Design
content: |
Percentage
of design: 0% |