Algemene informatie
| Vakcode | XB_41007 |
|---|---|
| Studiepunten | 6 EC |
| Periode | P1+2 |
| Vakniveau | 100 |
| Onderwijstaal | Engels |
| Faculteit | Faculteit der Bètawetenschappen |
| Vakcoördinator | R.Z. Brilleslijper |
| Examinator | R.Z. Brilleslijper |
| Docenten |
R.Z. Brilleslijper |
|
Onderdeel van opleiding(en)
Bachelor
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Praktische informatie
Voor dit vak moet je zelf intekenen. De inteken- en afmeldtermijnen staan op VU.nl
| Onderwijsvorm | Werkcollege, Deeltentamen schriftelijk, Hoorcollege |
|---|
Doelgroepen
Dit vak is ook toegankelijk als:
Doel vak
At the end of this course students will be able to ...... calculate limits using appropriately chosen methods, such as
l'Hôpitals rule or by identifying dominant terms.
... calculate derivatives, find local extreme values and use these to
graph functions.
... calculate integrals using appropriately chosen methods, such as the
substitution method, integration by parts or partial fraction expansion.
... solve simple differential equations with or without initial data.
... compute Taylor polynomials and manipulate Taylor series.
... determine if a series converges using an appropriately chosen
convergence test.
... write down the arguments involved in solving a calculus problem in a
logically correct manner.
Inhoud vak
This course deals with calculus of functions of one variable.
In particular we cover
* manipulating algebraically with exponential, logarithmic and (inverse)
trigonometric functions
* determining limits by identifying dominant terms
* computing limits using l'Hôpital's rule
* calculating derivatives of any composition of elementary functions
* computing Taylor polynomials
* computing tangent lines to implicitly defined curves in the plane
* finding and classifying the (local) minima and maxima of functions
* graphing simple functions (e.g. rational functions, exponentials,
logarithms and compositions thereof)
* calculating areas under the graphs of elementary functions
* computing antiderivatives using integration by parts
* computing antiderivatives using an appropriately chosen substitution
* integrating simple rational functions (using "partial fractions")
* determining if an improper integral converges (and compute the area)
* solving first order differential equations of separable type and of
linear inhomogeneous type
* performing arithmetic with complex numbers
* determining if a series converges by comparing to a geometric series
or p-series.
* determining if a series converges using an appropriately chosen
convergence test
* determining the interval of convergence of a power series
* performing simple algebraic manipulations with power series
*simple analysis type epsilon proofs
Aanvullende informatie onderwijsvormen
Class meetings (twice per week, 2x2=4 hours), tutorials (once per week, 2 hours)
Toetsvorm
Weekly MyMathLab exercises (10%), a homework assignment on proofs (10%), two Midterm exams (20% and 25%)
and a Final exam (35%). There is a resit that covers the material of both midterm exams, the homework assignment, and the final; the resit has a weights of 90%, with the MyMathLab exercises retaining a 10% weight.
Vereiste voorkennis
Mathematics at exit level Wiskunde B or comparableLiteratuur
Calculus: A Complete Course, by Adams and Essex, 9th edition, Pearson2016. ISBN 978-0134154367