General Information
| Course Code | XB_41007 |
|---|---|
| Credits | 6 EC |
| Period | P1+2 |
| Course Level | 100 |
| Language of Tuition | English |
| Faculty | Faculty of Science |
| Course Coordinator | R.Z. Brilleslijper |
| Examiner | R.Z. Brilleslijper |
| Teaching Staff |
R.Z. Brilleslijper |
|
Part of programme(s)
Bachelor
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Practical Information
You need to register for this course yourself. The (de)registration deadlines can be found on VU.nl
| Teaching Methods | Seminar, Written partial exam, Lecture |
|---|
Target audiences
This course is also available as:
Course Objective
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.
Course Content
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
Additional Information Teaching Methods
Class meetings (twice per week, 2x2=4 hours), tutorials (once per week, 2 hours)
Method of Assessment
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.
Entry Requirements
Mathematics at exit level Wiskunde B or comparableLiterature
Calculus: A Complete Course, by Adams and Essex, 9th edition, Pearson2016. ISBN 978-0134154367