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## Single Variable Calculus

2019-2020

### 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
* solving homogenous linear second order differential equations with
constant coefficients
* solving systems of two linear first order differential equations with
constant coefficients
* 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

### Teaching Methods

Class meetings (twice per week, 2x2=4 hours), tutorials (once per
week, 2 hours), extra help session (for students with deficiencies,
once a week during the first half of the semester only, 1x2 hours)

### Method of Assessment

Weekly MyMathLab exercises (10%), three Midterm exams (15%, 20% and 25%)
and a Final exam (30%). There is a resit that covers the material of all
three midterm 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 comparable

### Literature

Calculus: A Complete Course, by Adams and Essex, 9th edition, Pearson
2016. ISBN 978-0134154367

### Target Audience

First year of the bachelor programme Mathematics

Participation in the first class is compulsory

### General Information

Course Code XB_41007 6 EC P1+2 100 English Faculty of Science prof. dr. G.J.B. van den Berg prof. dr. G.J.B. van den Berg prof. dr. G.J.B. van den Berg

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

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