Single Variable Calculus

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) in the form of normal tutorial class (first period) and
office hours to ask questions (second period)

TYPE OF ASSESSMENT
Weekly MyMathLab exercises (10%), three Midterm exams (15%, 20% and 25%) and a Final exam (30%).

ENTRY REQUIREMENTS
Mathematics at exit level Wiskunde B or comparable