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Single Variable Calculus - Period 1+2
Social Sciences & Humanities Program
Amsterdam, Netherlands
Dates: 8/20/22 - 12/24/22
Single Variable Calculus - Period 1+2
OVERVIEW
CEA CAPA Partner Institution: Vrije Universiteit Amsterdam
Location: Amsterdam, Netherlands
Primary Subject Area: Mathematics
Instruction in: English
Course Code: XB_41007
Transcript Source: Partner Institution
Course Details: Level 100
Recommended Semester Credits: 3
Contact Hours: 84
DESCRIPTION
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
Contact hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.
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
Contact hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.