Jan Bouwe van den Berg, janbouwe.vanden.berg@vu.nl 

Teaching assistants:

Tirza Jochemsen, t.c.jochemsen@student.vu.nl
She is in charge of both the office hours and the extra help sessions.

Literature:

“Calculus, a complete course” by R.A. Adams and C. Essex, 8^th ed., Pearson, ISBN 978-0321781079

Before starting the course, please carefully read the pages on

1. How to study Calculus
2. Classes
3. Tests and assignments
4. Time management and workload

 To view the week-to-week course content, click on Modules (in the navigation panel on the left) .

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 inhomogenous 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

You can find more on the page of the Learning outcomes of this course

Cursusbeschrijving / Course Description
zoals gepubliceerd op vu.nl / as published at vu.nl/en