Course syllabus

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Times and Locations:

Group 1: Tue 11:00–12:45 and Fri 15:45–17:30, room 2.01

Group 2: Tue 9:00–10:45 and Fri 13:45–15:30, room 2.02

Group 3: Tue 9:00–10:45 and Fri 13:45–15:30, room 2.01

Lecturers:

Rui Dong / Renee Hoekzema, group 1   (r.dong@vu.nl / r.s.hoekzema@vu.nl)

Michael McAssey (coordinator), group 2   (m.p.mcassey@auc.nl)

Sindo Núñez Queija, group 3           (r.nunezqueija@uva.nl)

Course Manual: Course Manual Calculus AUC Autumn 2025.docx

Resources:

Link to register for SOWISO course "Calculus AUC: Autumn 2025":

https://cloud.sowiso.nl/enroll/RdQsoWki

Preliminaries:

Before starting the course, please carefully read the pages on

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

To view the week-to-week course content, look at the course manual.


Course content:

This course deals with calculus of functions of one or more variables. 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 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 homogeneous linear second 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
  • Derivation of Taylor and Maclaurin series

Course summary:

Course Summary
Date Details Due