https://studiegids.vu.nl/en/courses/2025-2026/XB_41007At 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.This course deals with calculus of functions of one variable. In particular we covermanipulating algebraically with exponential, logarithmic and (inverse) trigonometric functionsdetermining limits by identifying dominant termscomputing limits using l'Hôpital's rulecalculating derivatives of any composition of elementary functionscomputing Taylor polynomialscomputing tangent lines to implicitly defined curves in the planefinding and classifying the (local) minima and maxima of functionsgraphing simple functions (e.g. rational functions, exponentials, logarithms and compositions thereof)calculating areas under the graphs of elementary functionscomputing antiderivatives using integration by partscomputing antiderivatives using an appropriately chosen substitutionintegrating 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 typeperforming arithmetic with complex numbersdetermining if a series converges by comparing to a geometric series or p-series.determining if a series converges using an appropriately chosen convergence testdetermining the interval of convergence of a power seriesperforming simple algebraic manipulations with power seriessimple analysis type epsilon proofsClass meetings (twice per week, 2x2=4 hours), tutorials (once per week, 2 hours)Weekly MyMathLab exercises (10%), a homework assignment on proofs (10%), two Midterm exams (20% and 25%) and a Final exam (35%). There is a resit that covers the material of both midterm exams, the homework assignment, and the final; the resit has a weights of 90%, with the MyMathLab exercises retaining a 10% weight.Calculus: A Complete Course, by Adams and Essex, 9th edition, Pearson 2016. ISBN 978-0134154367First year of the bachelor programme MathematicsParticipation in the first class is compulsoryMathematics at exit level Wiskunde B or comparable