Calculus 1

Course

URL study guide

https://studiegids.vu.nl/en/courses/2025-2026/X_400635

Course Objective

At the end of this course the student is able tocalculate limits, using several methods like l'Hopitals rule or the squeeze theoremcalculate derivatives and find local extreme valuescalculate integrals, using several methods like the substitution method, integration by parts, partial fraction expansionverify if a function is continuous, differentiable, Riemann-integrablecalculate and apply a Taylor polynomialformulate and apply several important theorems for continuous and/or differentiable functions, like the Intermediate Value Theorem, the Mean Value Theorem and the Fundamental Theorem of Calculus

Course Content

Real functions of one variable. Topics that will be treated are:Preliminaries, Real functions, Trigonometric functionsLimits, Continuity, Intermediate Value TheoremTranscendental Functions, Inverse FunctionsDifferentiation, Chain Rule, Mean Value TheoremApplications of Differentiation, Extreme Values, l'Hôpital's Rule, Taylor PolynomialIntegration, Fundamental Theorem of Calculus, Improper Integrals

Teaching Methods

Lectures (3 x 2 hours per week) and exercise classes (2 x 2 hours per week).

Method of Assessment

There is a midterm exam and a final exam. The midterm exam makes up for 40% and the final exam makes up for 60% of the final grade. There is one retake which covers all topics for the midterm exam and the final exam. Midterm exam or final exam cannot be retaken separately!

Literature

Adams and Essex, Calculus: A Complete Course, 10th edition, Pearson 2021, ISBN-13: 9780135732588. Older editions of the book are also fine, but please make sure that the numbering of the exercises match.

Target Audience

1 BA
Academic year1/09/2531/08/26
Course level6.00 EC

Language of Tuition

  • English

Study type

  • Premaster
  • Bachelor