Admission requirements
None, but completion of Mathematical Reasoning is recommended.
Description
This course is an intensive introduction to differential and integral calculus. The course starts with a study of limits and continuity of functions, and different rules of differentiation. We then learn how to use derivatives to approximate functions and to find their extreme values. In particular, we learn how to differentiate functions with more than one variable.
The second half of the course is dedicated to the study of integration. After introducing the basic definitions, we will learn how to integrate more complicated functions by using different methods of integration. We will also discuss some applications of integration like computing different types of areas and volumes.
Course Objectives
Skills
After successful completion of this course, students will be able to:
Compute limits, derivatives, and integrals of functions using various techniques.
Solve applied problems involving rates of change, motion, area, volume, and optimisation.
Interpret and construct graphical and numerical representations of functions and their derivatives/integrals.
Communicate clear, logical, and mathematically sound reasoning in the context of calculus problems and solutions.
Knowledge
After successful completion of this course, students will know and understand:
The foundational concepts of calculus, including limits, continuity, the derivative, the definite integral, and the Fundamental Theorem of Calculus.
How differentiation describes local linear behaviour and rate of change, and how integration quantifies accumulation.
The conceptual and practical links between a function, its derivative, and its integral.
The broad utility of calculus across scientific and mathematical contexts.
Timetable
Timetables for courses offered at Leiden University College in 2025-2026 will be published on this page of the e-Prospectus.
Mode of instruction
Mathematics is best understood through active engagement with the material. Students will be given a wide range of exercises to practice and are strongly encouraged to work through as many as possible. These exercises, along with other course materials, will be made available via Brightspace.
Class time will primarily be devoted to lectures, during which new material will be introduced and explained. Lectures will also include worked examples and opportunities to solve exercises together and discuss key ideas.
Assessment Method
The final grade will consist of the following components:
40% from quizzes at the end of every second lecture. The highest 5 out of 7 scores are counted at 8% each
45% from one in-class final exam (Week 8)
15% from active class participation; details will be made clear in the syllabus
Reading list
Readings will be posted on Brightspace.
Registration
Courses offered at Leiden University College (LUC) are usually only open to LUC students and LUC exchange students. Leiden University students who participate in one of the university’s Honours tracks or programmes may register for one LUC course, if availability permits. Registration is coordinated by the Education Coordinator, course.administration@luc.leidenuniv.nl.
Contact
Dean Wardell, d.a.wardell@math.leidenuniv.nl
Remarks
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