## Admission requirements

None

## 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, and finding the mean and median of a continuous probability density function.

## Course Objectives

After this course, students will have:

internalized the foundational concepts and methods of differential and integral calculus,

demonstrated the ability to communicate clear and correct calculus reasoning, and

applied various tools from calculus in order to solve complex problems

## Timetable

Timetables for courses offered at Leiden University College in 2021-2022 will be published on this page of the e-Prospectus.

## Mode of instruction

There will be two primary modes of instruction. Students will learn the basic terminology and methods from preassigned readings; class time is reserved for enriching that knowledge through examples, guided worksheets, practice problems, and group discussion. Each class will end with a short quiz on the material students have read in advance for that session.

## Assessment Method

In accordance with the learning objectives of internalization, demonstration, and synthesis, the final grade will consist of the following components:

30% from quizzes at the end of every lecture, except for the first lecture. The highest 10 out of 12 scores are counted at 3% each

30% from three homework assignments. Each of the three assignments is worth 10%.

30% from one in-class final exam.

10% from active class participation; details will be made clear in the syllabus.

## Reading list

Readings for each lecture will be posted on Brightspace. Students are expected to read the material before class.

## 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

Aline Zanardini, a.zanardini@math.leidenuniv.nl