Admission requirements
Students are expected to have followed Wiskunde B in their middle schools, or an equivalent course if from abroad. That is, students are expected to know elementary functions such as polynomials, rational functions, exponentials and logarithms, and trigonometric functions. Students are also expected to have been exposed to differential and integral calculus beforehand.
Description
In this course we will learn the foundational calculus that is needed for any statistician. The material taught will come up repeatedly in future courses in the Statistics and Data Science programme.
After a brief review of basic functions, sets, and important mathematical notation, students will learn about continuity of functions and then what it means for a function to be differentiable. We'll continue to discuss differentiation and how it's used to explain important properties of functions such as maxima/minima and the shape of graphs. We'll conclude this first part by looking at approximations of functions and briefly discuss Taylor's theorem.
The second part is focused on integration. We'll learn what an integral is and techniques of integration, and relate the integral to derivatives via the Fundamental Theorem of Calculus.
We will conclude by briefly looking at multivariate calculus, i.e. calculus of functions with more than one variable. This is needed in the most elementary applications in statistics, such as finding the line of best fit of a data set. We'll cover partial derivatives and how they can inform us about local maxima/minima.
Course objectives
- Students will be able to use elementary functions and mathematical notation in applied problems, where they directly model a scenario using mathematics and use the equations to understand more about the scenario.
- Students will understand the meaning of the derivative and be able to compute derivatives of diverse functions. Students can use the derivative to find maxima and minima of functions, including in applied scenarios, and can use the derivative to draw functions.
- Students will be able to approximate functions using Taylor polynomials and use Taylor's theorem to interpret how good an approximation is.
- Students will understand the meaning of the integral and be able to compute integrals using various techniques. Students can use the integral in applied scenarios to find the total rate of change of something via the Net Change Theorem.
- Students will be able to compute partial derivatives of multivariate functions. They will be able to find the local minima/maxima of multivariate functions and use this to be able to compute a line of best fit of a small data set.
Timetable
You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.
MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).
For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.
Mode of Instruction
This course is taught in-person. Students will have 2 hours of lectures and 2 hours of tutorials each week. It is expected that students go through a weekly reading before each lecture and that they are active in their learning process via trying practice problems.
Assessment method
The final grade is the best of the following marking schemes:
Scheme 1: Exam: 100%
Scheme 2: Exam: 70%, Homework: 30%
Reading List
Calculus a complete course – tenth edition,
Course notes, plus additional optional readings from:
Calculus a complete course – tenth edition,
Robert A. Adams & Christopher Essex, 2021, Pearson Education Canada ISBN 9780135732588
Registration
It is the responsibility of every student to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.
Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.
Extensive FAQ's on MyStudymap can be found here.
Contact
Garnet Akeyr, g.j.akeyr@math.leidenuniv.nl