Admission requirements
None.
This course requires more mathematical proficiency than the Mathematical Reasoning course and focuses on both the theory behind the mathematics as well as computations, as well as in general moving at a faster pace. Those who intend to take additional mathematics courses at the LUC are encouraged to take Mathematical Modelling, as well as those who will use mathematics in other courses as part of their major.
For both courses it is assumed that students satisfy the LUC mathematics admission requirements. If needed, they may make use of the two-week preparatory remedial course in January.
Students are assumed to be familiar with polynomials, trigonometric functions, exponential functions, and logarithms. No prior knowledge of calculus is assumed. A review document will be available on Brightspace before the beginning of the first lecture.
Description
This course begins with a look at the notion of continuity of functions and limits of functions, which is used as a jumping-off point for the study of differential calculus. We will examine what it means to be differentiable, the rules of differentiation, and how differential calculus is used in optimisation problems. The latter half of the course covers integral calculus, where a variety of techniques will be introduced so as to solve integrals. Finally, there will be some lectures devoted to both multivariate calculus, and linear differential equations. Problems will be focused on connecting calculus with real modelling problems that arise in areas such as economics and the physical sciences.
Course Objectives
Skills
After successful completion of this course, students will be able to:
Compute the derivatives and definite/indefinite integrals of numerous functions, as well as provide interpretations for these in various real-world contexts.
Find a mathematical model for optimization problems and problems involving the calculation of areas/volumes of objects, and then find the optimal solution.
Solve elementary linear differential equations.
Knowledge
After successful completion of this course, students will know and understand:
The notions of continuity, limits of functions, differentiability, and the Riemann integral.
The intimate connection between differential and integral calculus through the Fundamental Theorems of calculus.
The relevance of calculus in advanced topics in areas as economics and business, environmental sciences, physics, and machine learning.
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
This course will be taught via live lectures, where all the new material will introduced and explained. Students will also be given an exercise sheet at the end of each lecture that they are encouraged to work through to cement their understanding of the subject. If in-person lectures are not possible, this course will be taught live over MS Teams. Students will be added to their team before the first lecture.
Short, online quizzes (<20 minutes) will test the basic knowledge covered in the course.
Graded homework assignments will cover the material in more depth.
An essay will allow students to explore an application of their choosing in more detail, with a list of topics available to those who are unsure of what to investigate.
There will be an exam at the end of the course.
Students will also have access to a “maths lab”, run by student assistants, where they can discuss material and ask questions in a more informal setting.
Assessment Method
Quizzes (available after every lecture): 25%
Essay / participation: 5%
Homework assignments: 30%
Final exam: 40%
Reading list
The primary reading material is typewritten notes available on Brightspace. Students are encouraged to look at the reading material for each lecture before the lecture itself.
Numerous additional resources are available for those who wish to have more practice or alternative explanations of the concepts. A free online textbook is available here:
https://openstax.org/details/books/calculus-volume-1
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
Garnet Akeyr, g.j.akeyr@math.leidenuniv.nl
Remarks
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