Admission requirements
Required course(s):
None.
This course requires less mathematical proficiency than the Mathematical Modelling course and focuses more on computations than the theory behind the mathematics. Those who do not intend to take additional mathematics courses at the LUC are encouraged to take Mathematical Reasoning.
For both courses it is assumed that students satisfy the LUC mathematics admission requirements.
Students are assumed to have a basic familiarity with polynomials, as well as in manipulating equations to isolate a variable. Those who do not feel comfortable with these topics are advised to review these subjects before the first lecture.
Description
This course begins with a review and introduction of the mathematical foundations needed later in the course, including functions such as the exponential and logarithmic function, and trigonometric functions. The latter half of the course is devoted to studying rates of change and optimisation problems, and serves as an introduction to differential calculus. At all points throughout the block, examples will be drawn from areas such as physics, economics, biology, chemistry, population dynamics, and the environmental sciences.
Course Objectives
Skills
After successful completion of this course, students will be able to:
Solve equalities and inequalities that involve a range of advanced functions, including polynomial, exponential, logarithmic and trigonometric functions
Describe and compute the domain, range and graph features of advanced functions
Calculate the derivatives of advanced functions and interpret the derivative as a rate of change.
Solve optimization problems where a maximal / minimal answer is desired subject to constraints.
Work with derivatives in the context of real-world scenarios, drawn from economics, the physical sciences, and population dynamics.
Knowledge
After successful completion of this course, students will know and understand:
How to work with basic functions, including polynomials, trigonometric functions, exponential functions, and compositions of these functions with one another.
The meaning of the derivative of a function both as the slope of a tangent line, and as rate of change of some phenomenon.
The relevance and ubiquity of differential calculus in numerous fields, such as in marginal cost in economics, the relationship between distance, velocity, and acceleration in physics, and in regression models used everywhere in machine learning.
Timetable
Timetables for courses offered at Leiden University College in 2024-2025 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 be introduced and explained. In addition to the two weekly sessions spent on guided practical work and explanations, you are expected to work on average ten hours a week on self-study. Exercises will be provided for students to work through outside class hours to cement their understanding of the subject.
Assessment Method
Midterm exam 30%
Participation: 10%
Homework assignments: 25%
Final exam: 35%
Reading list
The primary reading material is Volume 1 of the Openstax Calculus textbook, 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
TBA
Remarks
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