[BSc], GED, ID, PSc, EES, S, Ec
- Classes of 2013-2016: Numeracy.
This course is as an intensive introduction to the calculus of elementary functions and its applications to science, economics, and statistics. We will begin with the fundamental concepts of limits, continuity, and derivatives, and explore the derivatives and integrals of polynomials, rational functions, exponentials, logarithms, and trigonometric functions. Students will learn to differentiate composite functions using the chain rule, logarithmic differentiation, and other tools, as well as techniques for integration such as integration by substitution or integration by parts. In the later weeks of the course, we will explore derivatives of multivariate functions of multiple variables, problems of extremisation, and model exponential growth, sinusoidal oscillation, and logistic convergence through simple differential equations.
Students will primarily learn material through a combination of lecture and group discussion, where we explore concepts and phenomena by asking questions and discovering the answers together. In addition, students will receive instant feedback in class to check their understanding and guide the lecture portions of class time. We will use examples from astronomy, economics, population dynamics, and other real-life settings to show how calculus can be applied in practice.
Students will engage interactively with course content in class, by participating in class discussions and frequent, ungraded quizzes. They will learn the basics of calculus topics and their use in various applications, and demonstrate their knowledge throughout the course through weekly, graded quizzes; they will also gain the ability to clearly express their understanding in weekly take-home assignments. At the end of the course, they will demonstrate their synthesis of all the concepts they have learned in a final, comprehensive, take-home exam.
There will be no required readings other than weekly handouts/assignment sets.