This course is an introduction to mathematical modelling using basic functions, difference equations, and differential and integral calculus. Models will come from biological science, environmental science, physical science, and economics. Through the mathematical modelling process, this course contributes to the student's achieving several of the university's learning objectives. In particular, the learning objectives of numeracy, literacy, understanding of forms of inquiry, and depth and breadth of understanding are well served by this course. Through the mathematical modelling process, the students will begin to operate across disciplinary boundaries as they are introduced to the different disciplines' concepts and their associated vocabulary.
Special emphasis is placed on linear and quadratic functions as the modelling functions.
The concept of the composition of functions is applied to modelling processes made up of sequential subprocesses. Concept of inverse function is used to develop the relationship between the exponential and logarithmic functions. The basic properties and graphs of the functions in Section 5 and 6 are studied with emphasis on their use as modelling functions. There is an emphasis on geometric and arithmetic sequences and their corresponding series, and their use as discrete models. First order linear difference equations are presented as generalization of these sequences with emphasis on the modelling applications.