Prerequisites

This course serves as an introduction to modelling using differential equations as well as methods of solution for differential equations, and serves as a continuation from the first semester. In this course we will investigate analytical and graphical solutions of differential equations. Approximate solutions to differential equations will be covered in your second year courses, and beyond. Here, we will study the process of mathematical modelling along with the theory, methods of solution and applications of ordinary differential equations.

As you progress through the course, you will often have to compute derivatives and integrals by hand, and so you need to be very comfortable in doing these computations. You have all just covered these topics in MATH1036A: Calculus in the first semester so you should all be familiar with the rules of differentiation and integration, as well as their applications. If this is not the case for you, you need to be prepared to do a review of your first semester calculus course.

Some of the key topics and concepts are listed below. Students should know

  • how to differentiate and integrate all elementary functions
  • the methods of integration, including methods of substitution and integration by parts
  • the rules and laws of exponents and logarithms, including the special laws associated with the natural exponent and logarithm.
  • exponential and logarithmic functions, particularly the natural exponential and the natural logarithmic function. The natural exponential is \(f(x) = e^x\) and the natural logarithm is the inverse to the exponential, denoted by \(\ln x\). You should be familiar with the properties of the exponential function, in particular the relation between the natural logarithm and natural exponential as given by \(y=e^x \iff x=\ln y\).
  • trigonometric functions

It is assumed that you are competent and comfortable with differentiation and integration. These sections will not be retaught in this course so it is imperative that you have your MATH1036A Calculus notes handy so that you can refer to them throughout the course. There are also a plethora of online resources such as Khan Academy where you can review your calculus knowledge.