Course overview
Mathematical models are used to understand, predict and optimise engineering systems. Many of these systems are deterministic and are modelled using differential equations. This course provides an introduction to differential equations and their applications in engineering. The following topics are covered: Linear ordinary differential equations of second and higher order, series solutions, Fourier series, Laplace transforms, partial differential equations, Fourier transforms.
Course learning outcomes
- Derive mathematical models of physical systems
- Present mathematical solutions in a concise and informative manner
- Recognise ODEs that can be solved analytically and apply appropriate solution methods
- Solve more difficult ODEs using power series
- Know key properties of some special functions
- Express functions using Fourier series
- Solve certain ODEs and PDEs using Fourier and Laplace transforms
- Solve problems numerically via the fast Fourier transform using Matlab
- Solve standard PDEs (wave and heat equations) using appropriate methods
- Evaluate and represent solutions of differential equations using Matlab