This course shows the modelling process in the context of differential equations and case studies from a number of areas such as population dynamics, economics, electric circuits, mechanical systems, fluid flow, physics and astrophysics. Analytic methods from the elementary theory of differential equations and calculus will be provided to allow for the analysis of the various models being investigated. Numerical solutions as well as a study of the qualitative behaviour of solutions will be combined with analytic solutions to obtain a better understanding of possible model behaviour.

Topics to be covered include:

First order differential equations; second order linear equations; systems of first order equations; nonlinear differential equations; Laplace transforms.

Advanced Vector Calculus - Curves and surfaces in three dimensions; parametric representations; curvilinear coordinate systems; Surface and volume integrals; use of Jacobians; gradient, divergence and curl; identities involving vector differential operators; the Laplacian; Green’s and Stokes’ theorems.

On successful completion of this course, students will be able to:

1. Explain the fundamental concepts of ordinary differential equations and their role in modern mathematics.
2. Use ordinary differential equations to model simple electric circuits, population growth and mass-spring systems, as well as other applications.
3. Understand the basic notion of ordinary differential equations and the underlying principals of modelling physical processes.
4. Demonstrate accurate and efficient use of the Laplace transforms and their applications in the solution of ordinary differential equations.
5. Apply problem-solving using concepts and techniques from ordinary differential equations and Laplace transforms relevant to diverse situations in physics, engineering, financial mathematics and in other mathematical contexts.

Assessment will be based on:

• One mid-semester exam (25%; LO 1-5)
• 10 Assignments (25%; LO 1-5)
• Final exam (50%; LO 1-5)

48 lectures and 10 tutorials

MATH1014 or MATH1116 or ENGN1222.

MATH2013, MATH2023, MATH2027, ENGN2212, MATH2405

 *) Dennis G. Zill, A First Course in Differential Equation with Modelling Applications.
 *) James Stewart, Essential Calculus (the same textbook used in MATH1013 and MATH1014).