Engineers are often called upon to use knowledge of their engineering discipline, science, mathematics and logic to find suitable solutions to a wide range of problems. Understanding a given problem, and then developing an appropriate mathematical model to analyse solutions to this problem, are essential steps in the problem solving process. The emphasis of this course is on developing the mathematical reasoning ability needed to make these steps in problem solving. This will include the formulation of mathematical models and the development of the general skills needed to analyse these models, including both analytical and numerical techniques. Examples from a variety of practical engineering problems will be examined throughout the course.