In physics, economics and engineering, we frequently encounter quantities (for example energy) that depend on many variables (such as position, velocity, temperature). Usually this dependency is expressed through a partial differential equation, and solving these equations is important for understanding these complex relationships.

In this course we will study first and second order partial differential equations. The solution methods studied in this course will include the method of characteristics, separation of variables, Fourier series and Fourier transforms.

This course will be useful for majors in economics, mathematical finance, engineering and physics. We will illustrate the theory with examples from these disciplines.

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Apply a range of techniques to find solutions of standard Partial Differential Equations (PDE)

2. Understand basic properties of standard PDE's.

3. Demonstrate accurate and efficient use of Fourier analysis techniques and their applications in the theory of PDE's.

4. Demonstrate capacity to model physical phenomena using PDE's (in particular using the heat and wave equations).

5. Apply problem-solving using concepts and techniques from PDE's and Fourier analysis applied to diverse situations in physics, engineering, financial mathematics and in other mathematical contexts.

Assessment will be based on:

• Assignments (30%; LO 1-5)
• Mid Semester (25%; LO 1-5)
• Final examination (45%; LO 1-5)

MATH2305 or MATH2405

MATH2014, MATH2114, MATH2406, MATH3109 and MATH3209