MATH2306 Partial Differential Equations and Applications

Later Year Course

Offered By	Department of Maths
Academic Career	Undergraduate
Course Subject	Mathematics
Offered in	Second Semester, 2010 and Second Semester, 2011
Unit Value	6 units
Course Description	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. We will develop the requisite vector calculus and multivariable calculus along the way. 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.
Learning Outcomes	On satisfying the requirements of this course, students will have the knowledge and skills to: 1. Explain the fundamental concepts of multivariable vector calculus and their role in modern mathematics and applications to fluid mechanics, electromagnetism, Maxwell equations and Partial Differential Equations (PDE). 2. Understand basic notion of PDE and be able to demonstrate capacity of modeling physical phenomena using PDE thorough detailed study of the heat and wave equations. 3. Demonstrate accurate and efficient use of the Fourier analysis techniques and their applications in the theory of PDE. 4. Apply problem-solving using concepts and techniques from vector calculus, PDE and Fourier analysis applied to diverse situations in physics, engineering, financial mathematics and in other mathematical contexts.
Indicative Assessment	Assessment will be based on: Assignments (30%; LO 1-4) Mid Semester (25%; LO 1-4) Final examination (45%; LO 1-4)
Areas of Interest	Mathematics
Requisite Statement	MATH2305 or MATH2405
Incompatibility	MATH2014, MATH2114, MATH2406, MATH3109 and MATH3209
Science Group	B

The information published on the Study at ANU 2010 website applies to the 2010 academic year only. All information provided on this website replaces the information contained in the Study at ANU 2009 website.