ANU - STUDYAT - PDE's & Applications

Offered By:

Department of Maths

Academic Career:

Undergraduate

Course Subject:

Mathematics

Offered in:

Second Semester, 2010

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

Partial Differential Equations and Applications MATH2306 - Details