This course is a collaboration between faculty at three institutions across the world: the George Washington University (Washington, DC, USA); University of Southampton (UK) and Pontifical Catholic University of Chile (Santiago, Chile).* A credit-bearing course will run at each institution at the same time as this MOOC, and students at all locations will participate in the same learning community with MOOC participants.
The course aims for students to achieve the following:
- connect the physics represented by a mathematical model to the characteristics of numerical methods to be able to select a good solution method;
- implement a numerical solution method in a well-designed, correct computer program;
- interpret the numerical solutions that were obtained in regards to their accuracy and suitability for applications.
WHO IS THE COURSE FOR?
Numerical methods for differential equations are relevant across all of science and engineering. This course is for anyone with mathematical, scientific or engineering backgrounds who wishes to develop a grounding in scientific computing. Using a range of hands-on lessons, participants in the course will develop the basic skills to tackle modern computational modelling problems.
In developing this course, the instructors are inspired by the philosophy of open-source software. One of the tenets of the course is that we can use the web to interact, connect our learning, teach each other by sharing our learning objects. Therefore, this course is especially for those who are eager to participate in distributed knowledge creation on the web. Join us in this adventure!
The connected courses and MOOC are aimed at first-year graduate students or advanced seniors, but assume only a background in vector calculus, linear algebra, and differential equations. We won't assume more than a beginner's programming experience and will guide students to develop a foundation in numerical methods, and hands-on experience coding up solutions to differential equations.