# Distance Learning - Ordinary and Partial Differential Equations

Models, methods and applications

## DESCRIPTION

Originator and trainer: Dr. Daniel J. Duffy.

The goal of this hands-on and self-contained course is to introduce ordinary and partial differential equations (ODEs and PDEs). These equations form the basis for modelling many kinds of phenomena in areas such as science, engineering, computational finance and more generally, mathematical physics. The approach is to examine representative model ODEs and PDEs and then to extend them to more complex and larger problems.

We introduce the topics in the course using a building-block approach: we first take a scoped version of a differential equation and we examine it from a number of viewpoints until we understand its properties and behaviour. Then we decide how to extend and generalise the differential equation to new situations including:

• From linear to nonlinear equations.
• From one dimension to higher dimensions.
• From diffusion equations to convection-diffusion-reaction equations.
• Applying your ODE/PDE skills to real-life applications.

The approach is similar to the following statement by Paul Halmos:

..the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly great generality is in essence the same as a small and concrete special case.

Subjects Covered

• PDEs categories and how to recognise them.
• Analytical methods for solving ODEs and PDEs.
• Underlying mathematical  analysis tools.
• Focus on real-world relevant problems.
• Preparation for numerical projects for ODEs and PDEs.

Course Benefits

• Comprehensive overview of the world’s most important PDEs.
• PDE classification and essential properties.
• Mathematical analysis in order to understand the PDE landscape.
• How PDEs model real-life phenomena.
• Numerous exercises, quizzes and answers to test what you have learned.
• Perfect preparation for numerical methods in engineering, science and finance.
• Competitively priced.

Application Areas

• Fluid flow.
• Heat transfer.
• Mathematical physics.
• Computational finance.

For whom is the Course and what are the Prerequisites?

This course is suitable for professionals in industry and finance as well as for advanced undergraduate and MSc/MFE students. The prerequisite knowledge is calculus to the level in the book by D.V. Widder 1989 Advanced Calculus Dover. It is also an advantage if you are exposed to applications in which differential equations play a role or if you are writing a thesis in which they are needed.

The level of the course is similar to that in second and third year university courses in applied mathematics and engineering, for example. The main difference is that this focused course is dedicated to differential equations and their applications.

If you have any queries please do not hesitate to contact me, Daniel Duffy dduffy@datasim.nl to discuss the course.

Structure of Course and Student-Trainer Interaction

This course takes an incremental/inductive approach by first examining model problems in detail and then extending them to more advanced applications. Student progress is measured by working on graded exercises.  Regular communication takes places by e-mail and Skype.

Students receive a certificate on successful completion of the course.

The optimal way to learn in our opinion is by executing the following steps. This discussion pertains to studying and learning the contents of a single module:
1. Listen to the audio show and use the printed PowerPoint slides as backup.
2. Read the relevant material in the provided book(s).
3. Do the exercises; compile and run the programs.
4. If you are having problems, go back to one of more of steps 1, 2, 3.
5. If step 4 has been unsuccessful then post your problem on the Datasim forum.
6. Go to next module.