Practical Numerical Methods with Python MAE 6286

Start Date:Sep 1, 2017

Duration:15 weeks

Price:Free

https://openedx.seas.gwu.edu/courses/course-v1:MAE+MAE6286+2017/about

Course Description

This is a first course in numerical methods for advanced students in engineering and applied science. It was developed in 2014, both as a massive open online course (MOOC) and a regular course at the George Washington University. Similar courses have been taught at partner institutions: Southampton University (UK), Pontifical Catholic University of Chile, and Université Libre de Bruxelles. The original MOOC instance stayed online until August 2017, reaching 8,280 registered users. This is a refreshed instance of the course, as the GW SEAS Open edX has been re-installed with the latest version of the software in August 2017. Users of the old site can access with their same login credentials, but course enrollments were not kept—please enroll again if you are still interested in this course!

What You'll Learn

• 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

Instructors

Lorena A. BarbaAssociate Professor of Mechanical and Aerospace EngineeringThe George Washington University

Prof. Bernard KnaepenProfessor of PhysicsUniversité Libre de Bruxelles

Dr. Ian HawkeLecturer of MathematicsSouthampton University

Course Outline

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1. Getting Started 
   1. Initial Survey 
      1. Country survey
      2. Geochart of participants
      3. Survey
   2. How is this course going to work? 
      1. What to expect from the instructors
      2. What is expected of you
      3. What are the connected courses?
      4. What's this course about?
   3. Course communication channels 
      1. Discussion board
      2. Twitter
      3. Gitter chat room
   4. Why Python? 
      1. Python is a good learning language
      2. Python can get you a job
      3. An HPC expert uses Python
      4. Why Python tweet-up
   5. Are you new to Python? The basics. 
      1. For total beginners
      2. For beginners: quiz
      3. Python Libraries
      4. Variables
      5. Whitespace in Python
      6. Conditionals and Functions
      7. Defining functions
      8. Slicing arrays
      9. Boolean Logic
      10. Copying vs. Pointing
      11. New to Python: quiz
   6. Get Python 
      1. How to work with Python on the cloud
      2. How to get Python on your computer
   7. Ways to get help 
      1. StackOverflow
      2. Anaconda help
   8. Jupyter notebooks 
      1. How to launch the Jupyter notebook
      2. How to execute code in the Jupyter notebook
      3. How to use Markdown in the Jupyter notebook
      4. Extra tips with the Jupyter notebook
   9. What's git and why do I need it? 
      1. Version Control
      2. Why do I need this?
      3. How does version control work?
      4. Quiz: version control
   10. Using git and GitHub 
       1. Getting started with GitHub
       2. git setup
       3. Configuring a git editor
       4. Creating a git repository
       5. Making your first commit
       6. Editing a tracked file
       7. Viewing a repo's history
       8. Uploading your repository to GitHub
       9. "Why GitHub?" tweet chat
   11. Downloading (cloning) the notebooks 
       1. Forking the Numerical-MOOC Repository
       2. Making your first commit to your fork
   12. Self-Assessment checklist 
       1. Self-assessment purpose and surveys
       2. New to Python
       3. Get Python
       4. New to GitHub
2. Module 1: The Phugoid Model 
   1. Introduction. Phugoid theory 
      1. Introduction
      2. Lanchester's "Aerodonetics"
   2. Module 1 graded assessment 
      1. Tools of scientific Python
      2. Numerical solution of initial value problems
      3. Coding assignment: Rocket flight
   3. Dig deeper: Euler's method and beyond 
      1. Euler's method is a first order method
3. Module 2: Space and Time 
   1. Introduction to finite-difference solution of PDEs 
      1. Jupyter Notebooks
   2. Module 2 graded assessment 
      1. Stencils
      2. Numerical Solutions
      3. Coding Assignment: Traffic Flow
   3. Dig deeper: Analysis of numerical schemes 
      1. Analysis of schemes
4. Module 3: Riding the Wave 
   1. Riding the wave: Convection problems 
      1. IPython Notebooks
      2. Schemes for convection
      3. References
   2. Practice with Burgers' equation 
      1. Burgers with MacCormack
      2. Add damping
   3. Module 3 graded assessment 
      1. Flux limits
      2. Taylor Time
      3. Coding Assignment: Sod's Shock Tube
5. Module 4: Spreading Out 
   1. Spreading out: diffusion problems 
      1. Jupyter Notebooks
      2. Boundary conditions
   2. Module 4 graded assessment 
      1. Boundary Conditions
      2. Coding Assignment: Reaction-DIffusion
6. Module 5: Relax and Hold Steady 
   1. Relax and hold steady: elliptic problems 
      1. Module 5 Jupyter Notebooks
      2. Iterative solvers
   2. Module 5 graded assessment 
      1. Iterative Methods
      2. Coding Assignment: Stokes Flow