- Meeting times: Monday & Wednesday from 1:25-2:45 PM.
- Instructor: James C. Sutherland, Professor of Chemical Engineering
- College of engineering guidelines discusses withdrawal policies, ADA policies, etc.
Course objectives & topics:
The objective of this course is to give students a working knowledge of solution techniques for:
- Numerical integration (quadrature)
- Linear and nonlinear systems of equations, with focus on those arising from solutions of ODEs and PDEs.
- Ordinary differential equations:
- initial and boundary value problems
- dealing with nonlinearities
- characterizing and handling stiffness
- Partial differential equations:
- Finite difference and finite volume discretization schemes
- Analysis of difference schemes including truncation error, numerical error, stability, etc.
- Application to reaction-diffusion systems arising from steady state and transient applications
- Introduction to hyperbolic (convective) systems
- Linear and nonlinear regression
- Optimization (time permitting)
The course will also provide students with significant experience programming in Python.
We will be using Piazza for discussion this semester. You can add images, code snippets and LaTeX equations in questions and answers. Please use this frequently – I think that it will be very helpful to you.
I encourage you to ask all questions about the class (lectures, homework, etc.) through Piazza so that everyone has the benefit of answers.
I will be using Piazza for announcements etc. so check that regularly in addition to the class web page.
Google’s jamboard provides an interactive whiteboard tool that can be useful when talking with each other. We’ll use this occasionally in class and in help discussions.
I don’t require a textbook for the class. I’ll post my own lecture notes on the lectures page for your reference. But below are several references that I think are pretty good:
- Numerical Methods for Engineers, Chapra & Canale, McGraw Hill. This book covers a wide variety of topics in numerical methods, and is a great addition to any personal library. It provides examples in Matlab.
- Numerical Methods for Engineers and Scientists, Joe D. Hoffman, ISBN 0-8247-0443-6. This is another great book that covers a variety of topics, but provides examples in Fortran, which isn’t too useful.
- Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, Lloyd N. Trefethen. This online, freely-available book is a great reference on ODEs and PDEs.
- Recorded lectures on a variety of numerical methods topics by Lloyd N. Trefethen.
Python is very ubiquitous and a google search can usually turn up answers to many of your questions. But here are a few ideas of places to look if you want to learn python:
- General Python programming resources:
- A brief tutorial on arrays in python that includes discussion of python lists as well as numpy arrays.
- Python has a vast number of libraries to simplify many tasks. Among those that you will probably use regularly:
- matplotlib provides very powerful (but sometimes challenging to use) plotting capabilities. A quick way to get started on a plot is to look at the matplotlib gallery to obtain code to generate a plot like the one you want to create. Here is another great resource on matplotlib.
- plotly is another great plotting library that allows more interactive plots.
- NumPy provides really powerful array handling capabilities like those in Matlab to allow you to create and manipulate arrays of data. It also has some algorithms that operate on the data. We will use numpy extensively in this class.
- SciPy has a large number of algorithms such as interpolation, quadrature (numerical integration), optimization, ODE solvers, linear algebra tools, etc. There is some duplication between NumPy and SciPy.
- pandas provides a lot of data analysis tools. This includes tools to read/write data, analyze and manipulate data, etc.
- SymPy provides support for symbolic mathematics within Python.
- If you are a Matlab user, here are a few resources:
Jupyter notebooks allow you to run Python code fragments interspersed with markup text including equations, plots, etc. This is really useful for communicating results, and will be the format required for homework submission.
You will need to familiarize yourself with Jupyter notebooks since you will be submitting homework as a notebook.
Here is a link to a Jupyter notebook that provides a crash course on some of the key features of a notebook.
Web-Based Access for Jupyter Notebooks:
There are two options for web-based access to Jupyter
- You should have access to juno.chpc.utah.edu using your University login credentials for the duration of the semester.
When you first log in, open a terminal (choose the “New” box then “Terminal”) and execute the following command:
wget -O - http://home.chpc.utah.edu/~u0424091/install_nbextensions.sh 2>/dev/null | bash
You should see “Nbextensions” appear in your jupyter browser window. Click on it and check the box labeled “(some) LaTeX environments for Jupyter”
- The chemical engineering virtual machine pool. Log in with your ICC credentials and use the UG (not graduate) VM pools. This will open a full windows machine where you can launch jupyter from the start menu.
These are great options if you have consistent web access and don’t want to perform a local python installation on your own laptop.
Local Python Installations
If you want to install it on your computer, I strongly suggest using Anaconda to install Python and Jupyter, and I also suggest using Python 3.5+ (not 2.7), which will be the default if you install python through anaconda.
You will probably want to install the
jupyter_contrib_nbextensions toolkit to super-charge your Jupyter notebook:
- If you are using the terminal, do:
conda install -c conda-forge jupyter_contrib_nbextensions
- If you are using the anaconda navigator application, go to “environments” and search for this package.
I assume that you are here to learn. I will do my best to help you achieve that goal. However, learning is primarily your responsibility. You should come to class prepared to participate in the lecture and ask questions. I am happy to meet with you outside of class to discuss questions you have. I also try to respond to email in a timely manner when possible.
Homework is designed to provide you with the opportunity to solidify concepts discussed in class. Homework assignments will typically require you to assimilate several concepts to solve a problem. I do this purposely, since I believe that this will help you to learn problem solving skills that will be crucial to your success as an engineer.
Homework assignments will be posted on the homework page of the course web site.
Solutions will be posted on the class web site shortly after the due date.
I strongly encourage you to work together on homework assignments. Discuss the problem and your solution approaches with each other. However, you must submit your own work. Copying others’ work is plagiarism and will not be tolerated. Consequences of cheating and plagiarism include failure of homework assignments, failure of this class, and possibly dismissal from the chemical engineering program.
Homework assignments must be submitted electronically as a *.zip file that contains a Jupyter notebook and any other files required to execute the notebook. For more information, see the homework page.
This is a tentative grading policy:
- 40% Homework
- 20% Each midterm (two midterms)
- 20% Project
Grades will be assigned on the following scale, normalized to the highest student in the class:
- 93: A, 90: A-
- 87: B+, 83: B, 80: B-
- 77: C+, 73: C, 70: C-
- 67: D+, 63: D, 60: D-
I reserve the right to adjust this scale downward if I deem it necessary.
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