ChEn 6703 – Advanced Numerical Methods for Chemical Engineers


Administrative Information

COVID-19 Considerations

Please be familiar with the University of Utah’s web page with information about the COVID-19 pandemic.

  • In accordance with CDC guidelines and University guidance, you are encouraged to wear a mask and be vaccinated against COVID-19 to protect yourself and those around you.
  • Vaccines are available free of charge on campus or at a variety of community pharmacies.
  • Asymptomatic testing is available and you are encouraged to take advantage of this resource regardless of your vaccination status.
  • If you are exposed to someone infected with COVID-19, feel at all ill, or have been diagnosed with COVID-19, you should immediately isolate/quarantine and should not attend class. Contact me ASAP to make arrangements.

Course objectives & topics:

The objective of this course is to give students a working knowledge of solution techniques for:

  1. Numerical integration (quadrature)
  2. Linear and nonlinear systems of equations, with focus on those arising from solutions of ODEs and PDEs.
  3. Ordinary differential equations:
    • initial and boundary value problems
    • dealing with nonlinearities
    • characterizing and handling stiffness
  4. 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
  5. Linear and nonlinear regression
  6. Introduction to optimization

The course will also provide students with significant experience programming in Python.


Getting Help:

Ed – discussion board

We will be using Ed for out-of-class 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 Ed so that everyone has the benefit of answers.

I will be using Ed for announcements etc. so check that regularly in addition to the class web page.

Reference materials

There is not a required 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:

Python programming:

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.

Jupyter Notebooks:

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:

  1. You should have access to using your University login credentials for the duration of the semester. This is the preferred option for remote access. Once you have logged in, choose “CHEN Jupyter” from the “Classes” drop-down menu.
  2. 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 3.6+ (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.

If you run into trouble here, I may be able to help with basic troubleshooting. Feel free to reach out on Ed.

Teaching Philosophy:

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 questions outside class (via Ed or email) in a timely manner when possible.

I expect that you will be in class unless you are ill. If you need to miss class, please inform me in advance.


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 via gradescope. For more information, see the homework page.

Grading policy

This is a tentative grading policy:

  • 40% Homework
  • 20% Each midterm (two midterms)
  • 20% Class 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.

Student Resources

There are a number of resources on campus that you should be aware of.  Here are a few highlights:

  • The college of engineering has a dedicated counselor who you can see free of charge.
  • The University counseling center 801-581-6826, available for appointments to discuss challenges you may be having. It also provides crisis intervention services.
  • SafeUT – smartphone application that provides access to resources.
  • – a collection of safety-related resources available on campus.
  • University Neuropsychiatric institute (UNI) hotline: 801-587-3000
  • National Suicide Prevention Lifeline: 1-800-273-TALK (8255)
  • To report suspicious activity or to request a courtesy escort, call campus police at 801-585-COPS (801-585-2677).

Addressing Sexual Misconduct

Title IX makes it clear that violence and harassment based on sex and gender (which includes sexual orientation and gender identity/expression) is a Civil Rights offense subject to the same kinds of accountability and the same kinds of support applied to offenses against other protected categories such as race, national origin, color, religion, age, status as a person with a disability, veteran?s status or genetic information. If you or someone you know has been harassed or assaulted, you are encouraged to report it to the Title IX Coordinator in the Office of Equal Opportunity and Affirmative Action, 135 Park Building, 801-581-8365, or the Office of the Dean of Students, 270 Union Building, 801-581-7066. For support and confidential consultation, contact the Center for Student Wellness, 426 SSB, 801-581-7776. To report to the police, contact the Department of Public Safety, 801-585-2677(COPS).