ChEn 6703 – Advanced Numerical Methods for Chemical Engineers

Midterm exam 2 will be on Wednesday, November 14.


Administrative Information

  • Meeting times: Monday & Wednesday from 1:25-2:45 PM in WEB 1460.
  • Instructor: James C. Sutherland, Professor of Chemical Engineering
    • Office location: MEB 3290H
    • Office hours: I do not hold formal office hours. I have an open-door policy and I am willing to meet with you any time that I am in my office. Alternatively, follow this link to set an appointment.
  • College of engineering guidelines discusses withdrawal policies, ADA policies, etc.

COVID19 Guidance

  • Based on CDC guidelines, the University requires everyone to wear face coverings in shared public spaces on campus, including our classroom. As a reminder, when I wear a face covering, I am protecting you. When you wear a face covering, you are protecting me and all of your classmates. If you forget your face covering, I will ask you to leave class to retrieve it. If you repeatedly fail to wear a face covering in class, I will refer you to the Dean of Students for a possible violation of the Student Code. Note that some students may qualify for accommodations through the Americans with Disabilities Act (ADA). If you think you meet these criteria and desire an exception to the face covering policy, contact the Center for Disability and Access (CDA). Accommodations should be obtained prior to the first day of class so that I am notified by CDA of any students who are not required to wear a face covering.
  • If you test positive for COVID19, you must self-report this to the university here.
  • Please sit in the same seat for each class period. This facilitates contact tracing in the event that someone contracts COVID19.

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. Optimization (time permitting)

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


Numerical Analysis:

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.
    • 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.
  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 3.5+ (not 2.7), which will be the default if you install python through anaconda.

You may 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.

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 email in a timely manner when possible.


In addition to the course website, I will use email regularly to send information to the class. You must have a valid University of Utah email address for all correspondence in this class, as outlined by the university?s policy.  If you prefer to use other email addresses, please set up a forward from your umail account (see here for instructions).


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.

Grading policy

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.

Student Resources

The University of Utah values the safety of all campus community members. To report suspicious activity or to request a courtesy escort, call campus police at 801-585-COPS (801-585-2677). You will receive important emergency alerts and safety messages regarding campus safety via text message. For more information regarding safety and to view available training resources, including helpful videos, visit

  • – a collection of student resources available on campus.
  • The University counseling center 801-581-6826, available for appointments to discuss issues you may be having.
  • SafeUT – smartphone application that provides access to resources.
  • University Neuropsychiatric institute (UNI) hotline: 801-587-3000
  • Crisis intervention
  • National Suicide Prevention Lifeline: 1-800-273-TALK (8255)

Addressing Sexual Misconduct

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