CH EN 2450 – Numerical Methods – Fall 2018

Instructor: Prof. Tony Saad
Phone Number: 801 585 0344
Office Hours: Tuesdays from 1:00 PM to 3:00 PM or by appointment
Office Location: MEB 2286

Course Catalog Description

Applications of numerical methods to interpolation, differentiation, integration, and the solution of systems of linear, nonlinear, and differential equations in chemical engineering.

Course Objectives & Topics:

The primary goal of this course is to provide engineering students with a basic working knowledge of numerical methods. In addition, this course aims at developing an appreciation of programming and how computers can be an asset for the modern-day engineer.

My goals in this class are:

    1. Teach you the importance of numerical methods
    1. Introduce you to the skills needed by modern engineers
    1. Emphasize the importance of knowing a few programming languages
  1. Emphasize learning and critical thinking

Matlab is the standard software environment used for implementation and application of numerical methods.

By the end of this class, students will have a working knowledge of the following:

  • Solution of linear systems of equations
  • Interpolation
  • Regression
  • Solution of nonlinear equations
  • Numerical differentiation
  • Numerical integration
  • Solution of ordinary differential equations (ODEs).
  • Solution of elliptic and parabolic partial differential equations.

The following are listed as prerequisites and corequisites for ChEn 2450:

  • Prerequisites:  ChEn 1703,  Algebra & calculus
  • Corequisite: Math 2250 – Ordinary differential equations & Linear Algebra

Textbook & Reading Material:

There is no textbook for this class. Material presented in this class will be based on the following resources:

  • Hoffman, J. D. (2001). Numerical methods for engineers and scientists. New York: Marcel Dekker.
  • Chapra, S. C., & Canale, R. P. (2010). Numerical methods for engineers . Boston: McGraw-Hill Higher Education.

Lecture Notes

Date Lecture Notes (PDF/Web) Screencast Jupyter Notebooks HW
Tuesday, 08/21/2018 Introduction
Why Python?
Thursday, 08/23/2018 Python Primer
Errors – Part 1
Why Python? HW1 Assigned
Tuesday, 08/28/2018 Errors – Part 2 Errors – Part 2
Thursday, 08/30/2018 Linear system: direct solvers 1 Linear Systems – Part 1 HW2 Assigned
Tuesday, 09/04/2018 Solution to HW1 (see screencast)
Solving the heat equation in Python
Solution to HW1
Solving the heat equation in Python
Thursday, 09/06/2018 Linear systems: iterative solvers 1 HW3 Assigned: Thomas Algorithm
Tuesday, 09/11/2018 Linear systems: iterative solvers 2 Solution to HW2 + Continuation of Iterative Linear Solvers
Thursday, 09/13/2018 Interpolation Interpolation – Part 1 HW4 Assigned: Iterative Linear Solvers
Tuesday, 09/18/2018 Solution of HW3
Interpolation 2 (use previous set of slides)
HW3 – Solution
Interpolation – Part 2
Thursday, 09/20/2018 Regression 1 Regression 1 Least Squares Regression.ipynb HW5 Assigned: Interapolation
Tuesday, 09/25/2018 No notes No screencast
Thursday, 09/27/2018 Use previous notes on regression Regression 2 – The Normal Equations & Nonlinear Models Normal Equations Example – GPA.ipynb

Regression of a Nonlinear Model Example

Tuesday, 10/02/2018 Exam 1 Review HW 5 Solution

Exam 1 Review

Thursday, 10/04/2018 MIDTERM 1 (Errors, linear systems, and interpolation)
Tuesday, 10/09/2018 NO CLASS – Fall Break
Thursday, 10/11/2018 NO CLASS – Fall Break
Tuesday, 10/16/2018 Numerical Integration Numerical Integration Numerical Integration Examples
Thursday, 10/18/2018 Numerical Differentiation Numerical Differentiation
Tuesday, 10/23/2018 NO CLASS NO CLASS
Thursday, 10/25/2018 Nonlinear Equations – All Slides HW 6 Solution

Nonlinear Systems 1

Tuesday, 10/30/2018 Closed Domain Methods – Bisection + Regula-Falsi (see slides above) HW 7 Solution

Closed Domain Methods (Bisection + Regula-Falsi)

Thursday, 11/01/2018 Secant and Newton Methods (see slides above) Secant and Newton Methods Root Finding Methods.ipynb
Tuesday, 11/06/2018 Systems of Nonlinear Equations (see slides above) Systems of Nonlinear Equations Nonlinear System Demo.ipynb
Thursday, 11/08/2018 ODEs – All Slides ODEs1
Tuesday, 11/13/2018 Exam 2 Review Exam 2 Review

ODEs 2 – Forward Euler Method

Thursday, 11/15/2018 EXAM 2 EXAM 2 EXAM 2 EXAM 2
Tuesday, 11/20/2018 Implicit Methods for Initial Value Problems Explicit Time Integration.ipynb

Motivation for Implicit Methods.ipynb

Cyclical Systems.ipynb

System of Equations – Kinetics Example.ipynb

Thursday, 11/22/2018 NO CLASS – Thanksgiving
Tuesday, 11/27/2018 Boundary Value Problems
Thursday, 11/29/2018 Basic Intro to Numerical PDEs Boundary Value Problems – Nonlinear RHS
Tuesday, 12/04/2018
Thursday, 12/06/2018
Tuesday, 12/11/2018

Administrative Information

See here for fall semester schedule:

Event Date
Semester Length Classes
Classes begin Monday, August 20
Last day to add without a permission code Friday, August 24
Last day to wait list Friday, August 24
Last day to add, drop (delete), elect CR/NC, or audit classes Friday, August 31
Last day to withdraw from classes Friday, October 19
Last day to reverse CR/NC option Friday, November 30
Classes end Thursday, December 6
Reading day Friday, December 7
Final exam period Mon.-Fri., Dec. 10-14
  • Getting Help: Meeting times: coming soon
  • Discussion sections: coming soon
  • Teaching Assistants: coming soon
  • College of engineering guidelines discusses withdrawal policies, ADA policies, etc.
  • Attend the discussion section you are registered for.  You may attend other ones in addition for extra help.
  • Use the course website, lectures, and online resources.
  • If all the above fails, then feel free to stop by and we can discuss any gaps in your understanding of the subject matter.


This class will make exclusive use of Python – a modern programming language that is suitable for scientific computing. Python is easy to use and  – most importantly – free!

We will also focus on using Python within Jupyter Notebooks: a great way to combine text, math, and programming into one document that is edited and executed in a web browser (See this example). You will learn about that in the class. You will also have access to python through your web browser (after the class starts). If you want to download your own Python + Jupyter Notebook, then download the Anaconda distribution here.

Please go here for an easy tutorial on Python by Prof. Saad. In addition, Prof. Saad will hold a few in-class lectures on learning Python.

Accessing Matlab

There are several options for accessing MATLAB.

  • The most convenient for ChEn students is probably via the ICC (MEB 2285), which is a Chemical Engineering computer lab.  To set up an account, follow this link.  You can also gain remote access to this lab from any computer with a (fast) network connection.
  • You can purchase the student version of MATLAB.  There are also several free MATLAB alternatives, including Octave and FreeMAT.  These don’t have all of the features of MATLAB, but are probably sufficient for what you will need in this class.
  • The CADE lab in WEB has Windows (WEB 210), Mac (WEB 210) and Linux (WEB 246) computers. Walk in and find one of the system administrators to get set up with an account.  Also, you can access the Linux machines remotely if you have a fast internet connection.  Only try this if you are familiar with X-windows and SSH.
  • Library computers running Windows.  (I don’t think that MATLAB is installed on the Mac computers in the library)


I will use your Email address to communicate with you and send information to class. Please make sure that you have access to your utah email address.


  • Homework is a fundamental piece of the learning process. It will help you strengthen the concepts you learned in class and apply them to new problems.
  • The goal of homework is to get you to familiarize yourself with the nomenclature and the types of problems that can be solved with numerical methods.
  • Homework assignments will be posted on the homework page of the course web site. Unless otherwise stated, homework is due by the beginning of class on the date indicated on the schedule.
  • Solutions will be posted on the class web site shortly after the due date.
  • Feel free to “work together” on homework assignments. Discuss the various solutions methods and attempt to learn or fill deficits in your understanding of the subject matter. However, you must submit your own original work. Please do not cross the line of plagiarism and cheating. Such behavior will not be tolerated.
  • Homework assignments must be submitted electronically via the course web page. You should write a report describing the problem, your solution, and presenting your results. Submit your report in either PDF or MS Word format. Any Excel or Matlab files that you used to solve the homework problem should also be submitted with your solution. For more information, see the Homework page.

In-Class comprehension quizzes

Every now and then, I will give you a short “comprehension” quiz. The quiz should take no more than five minutes to complete and will address the comprehension aspect of numerical methods. For example: What do you use interpolation for? Give an example of where linear systems arise?

The quiz will also challenge your critical thinking. For example, if the temperature at 8 AM was 25 degrees and at 9 AM it was 35 degrees. An engineer estimated the temperature at 8:30 AM to be 55 degrees. Does this make sense?

These quizzes are aimed to test your understanding of the subject matter in “words”.

Grading policy (tentative)

  • 20% each midterm exam (two midterms)
  • 25% Homework
  • 10% In-Class comprehension quizzes
  • 25% Final exam

Grades will be assigned on the following scale, normalized to the highest student in the class (who, by definition, is 100%)

  • 92< A ≤ 100,   89 < A- ≤ 92
  • 86 < B+ ≤ 89,   81 < B ≤ 86,   78 < B- ≤ 81
  • 75 < C+ ≤ 78,   70 < C ≤ 75,   67 < C- ≤ 70
  • 64 < D+ ≤ 67,   59 < D ≤ 64,   56 < D- ≤ 59
  • E ≤ 56

I reserve the right to adjust this scale downward if I deem it necessary.

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).

Academic Misconduct

All instances of academic misconduct will be handled in accordance with the Student Code (

Students with Disabilities (ADA)

The University of Utah seeks to provide equal access to its programs, services, and activities for people with disabilities. If you will need accommodations in this class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, (801) 581-5020. CDS will work with you and the instructor to make arrangements for accommodations. All written information in this course can be made available in an alternative format with prior notification to the Center for Disability Services.