HWRS 504/404 – Fall 2025
Numerical Methods for Environmental Transport Problems (University of Arizona)
1. Lecture time:
2. Lecture location:
Modern Languages Bldg, Rm 503
3. Instructors:
Bo Guo (Primary Instructor)
Office: John W.Harshbarger Bldg, Rm 318C
Phone: (+1) (520) 626-9971
E-mail: boguo@arizona.edu
Jianwen Du (Teaching Assistant)
Office: John W.Harshbarger Bldg, Rm 228B
E-mail: janewendu@arizona.edu
4. Course Description:
This course is for senior undergraduate and graduate students. The goal of this course is to introduce commonly used numerical methods for ordinary and partial differential equations encountered in transport problems in environmental systems. The course covers finite difference and finite element methods with emphasis on basic discretization schemes and how to select the appropriate numerical schemes for a given differential equation. We will also discuss accuracy, stability, and convergence properties of the introduced numerical methods. Students will Python or Julia or other programming languages to implement numerical schemes to solve example problems. Experience with Python or Julia is not required.
The 2025 edition retains its core coverage of finite-difference/finite-volume and finite-element methods and adds a new module on machine-learning approaches for partial differential equations, including physics-informed neural networks (PINNs) and operator-learning surrogates.
5. Prerequisites:
- Differential Equations or with permission of Dr. Bo Guo.
6. Assignments and Exams:
Homework Problem Sets
Five problem sets will be assigned throughout the semester, due in one or two weeks after release. When submitting on D2L, convert your file to PDF and name it as Last_name_HW1. For example, Guo_HW1.pdf. Whether you type or handwrite, the text and figures need to be readable to an average human being. Nonreadable homework will be returned without grading. See Schedule for the specific dates.
Exams
The class has mid-term and final exams. The mid-term is oral and the final is written. The final will be scheduled during the exam week. A review session will be scheduled before both exams.
Final Project: Only required for students who take the graduate version of the class HWRS 505.
Students will have two options for the final project:
- (1) Choose a journal paper that has a core contribution on a numerical method, understand the advancement of the numerical methods developed in the paper, implement the method and reproduce the key results, and apply the numerical method to some new example problems.
- (2) Choose a research problem in their own filed of interest and apply the numerical methods they have learned in the course to solve the chosen problem.
For either option, you will need to summarize your key findings in a formal report and deliver a presentation in class.
7. Course Grade:
Evaluation and Grading for HWRS 405 (Undergraduate)
- 55% Homework Problem Sets
- 40% Exams (20% each)
- 5% Class Participation
Evaluation and Grading for HWRS 505 (Graduate)
- 35% Homework Problem Sets
- 40% Exams (20% each)
- 20% Final Project (Final Report and Class Presentation)
- 5% Class Participation
Grading Scheme:
- A: 90-100
- B: 80-89.9
- C: 70-79.9
- D: 60-69.9
- E: <60