9  Syllabus

NoteAbstract

Numerical integration/differentiation. Numerical solution of initial-value problems, boundary value problems for ordinary differential equations, partial differential equations.

Spring 2026
Meeting times: 09:05‑11:00 MW, Amundson Hall 162
Number of credits: 4
Canvas page: https://canvas.umn.edu/courses/541907
Instructor: Jack Thomas
Email:
Office: Vincent Hall 331
Office hours: MWF https://z.umn.edu/JT-office

9.1 Summary

This is the second part of a two-semester sequence exploring the design and implementation of numerical methods to solve some of the most common types of problems arising in science and engineering. Typically these problems cannot be solved in terms of a classical analytical formula, and thus numerical methods must be used to approximate the solution. We study how and why numerical methods work, and also their errors and limitations.

In the first part we studied: how a computer does arithmetic, solving nonlinear equations in one variable, polynomial interpolation and approximation, numerical quadrature, and methods for solving linear systems of equations. This semester, we will study iterative methods for solving linear systems of equations, numerical integration and differentiation, solving initial and boundary value ODEs, and PDEs.

9.1.1 Prerequisites

Math 5485. This course assumes knowledge of calculus, linear algebra, and differential equations, and familiarity with some programming language.

9.1.2 Goals and Objectives

  • Gain familiarity with numerical methods for approximating solutions to common problems arising in science,
  • Be able to explain when and why certain methods do (or do not) work,
  • Justify your explanations with rigorous error analysis,
  • Test your understanding by implementing numerical methods and completing Jupyter notebooks.

9.1.3 Format

Two classes per week (9:05-11:00 MW). We will have \approx20 lectures (a combination of slides, blackboard, and Jupyter notebooks) and \approx 5 problem classes (we will mainly go through exam-style exercises based on the main content of the course).

9.1.4 Textbooks

We will use the following texts as well as written up lecture notes, interactive notebooks, and (parts of) research articles:

  • R. L. Burden, D. J. Faires, and A. M. Burden, Numerical Analysis, 10th Edition, Cengage, 2016
  • E. Süli and D. Mayers, An Introduction to Numerical Analysis, Cambridge University Press, 2003
  • T. A. Driscoll and R.J.Braun, Fundamentals of Numerical Computation. Available online https://fncbook.com/

Additional references will be provided in-class and on the course webpage.

9.2 Course Grading

The course will be graded by a combination of midterm (on the content of the first 7 weeks), final exam (on the content of the whole course), assignments (Juptyer notebooks), and an optional presentation.

9.2.1 Exams

  • Midterm: March 18
  • Final: May 11

9.2.2 Grading

The course grade will be determined by the following components:

  • Midterm 20%
  • Assignments 40%
  • A: Final Exam 40%, or
  • B: Final Exam 30%, Presentation 10%

You will be given the opportunity to give a short presentation in the second half of the semester. If your final exam score is higher than the score for your presentation, your final exam will be worth 40% and your presentation will be worth 0% (we will take the maximum of A and B, as above).

There will be at most 6 Assignments: most will be short and you will have ten days to complete them.

9.3 Course Policies

Attendance in class is mandatory. If you cannot attend the class for any reason, please let me know.

Assignments are due on Wednesdays at 23:59. Assignments must be uploaded to Canvas by the deadline. Late assignments will not be accepted and score 0, though the application for an extension can be considered at most twice under reasonable circumstances, and you must send an email to me as early as possible. If you get an extension, the assignment will be due on the following Monday at 09:00 (so that we may go through answers in class).

I encourage you to discuss the course material and assignment questions with your classmates. However, unless otherwise explicitly stated on the assignment, you must complete and write up your solutions on your own.

There is no make-up for the midterm exam: if you are absent with good reason, the corresponding proportion can be added to the final exam instead.

If accommodation for exams in the DRC center is needed, you have to send the accommodation letter to me as soon as possible.

9.3.1 Generative AI

The Board of Regents Student Conduct Code states the following in Section IV, Subd.1: Scholastic Dishonesty:

“Scholastic dishonesty means plagiarism; cheating on assignments or examinations, including the unauthorized use of online learning support and testing platforms; engaging in unauthorized collaboration on academic work, including the posting of student-generated coursework on online learning support and testing platforms not approved for the specific course in question; taking, acquiring, or using course materials without faculty permission, including the posting of faculty-provided course materials on online learning and testing platforms; …”

Generative AI systems and online assignment help tools are online learning support platforms, which cannot be used for course assignments. We are testing your knowledge and understanding, not your ability to use GenAI.

The use of online learning support platforms are forms of scholastic dishonesty and will be treated as such.

9.3.2 Important dates

Please see Spring 2026 Calendar for important dates.

9.4 University Policy Statements

The University’s Education & Student life policies are available in the online Policy Library.

The University seeks an environment that promotes academic achievement and integrity, that is protective of free inquiry, and that serves the educational mission of the University. To support this environment, the University seeks a community that is free from violence, threats, and intimidation; that is respectful of the rights, opportunities, and welfare of students, faculty, staff, and guests of the University; and that does not threaten the physical or mental health or safety of members of the University community.

As a student at the University, you are expected to adhere to Board of Regents Policy: Student Conduct Code.

The following links to University Policy Statements are provided for your reference:

Resources related to mental health, stress management, and counseling can be found at https://safe-campus.umn.edu/personal-wellbeing.