Course Objective

To develop proficiency in numerical analysis by mastering the following key topics:

• Differentiate among absolute error, relative error, accuracy, and precision, and evaluate the numerical error in computed results produced by common algorithms.
• Apply and critically assess root-finding techniques—including Newton’s, secant, and bisection methods—by estimating convergence order and verifying stopping criteria on nonlinear equations drawn from science and engineering.
• Compute, compare, and interpret numerical derivatives (finite-difference formulas) and integrals (trapezoidal, Simpson’s, and composite rules) by quantifying truncation and round-off errors for real-world data sets.
• Select, implement, and justify appropriate interpolation strategies (e.g., Lagrange polynomials, Newton forms, and cubic splines) for discrete data, and estimate interpolation error using theoretical bounds.
• Construct, program, and analyze single-step and multi-step schemes (e.g., forward Euler, classical Runge–Kutta) for initial-value ordinary differential equations, and assess stability and local/global error through step-size studies.
• Communicate numerical results effectively by documenting algorithmic choices, presenting error analyses, and defending conclusions in written reports that meet professional mathematical standards.

Prerequisites: MAS 3114 or MAS 4105 with a minimum grade of C and experience with a scientific programming language.

Texts & Resources

• Recommended Textbook: Tea Time Numerical Analysis by Leon Brin. Available open source: Open Textbook Library.
• Supplemental Book: Python Programming and Numerical Methods by Qingkai Kong, Timmy Siauw, and Alexandre Bayen. Available open source: Course site.
• Software Access: Free software access for UF students: https://info.apps.ufl.edu/.

Grades

Your course grade is based on the following components:

Grading Scale

Grade policy: Your grade is your responsibility. You have exactly one week once your assignment has been returned to you to discuss that grade. After that week, the grade is final. No additional points will be awarded to “boost” your grade.

UF grading policies for assigning points: Grades and Grading Policies < University of Florida

Coursework

Homework

Homework assignments will be administered and submitted through MyOpenMath, accessible via Canvas. Each assignment will be due weekly, with due dates posted on Canvas. Homework is designed to reinforce concepts from lectures and help you prepare for exams.

Computer Projects

A computer programming project will be assigned with each unit and will be done in groups randomly assigned via Canvas and will change with each project. If a student does not participate in a group, please indicate that within the assignment submission and no credit will be given to that student. Otherwise, all students within a group will receive the same grade. Free software access is available to all UF students at https://info.apps.ufl.edu/.

Discussion Board Participation

Canvas is organized by modules, which pertain to each exam. Module 1 corresponds to all the material related to exam 1. Within each module, there is a discussion board where students may ask questions or post answers. This discussion board is an opportunity to engage with your classmates and share insights, questions, and resources related to course content. You can earn a maximum of 5 points with each discussion board.

Each post is worth 1 point. You may earn a point by:

• Asking a mathematical question.
• Answering a classmate’s question.
• Sharing external resources (such as a helpful YouTube channel or website) that aided your study, with a brief description of how it helped you.

You may ask about any course content, including homework problems, Python, lectures, or computer projects. As long as your post is focused on mathematical or course-related content, it is acceptable. To earn full credit, your contributions should be relevant and thoughtful.

Exams

• Exam 1: September 26 (Friday) — 90 minutes
• Exam 2: October 31 (Friday) — 90 minutes
• Exam 3: December 3 (Wednesday) — 90 minutes
• Final Exam: December 10 (Wednesday) — 2 hours

Calculator Policy

You may need a scientific or graphing calculator to help with homework questions. A scientific calculator (non-graphing calculator) will be permitted on exams via Honorlock. You may use: Honorlock Scientific Calculator. You will also need to be familiar with software like Mathematica, Matlab, or Python.

UF Policies

This course complies with all UF academic policies. See information on attendance and make-up policies, DRC information, assigning grade points, Gator Evals, honesty policy, in-class recording, and academic/wellness resources here: UF Syllabus Policy Links.

Honorlock Online Proctoring

In order to maintain a high standard of academic integrity and assure that the value of your University of Florida degree is not compromised, course exams will be proctored. Some students will take their exams online and will be proctored by Honorlock. You will take your exam electronically using the course website. You do not need to register for your exam. However, you will need to have installed and enabled the Google Chrome Honorlock extension prior to taking your exams. You will need a webcam, speakers, microphone, laptop or desktop computer, and a reliable internet connection to take your exams. Wireless internet is not recommended. You may also need a mirror or other reflective surface. Google Chrome is the only supported browser for taking exams in Canvas.

Before Your Exam

Prior to each exam and in the same environment you plan to take the exam, review the Honorlock Guidelines (PDF), and go to Honorlock Support to run a system check. This process takes just a few minutes and is completely free. If your course offers an Honorlock Practice Quiz, it is strongly recommended that you take it to practice using Honorlock before your exams.

Important: If you are unable to take an exam because of a technical glitch on your end, that is your responsibility. However, if you do experience technical difficulties during the exam, Honorlock’s support menu will be visible on-screen for you to contact a support agent.

Getting Help

Honorlock offers 24/7/365 technical support. Begin a live chat on the Honorlock Support page, call 844-243-2500, or email Support@Honorlock.com.

Netiquette and Communication Courtesy

Security

• Don’t share your password with anyone.
• Change your password if you think someone else might know it.
• Always log out when you are finished using the system.

General Guidelines

• Treat the instructor with respect, even via email or in any other online communication.
• Use proper titles (Dr., Prof.; otherwise Mr. or Ms.).
• Use clear, concise language with correct spelling and grammar.
• Avoid slang and texting abbreviations.
• Use standard fonts (e.g., Times New Roman, 12–14 pt).
• Avoid using ALL CAPS (it can be interpreted as yelling).
• Be cautious with humor or sarcasm; tone can be lost online.
• Protect personal information and avoid sending confidential info via email.

Email

• Use a descriptive subject line; be brief.
• Avoid attachments unless recipients can open them.</ li>
• Prefer plain text over HTML.
• Sign with your name and return email address.
• Think before sending to multiple people; use “Reply All” sparingly.
• Verify the author intended information to be forwarded before doing so.

Discussion Boards

• Check existing threads before posting.
• Be open-minded and summarize when many respond.
• Stay on topic and read the thread before replying.
• Be concise but thorough; add value rather than repeating.
• Review and edit posts; avoid short, generic replies like “I agree.”
• Quote key lines when referring to earlier posts and give proper credit to sources.
• Answer accurately; don’t guess.
• Be respectful; disagree without being critical or personal.
• Avoid sarcasm or anger; don’t type in ALL CAPS.

Tentative Weekly Schedule

I reserve the right to change anything in this syllabus if needed. Please check Canvas for changes.