MATH 426 Numerical Analysis

Fall 2021, UAF

Instructor:
   Ed Bueler
   Chapman 306C
   office hours: bueler.github.io/OffHrs.htm
   elbueler@alaska.edu

Class:
   MWF 11:45am -- 12:45pm
   Duckering 352 (F01) and online (FXA)
   CRN: 74440 (F01) and 76011 (FXA)

Textbook: Driscoll & Braun, Fundamentals of Numerical Computation, SIAM Press 2017 (ISBN-13: 978-1-611975-07-9)

Course Websites:

There are two websites:

public materials and schedule: bueler.github.io/M426F21/
enrolled students: Canvas course website at https://canvas.alaska.edu/courses/2350

The public site has a daily schedule of topics, due dates, PDF assignments, Matlab examples, and other helpful content. It will be updated frequently to reflect what topics were actually covered.

The Canvas site has password-protected content such as grades and exam/homework solutions. It also has the Zoom lecture link and recorded Zoom sessions for each day. However, most information is at the public site.

Description

This course introduces numerical analysis using lecture, small group work in class, homework, and exams. We will learn methods for solving certain problems of applied mathematics on computers, and why those methods work. We will solve (and reconsider) problems in calculus, linear algebra, and differential equations, and in some areas that are new to you.

Catalog description: Direct and iterative solutions of systems of equations, interpolation, numerical differentiation and integration, numerical solutions of ordinary differential equations, and error analysis.

Goals and Outcomes

By the end of the course you will be able to evaluate and use numerical tools for solving a variety of mathematical, scientific, and engineering problems. You will be able to program basic methods, for example for prototyping more substantial solutions. You will have the mathematics needed for numerical approaches to new problems like optimization and partial differential equations. Student competence with actual scientific computing, not just theory, is a goal; you will be comfortable using Matlab (or equivalent) both as a "supercalculator" and as a programming language.

Prerequisites

Official prerequisites: MATH F302 Differential Equations OR MATH F314 Linear Algebra. Recommended: Knowledge of programming.

Regarding the two MATH courses here, some mathematical maturity beyond calculus is more important than the specific content of either course. However, we will indeed solve basic differential equations and linear systems by numerical means.

"Knowledge of programming" might translate to "some computer science course or an engineering computer techniques course". However, what is actually needed is willingness to learn programming in the (easy and protected) environment of Matlab. Many students have succeeded with this as their first programming class.

Students come from math, statistics, computer science, physics, geophysics, engineering, and other majors at UAF. Thus I will devote substantial class time, especially at the beginning of the semester, to collecting the bits of needed prequisite knowledge. However, you must show initiative in a meaningful and timely way, especially when I make it clear that review is needed.

Student Obligations

You will be expected to understand both the theory and practice of numerical analysis as presented in the lecture and the textbook. Both theory and practice will be emphasized on homework and exams.

You will use the mathematical programming language Matlab, or the free equivalent Octave, or another equivalent language, on every homework assignment. (Even the first assignment!) I will help with getting started, especially in the first week. On many homework problems you will be expected to turn numerical algorithms into functioning programs. Other problems will ask you to explain a concept and/or to demonstrate an idea by a hand calculation.

Lectures and homework together make up the core of the class. Getting the most out of these is your responsibility. You should ask questions in class, both about the lecture content and about the homework assignments.

The Hybrid Classroom:

There are two sections of the class, in-person (F01) and online (FXA), but they are treated as one course and they occur simultaneously.

In this "hybrid" set-up, each lecture will be a recorded (and recurring) Zoom session generated from Duckering 352. The link for the Zoom session is inside Canvas; go to https://canvas.alaska.edu/courses/2350. The Zoom recordings will be linked from inside Canvas, and thus not be public.

My intention is to treat all students the same regarding proctored assessments (see below) and participation during class time. However, students in each section have some obligations to help make the hybrid mode work:

F01 in-person students: To allow in-class play with Matlab, and to help classroom communication for e.g. group work, please bring a laptop if you can, and join the Zoom session so you see the online students.
FXA online students: Please sign into the Zoom session (link at https://canvas.alaska.edu/courses/2350) before class and participate as energetically as you can. Keep your camera on if possible. For in-class group work you will want to get the PDF of worksheets etc. from bueler.github.io/M426F21/ before class starts if possible. Note that you must turn in homework and take-home assessments electronically, namely as clear and combined PDFs, which may require scanning documents. You will need to schedule proctoring for the in-class assessments (see below).

Homework and Exams

Weekly homework forms 40% of your score for the course. Homework assignments, and their due dates, will be regularly posted at the Course Website bueler.github.io/M426F21/. Homework is due on the date assigned, and late homework will not be accepted unless approved in advance.

There will be a Quarterterm Quiz, a Midterm Exam, and a Final Exam. All of these are proctored, either in-class or at a testing center.

Assessment
Homework
Quarterterm Quiz
Midterm Exam
Final Exam

Percentage
40%
5%
20%
35%

Dates
weekly
Friday 24 Sept., proctored in-class or at a testing center
Friday 15 Oct., proctored in-class or at a testing center
Friday 10 Dec., 10:15am-12:15pm, proctored in-class or at a testing center

Grade Determination

Based on your raw score total using the above percentages, I will assign grades according to the following ranges:

90 - 100 % = A, 79 - 89 % = B, 68 - 78 % = C, 57 - 67 % = D, 0 - 56 % = F.

These ranges are a guarantee, a lower bound. I reserve the right to increase your grade above these ranges based on the actual difficulty of the work and/or on average class performance. Any such increases will preserve the ordering of students by weighted total score.

Policies:

The Dept of Mathematics and Statistics has reasonable policies on incompletes, late withdrawals, early final examinations, etc.; see www.uaf.edu/dms/policies. You are covered by the UAF Student Code of Conduct. UA is an AA/EO employer and educational institution and prohibits illegal discrimination against any individual: alaska.edu/nondiscrimination. I will work with the Office of Disabilities Services (208 WHIT, 474-5655) to provide reasonable accommodation to students with disabilities.

Student Protections Statement. UAF embraces and grows a culture of respect, diversity, inclusion, and caring. Students at this university are protected against sexual harassment and discrimination (Title IX). Faculty members are designated as responsible employees which means they are required to report sexual misconduct. For more information on your rights as a student and the resources available to you to resolve problems, please go to the following site: catalog.uaf.edu/academics-regulations/students-rights-responsibilities.

COVID-19 Statement. Students should keep up-to-date on the university's policies, practices, and mandates related to COVID-19 by regularly checking this website: sites.google.com/alaska.edu/coronavirus/uaf Further, students are expected to adhere to the university's policies, practices, and mandates and are subject to disciplinary actions if they do not comply.