Math 310 Numerical Analysis

FALL 2017, UAF

bueler.github.io/M310F17

Instructor: Ed Bueler
Office: Chapman 301C.
bueler.github.io/OffHrs.htm
eMail: elbueler@alaska.edu

Times & Room: TTh 11:30 am -- 1:00 pm Reichardt 202
CRN: 74134
Text: J. F. Epperson, An Introduction to Numerical Methods and Analysis 2nd ed., Wiley 2013

Course Topics and Content:

This course will introduce you to numerical methods and their analysis. You'll learn methods for solving problems of applied mathematics by using computers, and how well those methods work. The problems come from calculus, linear algebra, and differential equations. Specific topics include solving single nonlinear equations (root-finding), interpolation with polynomials and piecewise functions, numerical integration (quadrature), solving differential equations, and solution of linear systems of equations. The main purpose of all this is pretty simple: use computers to solve problems you cannot do by hand.

We will not be satisfied with generating pretty pictures. Instead, we care whether our numbers correctly-approximate the exact answer, even in cases where we never know it. Abstract and precise thought, that is, actual mathematics, is essential for showing that our approximations are correct, and, just as importantly, when making choices among numerical methods.

You will be expected to understand both the theory and practice of numerical methods. Both will be covered in lecture and every homework assignment. Exercises will ask you to explain a concept, demonstrate an idea by a short hand calculation, use inequalities to bound the size of some quantity, or write running programs. In some exercises you will be asked to "show" or "prove" precisely-stated facts (propositions). While formal proof style is not important, but you will need to give clear and sufficiently-general logical arguments.

On the homework you will be expected to turn numerical algorithms into functioning programs using the mathematical programming language Matlab, its free equivalent Octave, or the free alternative Python. (See the separate "Comparison" document. From now on I simply refer to these languages as "Matlab".) You will turn-in both the code you wrote and its outputs. Programs, and use of Matlab as a supercalculator, will be part of every assignment over the semester.

Getting the most out of both the lectures and homework is your responsibility, though I must make them worth your time. You should ask questions in class, both about the lecture content and the homework assignments.

Goals and Outcomes:

At the end of the course you will be able to evaluate and use numerical tools for solving many scientific and engineering problems. You will be able to code some of the basic methods (i.e. for prototyping more serious solutions), and you will have the mathematical start needed for learning numerical approaches to new problems like optimization and partial differential equations. Student competence with actual scientific computing is a goal of the course: You will be comfortable using Matlab as a "supercalculator" and as a programming language.

How Your Grade is Determined:

Weekly homework forms 50% of your score for the class. Homework assignments, and their due dates, will be regularly posted at the Course Website bueler.github.io/M310F17/. The site also has a daily schedule of topics which will be updated on an ongoing basis to reflect what topics were actually covered each day.

There will be one in-class Midterm Exam, covering basic concepts and definitions, and an in-class Final Exam. In summary:

Work
Homework
Midterm Exam
Final Exam

Percent of Grade
50%
20%
30%

Dates
weekly
in-class Tuesday 24 October
in-class Tuesday 12 December, 10:15 am -- 12:15 pm

Based on your raw (homework, project, and exams) total, I guarantee grades according to the following schedule:

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

This schedule is a lower-bound guarantee. That is, I reserve the right to increase your grade above this schedule based on the actual difficulty of the work and/or upon average class performance.

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. I will work with the Office of Disabilities Services (208 WHIT, 474-5655) to provide reasonable accommodation to student with disabilities.

Prerequisites:

Officially: MATH F302 Differential Equations or MATH F314 Linear Algebra or permission of instructor.

The idea of the prerequisites is that you will have completed the calculus sequence (MATH 251-253) plus a bit more. Both differential equations and linear algebra topics do occur in MATH 310, but this course depends very little on previous course exposure; basic ideas are introduced as needed.

However, some prior exposure to programming is useful, even though Matlab is introduced from the beginning.

Students come to this class from math, computer science, physics, geophysics, engineering, and indeed from any of the technical subjects at UAF. I am aware of this fact! I will devote substantial class time, especially at the beginning of the semester, to collecting together bits of needed prequisite knowledge. However, you must show initiative in recalling prerequisite knowledge in a meaningful and timely way, especially when I point out directly when and where it is needed.