syllabus-math-420-spring-2021.tex

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\begin{center}
    \textbf{Numerical Analysis}  \\
    {MATH 420--01, Spring \ay} \\
\end{center}

\vskip0.25in
\normalsize

\begin{center}
%\begin{minipage}{5.0in}
\begin{description}
    \item[Instructor:] Dr.\  Willis, Professor of Mathematics
    \item[Office:]  Discovery Hall, Room 368
    \item[Telephone:] 308 865-8868
   \item[Email:] willisb@unk.edu
   \item[Office Hours:] Monday, Wednesday, and  Friday, \mbox{10:00--11:00}; Tuesday and Thursday 9:30 -- 11:00; Monday and Wednesday 13:25 -- 15:00;  and by appointment.  My office hours are  \emph{remote only}.  The Zoom 
Meeting ID: 616 568 5706 
\end{description}
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\noindent Teaching during a pandemic is something that I some experience with, but it's still  an experiment.  We are mathematicians, so we are problem solvers. All of us will need to learn new skills and to find solutions to problems as they arise.  I doubt that we can plan for everything that might happen, but we can plan to be flexible and to be creative problem solvers.  At anytime in the term, if you have a suggestion or a concern, please let me know--I will consider your suggestion.

If I need to quarantine or if I am ill,  I will continue teaching our course online for as long as I am able. If you are unable to attend class, uncomfortable attending class,  or need to quarantine, you will be able to continue with the class. Having said that,  attending class in person, taking notes, following along,  and participating  in class discussions is the most effective way to learn mathematics. If you choose to not attend class,  learning might be a challenge and you might need to  require new skills (self-discipline and time management, for example), but there is \emph{no specific grade penalty} for not attending or not participating in class. Of course, if do not make a good effort to keep up with the course work (either live classes or recorded),  do not expect me to invest much time in helping you dig out of the hole you have dug.



If you choose to attend class remotely, I'll do what I can to make your experience as close to in-person as I can, but I cannot guarantee that the learning experience will be as good as attending in-person.
Generally, the recorded mathematics classes that I have viewed (MIT OpenCourseWare, for example) have a camera operator. We don't  have that luxury, making the remote classes harder to follow than the face-to-face classes.


This class might convert to remote learning, either permanently or temporarily,  for any number of reasons, including  an administrative decision (university-wide, college, or departmental), low-attendance due to  large numbers of class members who need to quarantine, or my own decision based on the safety of the class. The decision to convert to remote learning might be announced long before it happens, or it might happen without much warning. It's prudent, I think, for all class members to be prepared for this class, and possibly all classes, to be converted to remote learning. 

Regardless of how this class is taught, either face-to-face or remotely, our assessments (in-class work, online homework, semester exams, and final exam) will be the same. Also, the grading scale for assigning course grades will also be the same regardless of how this class is delivered.  And the course material will also be the same if the class switches to remote learning for part of the term.  Given that the \emph{assessments, topics}, and \emph{grading scales} will be the same regardless of delivery, our class will have \emph{one syllabus}, not multiple documents that attempt to cover all possibilities. Having a unified syllabus will, I think, help promote clarity.

Finally, please live your lives for the next fifteen weeks responsibly.  When you act recklessly with your health, you are jeopardizing the health of your classmates, friends, and family. The scientific evidence is that we all can help to squash the pandemic by acting responsibly to protect our own health and the health of others.  It would be, I think, a good semester to build or strengthen hobbies--I might suggest reading, creative writing, or learning to play the guitar solo in the dorm stairwell at 2 am.  And of course, it will be a good semester to put an extra effort into keeping up with your classwork, especially this class.


\subsubsection*{Course Objectives}

 Students will learn the properties of IEEE numbers and IEEE arithmetic; students will learn how to analyze algorithms for time complexity, numerical stability,  and accuracy; students will learn numerical methods
for interpolation;  students will learn the methods for numerical integration;  and students will learn methods for solving linear equations, nonlinear equations, and differential equations. Additionally, students will learn to 
use the Julia programming language.

\subsubsection*{Prerequisite}

To be in this class, you must have already earned a passing grade in Calculus II (UNK's MATH 202).\footnote{The catalog gives the prerequisite as MATH 260--eventually this will change to MATH 202.}

\subsubsection*{Course Resources}

\begin{enumerate}

\item Our primary textbook is \emph{First Semester in Numerical Analysis with Julia,} by Giray Ökten.  This is an open-source textbook that can be legally downloaded, printed, and  used without payment.\footnote{\tiny \url{https://open.umn.edu/opentextbooks/textbooks/first-semester-in-numerical-analysis-with-julia}.  \normalsize} For topics not covered in our textbook, we'll use class notes and other freely available resources.

\item Our secondary textbook is \emph{Tea Time Numerical Analysis,} by Leon Q. Brin.\footnote{ \tiny \url{http://lqbrin.github.io/tea-time-numerical/contents.html} \normalsize}

\item Class notes that are written on the board or distributed via Canvas.


\item Reliable Internet access.

\item  An Internet connected computer (not just a phone or tablet) that can run Zoom and  the Juila Language.  Both are free resources; download and install Julia it from \url{https://julialang.org/downloads/}.  I suggest that you install version 1.5.3.

\item If we need to convert this class to remote learning, your computer will need to have a microphone and a camera. For remote office hours, it can be useful to have a separate camera that can be pointed toward a well-lit writing surface.


\item Pencils, erasers, notebook for note taking. Colored pens or pencils are nice for note taking.


 \end{enumerate}





\subsubsection*{Grading}

Your course grade will be based on three in class examinations, weekly homework assignments, and a comprehensive final examination. Each
examination will be scaled to 100 points and the final examination will be scaled to 150 points.  The points available on each homework
assignment will vary.  Your course average will be determined on the percent of the available points.

Course grades will be based on a ten point scale; grades in the lower third of each decade will be a minus grade and grades in the
upper third of each decade will be a plus grade. For example, a course average of \(86.7\) will earn you a course grade of B+; a course average
of \(86.\overline{6}\) will earn you a course grade of B.

\subsubsection* {Policies}


\begin{enumerate}

\item All work you turn in for a grade must be your own.  If you need assistance in completing a homework assignment, you may ask me for help but nobody else. Googling for
answers, seeking help from the Learning Commons or other faculty members,  or using solution keys from previous terms (either from UNK or other universities) is also prohibited.  Each homework assignment you turn in for a grade must include the statement:

\begin{quote}
\fbox{``I have neither given nor received unauthorized assistance on this assignment.''}
\end{quote}
Using unauthorized materials while taking a test will earn you a failing course grade. Each exam will specify what resources are allowed. 

 \item The final examination will be \emph{comprehensive}. It will be given on Wednesday 5 May from 8:00 am to 10:00 am.


 \item Generally, weekly problem sets are due at 11:59 pm local time each Saturday. If you have an extended illness that keeps you from completing the homework, contact me immediately. Since homework is turned in electronically, requests to 
turn in homework late (due to minor illness or absences) will generally be declined.


\item The course calendar may change. Changes to the schedule can be made in class, but not noted anywhere else. It is your responsibility to
learn of changes to the schedule.



\item If you have questions about how your work has been graded,  \emph{immediately}  ask me for an explanation.

\item This class has \emph{no option for extra credit.}


\item  For pedagogical reasons, our class notes will sometimes differ in notation, style, and level of abstraction from the textbook.


\end{enumerate}




\subsubsection*{Students with Disabilities or Those Who are Pregnant}

It is the policy of the University of Nebraska at Kearney to provide flexible and individualized reasonable accommodation to students with documented disabilities. To receive accommodation services for a disability, students must be registered with UNK Disabilities Services for Students Office, 172 Memorial Student Affairs Building, 308-865-8988 or by email unkdso@unk.edu


It is the policy of the University of Nebraska at Kearney to provide flexible and individualized reasonable accommodation to students who are pregnant. To receive accommodation services due to pregnancy, students must contact Cindy Ference in Student Health, 308-865-8219. The following link provides information for students and faculty regarding pregnancy rights:  \small \url{ http://www.nwlc.org/resource/pregnant-and-parenting-students-rights-faqs-college-and-graduate-students} \normalsize 

\subsubsection*{Reporting Student Sexual Harassment, Sexual Violence or Sexual Assault}


Reporting allegations of rape, domestic violence, dating violence, sexual assault, sexual harassment, and stalking enables the University to promptly provide support to the impacted student(s), and to take appropriate action to prevent a recurrence of such sexual misconduct and protect the campus community. Confidentiality will be respected to the greatest degree possible. Any student who believes she or he may be the victim of sexual misconduct is encouraged to report to one or more of the following resources:

\begin{enumerate}

\item Local Domestic Violence, Sexual Assault Advocacy Agency 308-237-2599

\item Campus Police (or Security) 308-865-8911

\item Title IX Coordinator 308-865-8655

Retaliation against the student making the report, whether by students or University employees, will not be tolerated.

\end{enumerate}














\newpage

\subsubsection*{Course Calendar}

We will try to adhere to the following schedule, but we will modify it
if needed. The exam dates will only be changed for a compelling
reason; we won't delay an exam because we are behind the
schedule. Neither will an exam date be moved forward because we are
ahead of the schedule.

Section numbers for Chapter 6 are from \emph{Tea Time Numerical Analysis.}  

Homework assignments are due at 23:59 local time on Saturday on the week they are assigned. Homework assignments 1 and 2 are due on Saturday 6 February \the\year, for example.

\vspace{0.1in}

\begin{center}

\begin{tabular}  {|l|l|l|l|}
\hline
{\bf Week}  & {\bf Week} &  {\bf Section(s)} & {\bf Topic(s)} \\
\hline \hline 
\wk    & 1/25 &    \S1.2   &   Introduction to Julia   \hfill \\
\wk    & 2/1 & \S1.1      &  Floating point numbers \& calculus tools   \hfill \textbf{HW  \qz,  HW \qz} \\
\wk    & 2/8 &    \S2.1 & Errors and convergence rates    \hfill \textbf{HW  \qz} \\
\wk    & 2/15  & \S2.2 -- \S2.7 &  Root Finding   \hfill  \textbf{HW \qz} \\
\wk    & 2/22 &  \S2.2--\S2.7   &  Root Finding    \hfill \textbf{\ex\-\-, 26 February},  \textbf{HW  \qz  }   \\
\wk    & 3/1    &  &  Linear equations  \hfill  \textbf{HW  \qz }  \\
\wk    & 3/8     & \S3.1--\S3.4 & Interpolation \hfill \textbf{ HW  \qz }   \\
\wk   & 3/15   & \S3.1 -- \S3.4   &   Interpolation   \hfill \textbf{ HW  \qz} \\
\wk  &  3/22    & \S4.1--\S4.2 &  Numerical  integration  \hfill \textbf{HW  \qz}     \hfill \\
\wk &  3/29     &   \S4.3 --\S4.4 &   Gaussian integration \& multiple integrals    \hfill \textbf{\ex\-\-, 2 April},  \textbf{HW  \qz  }  \\
\wk  & 4/5 &   \S5.1--\S5.2 & Discrete \& continuous least squares  \hfill \textbf{HW    \qz} \\
\wk   & 4/12  & \S5.3 &  Orthogonal polynomials and least squares  \hfill \textbf{HW \qz}   \\
\wk   & 4/19   & \S6.1--\S6.2   & Differential equations \hfill  \textbf{ \ex, 23 April},  \textbf{HW  \qz  }     \\
\wk   & 4/26   &  \S6.3   & Differential equations   \hfill \textbf{ HW \qz  } \\
\wk   & 5/       &  &   \textbf{Final Exam, Wednesday 5 May, 8:00 am--10:00 am} \\ \hline
\end{tabular}
\end{center}




\end{document}

\vspace{0.1in}

\begin{center}

\begin{tabular}  {|l|r|l|l|}
\hline
{\bf Week}  & {\bf Week of} & {\bf Month}&  {\bf Topic(s)} \\
\hline \hline
\wk    & 12 & Jan  & algorithms and an introduction to Maxima (classnotes) \\\
\wk    & 19 &     &  IEEE arithmetic and the condition number (Chapter 0) \\
3    & 26 &     & interval arithmetic and running errors (classnotes) \\
4    & \phantom{1}2 & Feb   &  solving equations, Chapter 1 \\
5    & 9  &  & solving equations, Chapter 1; \textbf{Exam 1, 13 Feb.} \\
6    & 16 & & numerical linear algebra, Chapter 2 \\
7    & 23 &  & numerical linear algebra, Chapter 2 \\
8    & \phantom{1}2 & Mar  & interpolation and least squares, Chapters 3 and 4 \\
9    & 9 &    & numerical differentiation and integration, Chapter 5; \textbf{Exam 2, 13 March} \\
10    & 23 &      & numerical differentiation and integration, Chapter 5 \\
11   & 30 &     & initial value problems, Chapter 6 \\
12   & 6  & April   &   initial value problems, Chapter 6 \\  
13   & 13 &        & partial differential equations, Chapter 8 \\
14   & 20 &     & partial differential equations, Chapter 8; \textbf{Exam 3, 24 April} \\
15   & 27 &     & Fourier series  (classnotes) \\ \hline
     &      &     & \textbf{Final Exam, Wednesday 6 May, 10:30--12:30} \\ \hline
\end{tabular}
\end{center}


\end{document}

\begin{tabular}  {|l|l|l|l|}
\hline
{\bf Week}  & {\bf Week of} & {\bf Month}&  {\bf Topic(s)} \\
\hline \hline
1    & \phantom{1}9 &Jan  & Introduction \\
2    & 16 &   & Floating point numbers \\
3    & 23 &  & Condition number \& relative difference \\
4    & 30 &  & Floating point arithmetic \\
5    & \phantom{1}6 &Feb & Sums \& hypergeometic functions; \textbf{Exam 1, Friday, 11 Feb.} \\
6    & 13 &    & Linear algebra \\
7    & 20 &     & Matrix norms and condition numbers \\
8    & 27 &     & LU factorization \\
9    & \phantom{1}6 & Mar      & Eigenvalues \\
10   & 20 &    & Least squares; \textbf{Exam 2, Friday, 25 March} \\
11   &   27   &  & Interpolation \& approximation \\
12   &   \phantom{1}3 & April   & Nonlinear equations \\
13   &   10 &     &  Numerical Integration \\
14   &   17 &     & Finite differences; \textbf{Exam 3, Friday, 22 April} \\
15   &   24 &     & Partial Differential Equations \\ \hline
     &      &     & \textbf{Final Exam, Wednesday, 3 May, 8:00--10:00} \\ \hline
\end{tabular}

3    & 24  & \S2.3---\S2.4  & Norms and condition numbers \\
4    & 31  & \S3.1---\S3.3  & Least squares \\
5    & 7 Feb & \S4.1           & Eigenvalues; {\bf Exam 1, Friday, 10 Feb}\\ \hline
6    & 14 Feb & \S4.2           & Eigenvalues  \\
7    & 21 & \S5.1---\S5.2  & Nonlinear equations \\
8    & 28  & \S7.1---\S7.2  & Interpolation \& Approximation \\
9    & 7 Mar  & \S8.1---\S8.3    & Numerical integration; {\bf Exam 2, Friday, 24 March}\\
\hline
10   & 21 Mar & \S8.4           & Adaptive Integration \\
11   & 28 & \S8.7, \S9.1---\S9.2  & Finite Differences and Initial Value Problems \\
12   & 4 Apr & \S9.3---\S9.4  & Differential Equations  \\
13   & 11  & \S11.1---\S11.2 & Partial Differential Equations \\
14   & 18   & \S11.2  &   Partial Differential Equations; {\bf Exam 3, Friday. 21 April} \\
15   &  & \S12.1---\S12.3  & Fast Fourier Transform \\ \hline
16    &  & \S1.1---\S12.3    &  {\bf Final Exam Wednesday 3 May 8:00--10:00}  \\
\hline
\end{tabular}
\end{center}
\end{document}


   1.  Scientific Computing
   2. Systems of Linear Equations
   3. Linear Least Squares
   4. Eigenvalue Problems
   5. Nonlinear Equations
   6. Optimization
   7. Interpolation
   8. Numerical Integration and Differentiation
   9. Initial Value Problems for Ordinary Differential Equations
  10. Boundary Value Problems for Ordinary Differential Equations
  11. Partial Differential Equations
  12. Fast Fourier Transform
  13. Random Numbers and Stochastic Simulation 










\begin{center}

\begin{tabular}  {|l|l|l|l|}
\hline
{\bf Week}  & {\bf Week of} & {\bf Month}&  {\bf Topic(s)} \\
\hline \hline
1    & 14 & Jan  & Floating point numbers, Chapter 0 \\
2    & 21 &     & The condition number \& IEEE arithmetic, classnotes \\
3    & 28 &     & Running errors \& IEEE arithmetic, classnotes \\
4    & \phantom{1}4 & Feb   &  Solving equations, Chapter 1 \\
5    & 11  &  & Solving equations, Chapter 1; \textbf{Exam 1, 15 Feb.} \\
6    & 18 & & Numerical linear algebra, Chapter 2 \\
7    & 25 &  & Numerical linear algebra, Chapter 2 \\
8    & \phantom{1}3 & Mar  & Interpolation and least squares, Chapters 3 and 4 \\
9    & 10 &    & Numerical differentiation and integration, Chapter 5 \\
10    & 24 &      & Numerical differentiation and integration, Chapter 5;   \textbf{Exam 2, 28 March} \\
11   & 31 &     & Initial value problems, Chapter 6 \\
12   & \phantom{1}7  & April  &   Initial value problems, Chapter 6 \\  
13   & 14 &       & Partial differential equations, Chapter 8 \\
14   & 21 &     & Partial differential equations, Chapter 8; \textbf{Exam 3, 25 April} \\
15   & 28 &     & Fourier series, classnotes \\ \hline
     &      &     & \textbf{Final Exam, Wednesday 6 May, 10:30--12:30} \\ \hline
\end{tabular}
\end{center}








\end{document}

\subsubsection*{Prerequisites }

A three semester calculus sequence should provide you with
the background needed for this class.  If you are uncertain
if you are ready for this class, please speak with me.

\subsubsection*{Grading }

Your course grade will be based on three examinations,
homework assignments, and a comprehensive final
examination.  The grading weights are

\vspace{0.1in}

\fbox{
\begin{minipage}{4.0in}
   Homework assignments \dotfill 35\% total \\
   Three examinations \dotfill 15\% each \\
   Final examination \dotfill 20\%  \phantom{each}
\end{minipage}
}

\vspace{0.1in}

\noindent Your home work grade will be based on the percent of the total available
points.


\subsubsection*{Homework}

Throughout the term you will be given problems that are to
be turned in for a grade.  The work you turn in
is expected to be {\em accurate, complete, concise, neat,}
and {\em well-organized.} The major steps of your
calculations should be explained using English sentences.
Homework assignments are due promptly at the start of class
the day they are due. {\em Late homework will not be
accepted.}

{\em Unless otherwise specified, all homework is to be
completed on your own.} If you are found in violation of
this policy, you will receive a zero on that
assignment.  If you are struggling with a homework  assignment, please ask
me for assistance. For everyone's benefit, I request
that you  ask me questions about assignments days, not hours, before it is due.

\subsubsection*{ Examinations}

Your three examinations and the final examination will
be in class and will be closed book and notes.  The
examinations are scheduled for {\em Friday 15 February},
{\em Friday 29 March}, and  {\em Friday 19 April}.
The final examination will be {\em Wednesday 8 May}
from 13:00--15:00.

\subsubsection*{Policies}

Regular class attendance and class participation are
required.  Please arrive to class on time. If have more than
five unexcused absences, your course grade will be reduced by
at least one half a letter grade.

If a exam conflicts with an official university sponsored
event, you will be allowed to take the exam early
provided you make arrangements at least four days before
the test.  Permission to take a test early for other
reasons will be given at my discretion.

If you are ill and are not able to take a test, you must call
or email me {\em before the test.} You will not be
allowed to take a test after I have returned the
test to the class.  Since I almost always return tests
the following class day, it is imperative that you make
arrangements will me without delay.

The final examination will be comprehensive.  It will be
given at the time determined by the University schedule.
(XXXX {\sc p.m.}) Except for extraordinary circumstances,
requests for taking the final examination at a different
time will not be granted.  All such requests must be made
before travel plans are made.

If your course average is $x$, your final grade
will be assigned according the function

\[ \mbox{grade}(x) =
  \left\{ \begin{array}{ll}

         F, & x \leq 60  \\

         D, &   60 < x \leq 65 \\

         D+, &  65 < x \leq 70 \\

         C,  &  70 < x \leq 75 \\

         C+, &  75 < x \leq 80 \\

         B,  &  80 < x \leq 86 \\

         B+, &  86 < x \leq 93 \\

         A,  &  93 < x

     \end{array}
    \right.
\]



Incomplete grades will be assigned according to University and
Departmental policies.



\subsubsection*{Office Hours and Getting in Touch with Me}



My office hours are listed on my office door and on this
syllabus.  You can also make an appointment for a specific
time to see me.  Additionally, anytime that I am in my
office, I will be glad to help you unless I am terribly
pressed for time.



\newpage



\subsubsection*{Course Calendar}



We will try to adhere to the following schedule, but we

will modify it if needed.



\vspace{0.1in}

\begin{center}



\begin{tabular}  {|l|l|l|}

\hline

Week  & Section(s) &  Topic(s) \\

\hline \hline

1     & \S1.1 -- 1.3  & Floating point numbers \\

2     & \S2.1 -- 2.2  & Linear equations \\

3     & \S2.3 -- 2.4  & Norms and condition

numbers \\

4     & \S3.1 -- 3.3  & Least squares \\

5     & \S4.1        & Eigenvalues  \\ \hline

6     & \S4.2        & Eigenvalues and first exam, Monday

16 Feb \\

7     & \S5.1        & Nonlinear equations \\

8     & \S5.2        & Nonlinear equations \\

9     & \S7.1        & Interpolation \\

10    & \S7.2        & Interpolation   \\ \hline

11    & \S8.1 -- 8.2  & Numerical integration and second exam,

Monday 30 March \\

12    & \S8.3 -- 8.4  & Adaptive and Gaussian Quadrature \\

13    & \S8.7, 9.1   & Finite differences and Differential

Equations \\

14   &  \S9.2 -- 9.4  & Differential Equations \\

15   &  \S12.1 -- 12.3  & Fast Fourier Transform, third

exam due Wednesday 6 May \\ \hline

     & \S1.1 -- 12.3    &  Final exam XXXXX  \\

\hline

\end{tabular}

\end{center}



\end{document}