Prerequisites:
No official prerequisites.
We use throughout the semester Taylor expansions, McLaurin series, and some
basic programming in Matlab. If your knowledge on these topics is rusty,
it's a good idea to review these before we need them.
Email:
Use your university email account to email me
pwappero@vt.edu
and for a timely response,
include `Math 5474' in the subject line.
Office Hours:
Tuesday 10:00-11:30am, Wednesday 1:00-2:30pm, or by appointment (send an email with 3 available timeslots)
Try to resolve minor issues at the end of class or by email (scan a pdf
of your work and indicate where you experience problems).
Come prepared to office hours:
Completely and carefully read all relevant assignment instructions and
associated notes and textbook sections.
Try to work out as much of the relevant assignment as possible.
Class Meeting Time :
Monday, Wednesday 4:00-5.15pm, McBryde 226
Special needs:
Virginia Tech welcomes students with disabilities into the University's
educational programs. The University promotes efforts to provide equal
access and a culture of inclusion without altering the essential elements
of coursework. If you anticipate or experience academic barriers that may
be due to disability, including but not limited to, chronic medical
conditions, deaf or hard of hearing, learning disability, mental health,
or vision impairment, please contact the Services for Students with
Disabilities (SSD) (540-231-3788, ssd@vt.edu,
or visit
www.ssd.vt.edu).
If you have an SSD accommodation letter, please make an appointment or
meet with me during office hours as early in the semester as
possible to discuss implementing your accommodations. You must give me
reasonable notice to implement your accommodations, which is generally
5 business days and 10 business days for final exams.
Text:
Finite difference schemes and partial differential equations (2nd Ed.) by
J. C. Strikwerda, Publisher: SIAM, ISBN: 0-89871-567-9.
Important:
If you buy the book through SIAM, there is a discount for SIAM members.
As a Virginia Tech graduate student, you should be able to join SIAM for
free.
Just follow the directions at:
How to join SIAM.
To buy the book from SIAM:
Text.
Course contents:
Math 5474 is a general introduction to the finite difference method.
The course is suitable and useful for mathematics, computer science,
and engineering students.
We discuss several common finite difference methods that are used
for partial differential equations in scientific and engineering applications.
The course provides a rigorous understanding of the mathematical concepts.
These are used to analyze finite difference methods and to understand the
differences between the various finite difference methods.
The mathematical tools will be demonstrated with computer simulations
to better understand the mathematical concepts and recognize them
in computer simulations.
We also discuss (briefly) the programming of finite difference methods
and efficient computational methods.
We will cover most of chapters 1-8 and 12 of the textbook.
Grading:
The numerative grade will be based upon
- Midterm test: 1/3 of final grade
- Final project: 1/3 of final grade
- Homeworks: 1/3 of final grade
All graded work counts. No scores are dropped.
The course grade will be assigned as follows:
90 guarantees an A (not an A-)
80 guarantees at least a B (not a B-)
70 guarantees at least a C (not a C-)
60 guarantees at least a D (not a D-)
+ and - grades will be given as well.
Homework policy:
Homework problems and due dates for homeworks will be posted on
my course website
.
The lowest score on your HW assignments will be dropped. Thus if there are
11 HWs, the best 10 count towards your grade.
For the homweworks, only selected problems will be graded
(partial credit). These problems will not be known
to students in advance.
Except for problems selected for grading, homework
will not be marked.
Important:
Submitted work should not only give the correct answer but also clearly
delineate the logic justifying the answer.
No credit should be expected for correct
answers if no work is shown.
Submission:
A hard copy needs to be submitted by the announced deadline. If you
have an emergency, like illness or travel, email a temporary electronic copy
(a pdf file, no links) to show you did the work in time. Then hand in
the hard copy when you return.
Late homework:
Homework that is handed in late is subject to a penalty (20 %) if it is
submitted by the beginning of the next class.
Homework given after the beginning of the next class will be given a zero.
To avoid a penalty or zero grade for a late homework
you must show convincing evidence/documentation that you had no alternative
(since homework problems are known well in advance, only a valid reason for
an absence of several days will be accepted as an excuse).
If you have a valid reason, I may allow you to hand
in homework late without any penalty or I may not count the particular
homework.
-
Allowed help on homeworks:
- Students may consult the textbook and class notes for homework.
-
Students may discuss homework assignments with other students, your
5474 instructor, and get help from
Tutoring Services.
-
Unallowed help on homeworks:
-
Copying a solution to a problem or a numerical code
from books, internet, or any other source is prohibited.
-
Using another person's solutions to the homework when writing up
an assignment is prohibited.
In writing up an assignment to be handed in, every student needs to work alone
(without other persons or other persons' papers). By handing in the homeworks,
a student certifies that what is written
accurately represents the student's own
understanding of the material expressed in the student's own words.
Test policy:
-
Format:
Test problems are in the style of the
homeworks and material discussed in class (theory and examples),
and are graded with partial credit.
Tests are closed book and closed notes.
Consultation, calculators, and other electronic devices are not permitted
on the test.
-
Missed tests:
If a test can not be taken as scheduled,
this should be communicated to your instructor as early as possible.
If a test can not be taken as scheduled, this should be communicated
to your instructor as early as possible.
Documentation from an appropriate
university office that shows that you had a reason that is serious,
unavoidable, and beyond your control, will be accepted.
If you miss the test for a valid reason, a make up test will be given during
the exam period. Otherwise, your case will be handled
on an individual basis.
-
Solutions to test problems
will be posted after the test.
IMPORTANT: Test and test solutions are intended only for use by
students enrolled in this crn this semester. Without the teacher's written
permission, no one may show, give, or otherwise make such class materials
available to anyone not enrolled in this crn this semester. Prohibited
activities include, but are not limited to, uploading a test or solutions
to problems and submitting such materials for online posting. The
prohibition on sharing solutions applies to all solutions, regardless of
who wrote the solutions.
Honor System:
The Virginia Tech Honor System applies to all graded work in this course.
The inclusion in an assignment of work (from any source)
done by someone whose name does not appear on the assignment or the
inclusion of the reproduction (by any means) of such work is a violation
of the Honor Code unless this inclusion is used in a way explicitly
authorized by the instructor.
If you have any questions about how the honor code applies to a particular
situation, it is your responsibility to ask. The Undergraduate Honor Code
pledge that each member of the university community agrees to abide by
states: `As a Hokie, I will conduct myself with honor and integrity at all
times. I will not lie, cheat, or steal, nor will I accept the actions of
those who do.'
Students enrolled in this course are responsible for abiding by the Honor
Code. A student who has doubts about how the Honor Code applies to any
assignment is responsible for obtaining specific guidance from the course
instructor before submitting the assignment for evaluation.
Students are strongly discouraged from misusing sites such as Chegg and
CourseHero, as well as misusing ChatGPT and other Generative Artificial
Intelligence. Students are strongly encouraged to consult their faculty
members regarding the use of such outside materials as the
misuse of these sources may constitute a violation of the Honor Code.
Ignorance of the rules does not exclude any member of the University
community from the requirements and expectations of the Honor Code
For additional information about the Graduate Honor Code, please visit:
Virginia Tech Graduate Honor System
Information
Attendance:
Although attendance does not count toward your grade, you are
responsible for any material and announcement that you miss in class.
If you miss a class, please copy the notes
from another student in class.
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Course Policy Sheet for Math
5474 ( #87274 )