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Time
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1:30 -- 2:20 PM on MWF
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Location
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ROOM 130 Lockett Hall. (This is a change from the room listed originally.)
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Calendar
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Our class meets starting Monday, August 25, 2025. The Final Exam will be Mon., Dec. 8, at 10AM - Noon.
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Leonard
Richardson
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Office 386 Lockett
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Office Hours
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- MWF 12:30 AM -- 1:20 PM in person in my office, 386 Lockett Hall.
- TTh online only, at this Zoom link: https://lsu.zoom.us/j/7111204773. Email me if you would like me to arrange a time for you on Tuesday or Thursday online.
I am available at many other times. Email first to make sure I'm able meet with you. I answer email many times daily---usually quickly.
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Office phone
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578--1568
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E-Mail
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rich@math.lsu.edu Email me for a quick response.
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WebAssign and Text Book
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Each student needs to click the WebAssign
link and self-register for Math 4038, section 1, with
Instructor Leonard Richardson, and the following class
key:
lsu18758839 When you register for WebAssign, which should be done on the first day of classes, please be sure to use your family name and given name in the same way that LSU has your name in Records and Registration. This is to make sure you get the correct credit for your homework. That is, the students' names must be alphabetized the same way LSU has it on class lists.
Webassign allows you to use Webassign for 14 days after registration before paying Webassign's fee. However, the textbook can be purchased either with or without
WebAssign access included. If you buy the book without WebAssign,
you'll need to pay WebAssign a fee directly. If you buy the
book with WebAssign you'll have a code to use so that you can
show WebAssign that you have already paid their fee.
The publisher has the following package deal for LSU
students in Math 4038: The ISBN for the special package
– 9781284273960 ADVANCED ENGINEERING MATHEMATICS
7th Edition, by Dennis G. Zill, and published by Jones and Bartlett. This ISBN package price includes the new printed book, the student solutions manual, and WebAssign for a custom price.
The campus bookstore should have the package deal available, or you can contact Customer Service at the Publisher to purchase the package deal, if it is your choice. The publisher charges less for the special ISBN package than the LSU Bookstore charges. Use this link to buy the special package for just $174 from the publisher directly: http://www.jblearning.com/cart/Default.aspx?bc=27396-0&coupon=LSUFRESHIP. According to Webassign, You can also buy just Webassign Access by itself for a $70.95. Use this link for the latter purpose:
http://www.jblearning.com/cart/Default.aspx?bc=08232-6&coupon=LSUMATH25>.
Be sure you obtain Edition
7 of the correct text, and also remember that there will be a
charge for WebAssign if you need to buy it separately. Webassign has told me that their charge for Webassign is $70.95. So if you are looking for an optimal price and you have a good price on the printed book, remember that you will need to buy Webassign access separately for this price. But the special package deal should include an access code for you included in the package price, along with the book and the student solutions manual.
Webassign access includes the use of the online e-book version
of Zill's book, but only for the semester of this course. I
think it is better for you as an engineer to have the whole
book as a permanent reference on your own bookshelf, but that
is just my opinion. It is not required to have a solutions
manual, but I think that most students find this helpful. Just
remember that you need to learn to solve the problems without
the solutions manual or notes. CAUTION: If you buy a used book, you will probably need to pay WebAssign separately. If the book is used, then even if there is still an enclosed Webassign code, it is no longer valid if the first purchaser has already used it. Bookstores prefer to sell used books because they make a much higher profit margin on used books than they do with new books. So be aware when you buy. I recommend the package deal to you because, for our time, it is a good value, and it has not been increased in price for several years.
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Syllabus
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Chapter 5: Series solutions
of linear differential Equations. Bessel functions and
Legendre functions.
Chapter 12 -- 15: Fourier analysis, Sturm-Liouville
problems and orthogonal function series. Separation of
variables for partial differential equations with boundary
conditions and initial conditions.
This course is cross listed with Mechanical Engineering
4563, though it is being taught only by the Mathematics
Department. It is intended as a course that serves the needs of
incoming graduate students in engineering who did not have such
a course in preparation for graduate study, together with
undergraduate Engineering majors who are preparing for graduate
study. The most important goal of this course is to teach the
method of separation of variables in linear partial
differential equations, with applications to important
equations of classical physics such as the wave equation, the
heat equation, and Laplace's equation.
Many years ago, this course was preceded by a course in
ordinary differential equations that included Fourier analysis.
The latter course no longer exists, so it is important in Math
4038 to teach enough Fourier analysis for the treatment of
partial differential equations by separation of variables.
There are also important applications of this method requiring
more general orthogonal function expansions, such as
Fourier-Legendre and Fourier-Bessel series. However, most
students in this course have not studied the use of power
series to solve ordinary linear differential equations. For
Bessel functions, one needs also the Frobenius method (a
generalization of the power series method) for regular singular
points. Thus the syllabus is organized as follows, with
optional additional topics listed at the end:
Chapter 5, sections 5.1—5.3.2: Solution of ordinary
linear differential equations by the method of power series,
including the Frobenius method and its application to the
solution of Bessel’s equation.
Chapter 12, sections 12.1—12.6.2: Orthogonal
functions, Fourier series, Sturm-Liouville problems,
Fourier-Bessel and Fourier-Legendre series.
Chapter 13, sections 13.1—13.8: Introduction to
separation of variables, with application of the methods of
Fourier expansions to boundary value problems involving the
classical linear partial differential equations encountered
most in applications.
Chapter 14, sections 14.1—14.3: Boundary value
problems in other coordinate systems, making use of various
orthogonal function expansions.
Chapter 15, sections 15.3—15.4: Introduction to the
Fourier integral and Fourier transform.
Optional Additional Topics: Professors should feel free to
add or replace some topics with others of comparable value,
within the overall goals and purposes of this course. For
example, if ones students seem to need the theorems of vector
integral calculus, sections 9.12—9.16 may be appropriate,
and one could include applications such as the derivation of
the heat equation, for example. If there is time to teach the
Fourier transform on the real line, one could solve the heat
equation on the infinite line as another example.
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Prerequisites
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Math 2057, plus one of the following: Math 2065, 2070, or
2090, or the equivalent.
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Special Instructions during Public Health or Safety Emergencies
Your health and safety are our top priority. If you are feeling ill please contact the LSU Student Health Center for medical advice. If you are experiencing excessive stress, the Student Health Center offers mental health support as well. And please observe all the University's requirements and recommendations during emergency conditions.
We have learned from recent years that there can be unexpected changes due to the unpredictable nature of emergencies such as pandemics or extremes of weather, so that the format of the course and/or requirements may be forced to change, and if this is the case we will take care to ensure that every student is treated in a fair and considerate manner. If you have any special individual difficulty, please contact me quickly so that I can do anything possible to assist you. That said, we are looking forward to the fall semester and hoping that it will be smooth sailing.
Organization of this Class
Please understand that it is from the effort of working your
way through assigned problems on paper that you learn mathematics.
It is by no means sufficient to read solutions in a solutions
manual! Although I hope you benefit from seeing solutions
presented in class, you must not expect to learn how to solve
problems just from watching. You must work out problems yourself,
the hard way, in order to learn this work. Examination problems
will be very similar to assigned homework problems. Thus your
daily effort on homework problems will be strongly reflected in
your test grades. Problems will be assigned using Webassign and
they will be graded by computer. Your overall homework average
converted to a 100% basis at the end of the semester will replace
your lowest hour test grade if that is to your advantage. If you
do not understand how the computer software is grading your
homework, please see me or email me so I can check online.
Sometimes, albeit rarely, WebAssign is actually wrong. If you need to consult me because of a problem while using WebAssign, please email me directly at rich@math.lsu.edu. Do not use WebAssign's communication feature because it is very unreliable. I have access on WebAssign to your answers, so you do not need to email me a copy of your WebAssign answer that is causing difficulties.
Be sure to keep your written solutions to the homework problems in a notebook. Otherwise, when you review for a test or for the final exam, you won't have your work from which to study. All WebAssign retains is your answers--the work must be saved and maintained by yourself. This is obvious, but please be aware of it!
Tests
These will be closed book, in-class tests. I will provide paper and no notes or communication devices or internet may be used during a test. The
problems will be similar to those in the homework. However, note
that the homework is done online and graded by computer without
partial credit therefore. But tests will all be graded by me and
there will be partial credit, since the work is at least as
important as the answer. At the end of the course, you will have
the benefit of replacing your lowest hour test grade with your
homework average (converted to a 100-point scale), provided that
one of your hour tests is lower than your homework average.
If you miss a test, it is your responsibility
to speak to me as soon as possible to determine whether
or not your excuse is acceptable. Here is some General
Guidance regarding appropriate reasons for absence from a test
or examination. If you are in doubt, ask me as soon as possible.
In any case, your lowest hour test grade can be replaced by your
homework average, as explained in the homework description below.
Lateness and Classroom Conduct
Please try to arrive on time for class. But sometimes it may be
unavoidable to be late. If you are late, please come right into
class, doing so as quietly as you are able so as not to
disturb other students. I do not want you to wait outside in the
hall. You should have as much classroom time as possible, so
please just come in--quietly--and take a seat even if you are
late.
Class time is a time for work. So when class begins please put
away all cell phones, smart phones, head phones, wrist watch
communicators, tablets, laptops, etc, and turn your attention to
the work of the class. Thank you.
Grades
We plan to have three hour tests, worth 100 points each, and a
two hour final examination, worth 200 points. Your lowest
hour test grade will be replaced by your homework average on a
100% scale, if it is to your advantage. I will remark that for most students the homework average does turn out to be better than the lowest hour test grade. I will grade your
hour tests and return them to you the very next class meeting each
time. Your final test average will be the sum of all your test
grades divided by 5. So your final test average will be less than
or equal to 100. The minimum grade for each letter grade is as
follows:
A+, 97 A, 93 A-, 90 B+, 87 B, 83 B-, 80 C+, 77 C, 73 C-, 70 D+,
67 D, 63 D-, 60 F, below 60. You should save all your graded work
for future study and in case you think your final grade is in
error.
Unhappy with your grades in Math?
Click
here for a Six-Step Plan to improve your grades!
Remarks
It is especially important not to fall behind. It is very
important to attend class and participate in homework discussions.
Please do not assume you can take care of difficulties later---see
me for help as soon as possible if there is something you do not
understand!
You are responsible for all assigned problems---not just
those which we go over in class! This is a course in which many
students have studied the prerequisites at other universities or
several years ago. Please ask questions both in class and
after class when confused or unsure. It is not possible to
anticipate each student's difficulties so you need to bring them
to my attention. HOWEVER, there are businesses both locally and
online that sell their own instructional services to students
for fees. LSU does not authorize or approve any such
services and does not recognize their competence to serve
your educational interests. Advertising for any such commerical
service is prohibited in our classroom. If you see such
advertising being circulated in our classroom please report it
to me. And buyer beware!
Computer Support
The full power of Mathematica is available on many LSU
computers, including those in the Math Department's computer labs
and in the Library as well. Students can access Mathematica on
Tigerware through their MYLSU accounts. The DSolve command can
solve many differential equations. There is a simplified Web
Mathematica which is free to use online if you click on the
link in this sentence. If you have not already had the Math
Department's course in Mathematica, you might find it simpler to
figure out how to use the Web Mathematica. It is not as versatile,
but the Plot3D function is there and works fast for
surface graphs. There is also a function-integrator which
can be fun to use without having to learn very much about
Mathematica. But do remember, this is an auxiliary resource. The
time you spend working on problems on paper is the most important
part of homework when it comes to learning the subject. With that
understanding, Mathematica can be fun and helpful too.
Tests, Homework Assignments, and Downloads
Homework will be online using
WebAssign. It will be
graded on a scale of 1 point per problem or per part thereof for
multi-part problems, and recorded. Please do every assigned
problem on time! These assignments are not intended to be
done in only one night. At the end of the course,
you will have the benefit of replacing your lowest hour test grade
with your homework average (converted to a 100-point scale),
provided that one of your hour tests is lower than your homework
average. In Webassign, you will have 6 tries to submit an
answer for each question. However, after the first 3 tries,
Webassign will change the question, usually by modifying one or
more coefficients appearing in the question. Different students
will also receive different randomized versions of the same type
of problem. Please let me know if you have
difficulties using Webassign.
If you encounter what seems to be
an error or glitch in the WebAssign grading. Please come to my office or at least email me and show me if you
have doubts about the correctness of WebAssign's grading. With the
previous edition there were a few such errors that needed to
be corrected. The computerized grading seems to
be pretty good but it is not perfect. One needs to learn how to
enter symbolic answers so that they will be understood. Be
sure to reload this page from the website each time you visit,
since the table below will be updated as the semester proceeds!
The University has clear policies
requiring academic honesty. If you email me about a pending
assignment, I may send a hint to the whole class in answer to your
question, not giving your name of course! Above all, never copy another person's
written work as though it were your own. Remember that your own
good name is irreplaceable. This is a sound principle which will
serve you well throughout your life. Solutions that are copied
tend to be recognizable as not coming from the student, and even
the precise source can be identified frequently. This means that
the honorable course of action is also the practical one.
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Due at Classtime on this
Date
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Assignments must
be turned in on WebAssign
in order to receive credit! Please let me
know promptly at rich@math.lsu.edu if you are having difficulties with the online
assignment system or if you feel the system did not grade your
work correctly. Please note that I may extend the
deadlines for some homework assignments, based on how far we
progress in class. This is not something that can be predicted
precisely, so check regularly on WebAssign to make sure you
know the corrected due dates. You can instruct WebAssign to
email you automatically when a change has been made in an
assignment or an assignment schedule.
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August 25
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Read this syllabus so you can ask questions about it in
class. Obtain a copy of the text so that you are ready to
begin work. If you have been away from mathematics courses for
a few years, it may be necessary to review what you learned
during the first three semesters of calculus. Visit the
Webassign website and log in today so you can see any pending
homework assignments. (These will become visible beginning
on Monday, August 25.) You will need to learn what symbols
or formats to use when entering answers to homework problems
using Webassign. Please read this Student
Guide to become familiar with Webassign.
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| September 22
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Please download a copy of this file showing the Gamma function and its reciprocal: The Gamma Function and its reciprocal.
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| September 24
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On Wednesday, September 24, I cannot be in class with you, so watch this asynchronous Zoom recording with your lesson for this day.
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| Septeember 29
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Please bring a list of questions to review for the first hour test.
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October 1
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The first hour test will be today.
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TR>
October 3 |
Please download the example in which the method of Frobenius failed for the smaller root of the indicial equation.
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October 5
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Please download Fall
2025 Test #1 with Solutions and overall class Statistics at the end. Please download also My Solutions for Test #1.
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October 20
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Please download (x+|x|)/2: Plot of Fourier Series on (-3pi,3pi) showing the 20th partial sum.
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| October 20
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Please download the following file, correcting an error in WebAssign's solution to Zill, 12.2, Question 4 on the assignment. Please download Correction to Zill 12.2 Question 4 .
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| October 29
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Bring review questions for the Second Hour Test, covering the work since the first hour test took place..
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| October 31
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Second Hour Test, covering the work since the first hour test took place.
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Please download Fall
2023 Test #2 with Solutions and overall class Statistics at
the end.
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Please download Joseph
Fourier's classic book On the Analytic Theory of Heat
and my lecture notes about Sturm-Liouville Problems. The download concerning Sturm-Liouville problems is intended to help you with our course. Fourier's book is not required, but I think everyone who uses Fourier series or the Heat Equation should have, in our modern time, a free pdf copy of Fourier's classic work.
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Download some supplemental files from classes taught in
past years: Fourier-Bessel
Series Examples and Fourier-Legendre
Series Examples and also Norm
and Zeros for Bessel functions and norms of Legendre
functions. These downloads are not assignments. They are
just supplements that add to what is in the text, including
some illustrations that are better, in my opinion.
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One can download an interesting discussion of a century long history of the solution to the wave equation here:
Please download D'Alembert's Solution to the Wave Equation and its history through Fourier.
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Third Hour Test
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Please download Test
#3 in Fall 2023 with Solutions and overall class Statistics at
the end.
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Bring questions to review for the final exam. Remember to fill out the end of semester course evaluation form on your MyLSU page.Study for the Final Exam!
This 200-point exam will cover the whole course in a uniform
manner, so remember to review from the beginning of the
course. Your final grade for the course will be the
larger of the following two: 1. The grade guaranteed by the
formula provided higher on this page. 2. One letter below the
final exam grade. For example, if your final exam grade is A-,
you are guaranteed at least a B- in the course. Thus the final
exam provides a safety net that supplements
the calculations specified above.
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Exam Week Office Hours TBA
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| December 8
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The Final Exam will be Mon., Dec. 8, at 10 AM - Noon.
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December 11
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Please download Fall
2023 Final Examination with Solutions and overall class
Statistics at the end.
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