Math 4038-1, Fall 2020: Information for Students

(Math 4038 is cross-listed as Mechanical Engineering 4563.)


1:30 -- 2:20 PM on MWF


The course will be conducted using ZOOM:
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Meeting ID: 977 8215 2232
Passcode: 752608

You are encouraged to use the microphone to ask questions during class, just the same as you would from your seat if we were in a classroom. Also, Zoom recordings will be available to all students online for 30 days. The reason we are using Zoom instead of a classroom: the Centers for Disease Control (CDC) advises that: "The more an individual interacts with others, and the longer that interaction, the higher the risk of COVID-19 spread. ... Lowest Risk: Faculty and students engage in virtual-only learning options, activities, and events."


Our class meets starting Monday, August 24, 2020. The Final Exam will be Sat., Dec. 12, 7:30am - 9:30am.

Leonard Richardson

Office 386 Lockett

Office Hours

TBA. Office Hours are strictly ONLINE ONLY, at this link: 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.

Office phone




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: lsu 8400 0111

The textbook can be purchased either with or without WebAssign 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 – 9781284161427 ADVANCED ENGINEERING MATHEMATICS 6th Edition. This ISBN package price includes the print book, the student solutions manual, and WebAssign for a custom price. The ISBN is non-returnable and the special package price is $174.00. 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.

Text and Syllabus

Text: Dennis G. Zill, Advanced Engineering Mathematics, 6th edition, Jones and Bartlett Learning. Be sure you obtain Edition 6 of the correct text, and also remember that there will be a charge for WebAssign if you need to buy it separately. 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.

The publisher has the following package deal for LSU students in Math 4038: The ISBN for the special package – 9781284161427 ADVANCED ENGINEERING MATHEMATICS 6th Edition. This ISBN package price includes the print book, the student solutions manual, and WebAssign for a custom price. The ISBN is non-returnable, and the special package price is $174.00. 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.


  1. Chapter 5: Series solutions of linear differential Equations. Bessel functions and Legendre functions.

  2. 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.


Math 2057, plus one of the following: Math 2065, 2070, or 2090, or the equivalent.

Special Instructions during Covid-19 Pandemic

  1. If you have any signs of illness, do not go to campus.
  2. In order to protect all campus community members, the University requires everyone to wear facemasks/cloths on campus. Failure to do so is a violation of the code of student conduct.
  3. No papers or objects will be passed between us in either direction at any time during the pandemic. If you have a question about something in your notebook or on an assignment or test, email a pdf image of your work to me and join me during Zoom Office Hours to go over it together online. To make a pdf file from any jpeg camera photo, place the file or files on your PC, right click on the file or group of files, select print, and then select print to pdf. This will make a pdf file with pages correctly ordered.
  4. Wash hands with soap and water or clean with sanitizer frequently, and refrain from touching your face.
  5. If you have to cough or sneeze unexpectedly, please be mindful of others nearby and cough or sneeze into your elbow or shield yourself the best you can.
  6. If you have been exposed to others who have tested positive for COVID-19, self-quarantine in a manner consistent with current CDC guidelines. Remember, you can always participate fully and interactively via Zoom in our class!
  7. You are required to respond to a daily symptom check request sent via email or text message each morning. Completing the symptom checker will take approximately one to two minutes. Once you have provided information about your symptoms, you will be given feedback on whether or not you are certified to return to campus and attend your classes. Additionally, if you test positive for COVID-19, you are required to report it in your daily symptom checker application.
  8. Your health and safety are our top priority. If you are feeling ill or overwhelmed with anxiety, please contact the LSU Student Health Center for medical advice and mental health support. General health care and mental health support are available for all enrolled students through telehealth appointments.
  9. Unexpected Changes to the Course: Due to the unpredictable nature of the situation, 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.
  10. Students must wipe their desks and chairs before and after each use. Cleaning supplies will be supplied to each classroom. It is recommended to always take the same seat in class so as to minimize the number of persons to whom you might be exposed during the semester.

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 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 WebAssign is actually wrong.


These will be open-book take-home tests on an honors system. All tests will be submitted online in pdf format and graded and returned to you via email. Do not communicate with your classmates during an examination. Turn in only your own work. 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. If you arrive late and have missed the attendance sheet being passed around the room, be sure to sign it after class. 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.


There will be 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 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!


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. Since the assignments you will see on WebAssign were generated automatically from old assignments in the 5th Edition of our text, I may change the assignments as the term progresses if the computer did not substitute equivalent problems from the new edition. So don't get too far ahead on the assignments lest you lose credit for your work!! 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.

The 6th edition of the text is new to me and there might be some errors or glitches in the WebAssign grading. Please come to my office and show me if you have doubts about the correctness of WebAssign's grading. With the previous edition there were some 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! If on the other hand you get a good idea from a book, or from talking with a friend, academic honesty requires that you acknowledge your sources openly. Above all, never copy directly from 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.

Due at Classtime on this Date

Assignments must be turned in on WebAssign in order to receive credit! Please let me know promptly 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.

August 24

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 so you can see any pending homework assignments. (These will become visible beginning at Sunday August 25, 2019.) 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.


Please download the example in which the method of Frobenius failed for the smaller root of the indicial equation.


Hour Test #1 today.


Please download Fall 2019 Test #1 with Solutions and overall class Statistics at the end.


Please download Joseph Fourier's classic book On the Analytic Theory of Heat and Sturm-Liouville Problems.


Second Hour Test


Please download Fall 2019 Test #2 with Solutions and overall class Statistics at the end.


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.


Sorry--no office hours today.


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.


Third Hour Test


Please download Test #3 in Fall 2019 with Solutions and overall class Statistics at the end.


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.


Exam Week Office Hours: M,T 1PM-3PM; W (1PM-2:30PM), Th 2-3PM, F 1-3PM

Saturday, Dec. 12

The Final Exam will be Sat., Dec. 12, 7:30am - 9:30am. The exam will be made available online at a time to be announced and will be due for return in pdf format at the end of the time assigned by the Registrar.


Please download Fall 2019 Final Examination with Solutions and overall class Statistics at the end.