LSU  | Mathematics

# Math 4038: Information for Students

## For Fall 2016

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

 Time 1:30 -- 2:20 PM Location 135 Lockett Hall Calendar Our class meets from Monday, August 22, 2015 through Friday, December 2, 2015. The Final Exam will be Friday, December 9, 3 PM -- 5 PM. Leonard Richardson Office 386 Lockett Office Hours MWF 11:30am–12:30pm. I am available at many other times. Call or email first to make sure I'm able meet with you. I answer email many times daily---usually quickly. Telephone 578--1568 E-Mail rich@math.lsu.edu WebAssign 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 7254 3219. 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 – 9781284080827 ADVANCED ENGINEERING MATHEMATICS 5E W/ACCESS CODE ADVANCED ENGINEERING MATHEMATICS 5E STUDENT SOL MAN ONLINE: WEBASSIGN ACCESS CODE NET PRICE $174.00 Text and Syllabus Text: Dennis G. Zill and Warren S. Wright, Advanced Engineering Mathematics, 5th edition, Jones and Bartlett Learning. Publication Date: 2014. Be sure you obtain Edition 5 of the correct text, and also remember that there will be a charge for WebAssign if you need to buy it separately. According to the WebAssign website, the cost for their service with Zill's book is$69.95 if purchased separately. So be sure to take this into account. Webassign access includes the use of the online e-book version of Zill's book, but only for the semester of this course. One can print pages from the online e-book, but apparently only 10 pages at a time. (It is not required to have a solutions manual, but I think that most students find this helpful.) But you could save a considerable amount of money by using the online book at Webassign and printing the chapters that we study. 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. The publisher has the following package deal for LSU students in Math 4038: The ISBN for the special package – 9781284080827 ADVANCED ENGINEERING MATHEMATICS 5E W/ACCESS CODE ADVANCED ENGINEERING MATHEMATICS 5E STUDENT SOL MAN ONLINE: WEBASSIGN ACCESS CODE NET PRICE \$174.00 Syllabus: 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. Originally 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 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. Prerequisites Math 2057, plus one of the following: Math 2065, 2070, or 2090, or the equivalent.

## Absences

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.

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

## 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 the next day!

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.

## 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.