PHY 441/641 & 442/642 - Mathematical Physics I and II
Textbook: Partial Differential Equations for
Scientists and Engineers by Stanley J. Farlow
Time and Place: MW 1:00 to 2:15 in BPB - 248
Instructor: Len Zane Phone: 895-1789
Office: BPB - 202 Email:
len.zane@unlv.edu
Office Hours: MW 11:15 to 1:00 p.m. or by
appointment
The goal of the course is to see how various areas
of mathematics come into play to solve problems in physics. The course will be based on the text by Stanley
J. Farlow but much material will be added to supplement the book. The approach will be based on the idea that
topics will be covered as needed to solve certain problems as opposed to the
standard approach of covering single topics in depth one after the other.
I often call this style of teaching mathematical
physics the Adesert
island@
approach to learning mathematics.
Imagine you are trapped on a desert island with lot=s
of time to think about physics. As you
ponder some physics problem and begin to work towards a solution various
mathematical skills are required. For
example, to solve a particular differential equation, it is not necessary
to develop all of the wonderful mathematics associated with the theory of differential
equations. In fact all that is needed is
the solution to the equation related to the problem you are working on.
In most cases, we will try to develop skills a
little more general than the ability to solve one particular differential
equation but less general than the usual development of differential equations
seen in most books on mathematical physics.
Sticking with differential equations a little while longer, many of the
most important differential equations that arise in classical physics are solvable
using infinite series. Hence learning
something about series solutions will help in solving a small but valuable
class of differential equations. The
same approach will be taken with respect to other topics.
One important supplemental topic that will be
covered in some detail is complex analysis with a special emphasis on
evaluating real integrals in the complex plane.
The utility of complex integration will show up periodically during both
semesters of this course.
I will often use Mathematica to help
visualize the solution to a problem.
Though I am a perennial novice with respect to this software, I highly
encourage you to consider using it during this course. The assignments will require some way of
numerically checking answers and graphing solutions. The use of Mathematica clearly
violates the spirit of the Adesert
island@
approach to mathematical physics but it is not hard to imagine a modern day
desert island with a solar powered personal computer that happens to have a
licensed copy of Mathematica on it!
The tricky balance to maintain with respect to Mathematica is to use it as one of the analytical tools in your
mathematics toolkit, but to not let it become a crutch that undermines your
analytical skills.
More information about buying a student version or
“leasing” a copy of Mathematica for a semester or academic year can be found at
www.wolfram.com. I
have also listed links on the course website, www.physics.unlv.edu/~lenz/, to two
videos produced by Mathematica to
help new users get started.
Another broad goal of the course is to link the development
of analytic skills with intuitive insights. I am a firm believer that the
analysis/intuition dichotomy is much like the yin/yang duality. The best
problem solvers are the ones that can bring balance to the analysis/intuition
split.
Grading: The grading will be based primarily on
assignments handed out during the semester.
(I am mulling over having quizzes to supplement the assignment but have
not yet made up my mind.) Some problems
will come from the text and others on handouts.
The assignments need to be done in a timely manner so that you and I are
thinking about the same stuff at the same time!
Assignments handed in after the due date will not be graded!
Students taking this course as a graduate course,
PHY 641, ought to do Aa
little better@
than the students enrolled in the undergraduate course, PHY 441. I apologize for the subjectivity of that
distinction but it is the best I can do.
Also the distinction will be made at the end of the semester based on
the cumulative scores. The assignments
will be graded the same way for all the students taking the course.
The final examination is scheduled for Tuesday,
December 7, 1:00 p.m. in room BPB-248.
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The books that deal with mathematical physics and
the other topics in this class are almost unlimited. The list below is obviously not exhaustive!
General Books
Jon Mathews and R. L.
Walker, Mathematical Methods of Physics B an excellent but higher level text. I used the book for the
graduate math physics course when I taught it in the old days!
Mary L. Boas, Mathematical Methods in the
Physical Sciences B This book has been used for PHY 441 in the past. A good book at the
appropriate level.
Royal Eugene Collins, Mathematical Methods for
Physicists and Engineers B This book is available in paperback and,
consequently, is much less expensive!
George B. Arfken, Mathematical Methods for
Physicists B This is another standard book that may be
available in paperback.
Complex Analysis
Tristan Needham, Visual Complex Analysis B a different and very graphical approach to complex analysis. A good book to get a
different perspective than presented in most other texts.
Kelvin and the Age of the Earth (We may or may not get to this topic this semester.)
Joe D. Burchfield, Lord Kelvin and the Age of
the Earth B Puts Lord Kelvin=s calculation in historical perspective.
G. Brent Dalrymple, The Age of the Earth B Gives a broad overview of efforts to calculate
the age of the Earth including a good section on Kelvin.