Lecture 7
Phys 3750
Long Wavelength Limit / Normal Modes
Overview and Motivation: Today we look at the long wavelength limit of the
coupled-oscillator system. In this limit the equations of motion for the coupled
oscillators can be transformed into the pa
Lecture 3
Phys 3750
Two Coupled Oscillators / Normal Modes
Overview and Motivation: Today we take a small, but significant, step towards
wave motion. We will not yet observe waves, but this step is important in its own
right. The step is the coupling toge
Lecture 2
Phys 3750
Harmonic Oscillations / Complex Numbers
Overview and Motivation: Probably the single most important problem in all of
physics is the simple harmonic oscillator. It can be studied classically or quantum
mechanically, with or without dam
SYLLABUS
Foundations of Wave Phenomena
Phys 3750
Spring 2013
TECHNICAL DETAILS
Instructor: D. Mark Riffe
Office: SER 222B
Phone: 797-3896
Email: [email protected]
Office Hours: M,W,F 3 4 p.m. at the Quadside Caf; otherwise, an appointment can be made
em
Lecture 4
Phys 3750
Normal Mode Coordinates / Initial Value Problem
Overview and Motivation: We continue to look at the coupled-oscillator problem.
We extend our analysis of this problem by introducing functions known as normalmode coordinates. These coor
Lecture 15
Phys 3750
The Dirac Delta Function
Overview and Motivation: The Dirac delta function is a concept that is useful
throughout physics. For example, the charge density associated with a point charge
can be represented using the delta function. As
Lecture 19
Phys 3750
Separation of Variables in Cartesian Coordinates
Overview and Motivation: Today we begin a more in-depth look at the 3D wave
equation. We introduce a technique for finding solutions to partial differential
equations that is known as s
Lecture 18
Phys 3750
3D Wave Equation and Plane Waves / 3D Differential Operators
Overview and Motivation: We now extend the wave equation to three-dimensional
space and look at some basic solutions to the 3D wave equation, which are known as
plane waves.
Lecture 17
Phys 3750
Fourier Transforms and the Wave Equation
Overview and Motivation: We first discuss a few features of the Fourier transform
(FT), and then we solve the initial-value problem for the wave equation using the
Fourier transform.
Key Mathem
Lecture 10
Phys 3750
General Solution using Normal Modes
Overview and Motivation: Last time we solved the initial-value problem (IVP) for
the 1D wave equation on a finite domain with "closed-closed" bc's using the general
form of the solution q(x, t ) = f
Lecture 11
Phys 3750
Introduction to Fourier Series
Overview and Motivation: Fourier series is based on the idea that many functions
of interest can be represented as a linear combination of harmonic functions. Is this
cool, or what?
Key Mathematics: Four
Lecture 6
Phys 3750
Traveling Waves, Standing Waves, and the Dispersion Relation
Overview and Motivation: We review the relationship between traveling and
standing waves. We then discuss a general relationship that is important in all of wave
physics the
Lecture 5
Phys 3750
Linear Chain / Normal Modes
Overview and Motivation: We extend our discussion of coupled oscillators to a
chain of N oscillators, where N is some arbitrary number. When N is large it will
become clear that the normal modes for this sys
Phys 3750
Midterm Exam 3
Name_
*You may use a pen/pencil and a 3"5", handwritten note card on the exam. Answer all questions as
completely as possible; show all of your work. If you run out of space on a problem, continue on the back
of that sheet of pape
Lecture 14
Phys 3750
Linear Operators / Functions as Vectors
Overview and Motivation: We first introduce the concept of linear operators on a
vector space. We then look at some more vector-space examples, including a space
where the vectors are functions.
Lecture 8
Phys 3750
1D Wave Equation General Solution / Gaussian Function
Overview and Motivation: Last time we derived the partial differential equation
known as the (one dimensional) wave equation. Today we look at the general
solution to that equation.
Lecture 13
Phys 3750
Vector Spaces / Real Space
Overview and Motivation: We review the properties of a vector space. As we shall
see in the next lecture, the mathematics of normal modes and Fourier series is
intimately related to the mathematics of a vect
Lecture 9
Phys 3750
General Solution with Boundary Conditions
Overview and Motivation: Last time we wrote down the general form of the
solution to the 1D wave equation. We then solved the initial-value problem for an
infinitely long system. Today we use t
Lecture 12
Phys 3750
Complex Fourier Series
Overview and Motivation: We continue with our discussion of Fourier series,
which is all about representing a function as a linear combination of harmonic
functions. The new wrinkle is that we now use complex fo
Lecture 20
Phys 3750
The Wave Equation in Cylindrical Coordinates
Overview and Motivation: While Cartesian coordinates are attractive because of
their simplicity, there are many problems whose symmetry makes it easier to use a
different system of coordina