Introduction to Methods of Theoretical Physics
Fall 1998 Schedule of Classes
This page may be updated and changed after the course has begun.
I will try to inform everyone when changes are made, but be sure to check the
current version of this page before doing your homework or preparing for class.
Most classes will be two consecutive 50-minute periods with a ten minute
break inbetween. The material that will be covered is indicated for each period,
as well as the relevant reading in the textbooks.
Textbook material is referenced by the chapter and section. A few of the classes
will be carried out in one two-hour block in one of the studio classrooms on
campus. The location for each class will be announced when known, and indicated
on the date.
The homework assignment indicated on a date is due on that date at the
start of class. Homework is due on most days.Follow the link to get a pdf file
describing the assignment. For postscript files and other information on homework,
see the homework page.
Class dates are listed here. Click on the date to get jump to that day.
- Oscillations
- August 25 (Tu), 27 (Th)
- September 1 (Tu), 3 (Th),
8 (Tu), 10 (Th)
- Mechanical waves
- September 15 (Tu), 17 (Th),
22 (Tu), 24 (Th)
- Electromagnetism
- September 29 (Tu)
- October 6 (Th),
8 (Tu), 15 (Th)
20 (Tu)
- Special relativity
- October 22 (Th),
27 (Tu), 29 (Th)
- Quantum mechanics
- November 3 (Tu), 5 (Th),
10 (Tu), 12 (Th),
17 (Tu), 19 (Th)
- General Relativity; Action; Course review
- November 24 (Tu)
- December 1 (Th), 3 (Tu)
| Tuesday August 25 |
|
No homework (First class) |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Introduction and examples
- F=ma as a differential equation
- Simple harmonic motion and energy
|
- Math: Power series
- Math: Complex numbers
- Simple harmonic motion, revisited
|
| Textbook reading and reference |
| |
- Nettel: 1.3
- Fletcher: 1.6-1.8
- Stewart: 10.9, 10.10, A48
|
| Thursday August 27 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Simple harmonic motion, once more
- Damped mechanical oscillations
- Energy in oscillations
|
- Forced Mechanical Oscillations
- Resonance
- Relative phase
|
| Textbook reading and reference |
- Nettel: 2.1, 2.2
- Fletcher: 3.1a, 3.1c
- Stewart: 15.7
|
- Nettel: 2.2, 2.3
- Fletcher: 3.2a, 3.2b
- Stewart: 15.7
|
| Tuesday September 1 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Electric circuits (review)
- RC and LR circuits
- Electrical oscillations
|
- Driven electrical oscillations
- Resonance and Impedance
- Q-factors
|
| Textbook reading and reference |
- HRW 5e: Chapter 28 and Sec.31-8,9
- Fletcher: 3.2c
- Stewart: 15.7
|
- Nettel: 2.1-2.3
- Fletcher: 3.2c
|
| Thursday September 3 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Coupled oscillations I
- Mechanical example
- Normal modes
|
- Coupled oscillations II
- Relative coordinates
- Matrix solution techniques
|
| Textbook reading and reference |
- Fletcher: 5.4 (Fig.5.12)
- Johnson: 1.6
|
- Fletcher: 5.8
- Johnson:
3.2
|
| Tuesday September 8 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Energy and motion
- Oscillations in terms of energy
|
- Approximations near potential minima
- The pendulum
|
| Textbook reading and reference |
| |
|
| Thursday September 10 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
| |
- Application to Forced Oscillators
|
| Textbook reading and reference |
| |
|
| Tuesday September 15 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Waves: Review from Physics I
- Wavelength, frequency, and speed
- Energy
|
- Stretched strings
- The wave equation
- General solutions
|
| Textbook reading and reference |
- HRW 5e: Chapter 17
- Fletcher: 4.1
|
- Nettel: 3.1, 3.2
- Fletcher: 4.2, 4.3
- Stewart: Chapter 12 (Partial Derivatives)
|
| Thursday September 17 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Natural wave motion
- Traveling waves
- Superposition
|
- Normal modes
- Standing waves
- Math: Orthonormality
|
| Textbook reading and reference |
- Nettel: 3.2, 3.3
- Fletcher: 4.4, 4.5
|
- Nettel: 3.3
- Fletcher: 4.6, 4.7
|
| Tuesday September 22 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Wave pulses
- Math: Fourier transform
|
- Math: Dirac delta function
- Applications
|
| Textbook reading and reference |
- Nettel: 1.4, 1.5
- Fletcher: 4.9
|
- Nettel: 1.5
- Fletcher: 4.9
|
| Tuesday September 29 |
|
No Homework Due (Exam) |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Scalar and vector fields
- Fluid velocity as a vector field
- Flux through open and closed surfaces
|
- The divergence theorem
- Simple examples
- Conservation of mass
|
| Textbook reading and reference |
- Nettel: 4.2
- Fletcher: 6.5
- Stewart: Chapter 13, 14
|
- Nettel: 4.2
- Fletcher: 6.5
- Stewart: Chapter 13, 14
|
| Thursday October 1 |
|
No Homework Due (Exam) |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Examples with radial fields
- The 3D Delta function
- Circulation and line integrals
|
- Curl of a vector field
- Stokes' theorem
- The gradient
|
| Textbook reading and reference |
- Nettel: 4.2
- Fletcher: 6.6
- Stewart: Chapter 13, 14
|
- Nettel: 4.2
- Fletcher: 6.6
- Stewart: Chapter 13, 14
|
| Tuesday October 6 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Review of Maxwell's Equations
|
- Review of Maxwell's Equations
|
| Textbook reading and reference |
- HRW5e: Chapters 24, 26, 29
|
|
| Thursday October 8 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Maxwell's Equations in differential form
- Current as flux of current density
- Static electric fields: Potential
|
- Maxwell's Equations in free space
- Formulating a solution
- Electromagnetic waves
|
| Textbook reading and reference |
| |
|
| Thursday October 15 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- General electromagnetic waves
- Polarization
- Energy in electromagnetic fields
|
- The Poynting vector
- Energy flux in waves
- Electromagnetic cavities
|
| Textbook reading and reference |
| |
|
| Tuesday October 20 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Simple waveguides
- Phase and group velocity
|
- Electromagnetic potentials
- Gauge transformations
|
| Textbook reading and reference |
- Nettel: Problem 4.13; Sec.7.2
- Fletcher: 4.4
|
- Nettel: 4.5
- Griffiths: 7.4
|
| Thursday October 22 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Interferometers
- The Michaelson-Morley experiment
|
- The need for special relativity
- The parable of the surveyors
|
| Textbook reading and reference |
| |
- Taylor and Wheeler: Chapter 1
|
| Tuesday October 27 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- The Principle of Relativity
- The invariant interval
|
- The Lorentz Transformation
- Addition of velocities
|
| Textbook reading and reference |
- Taylor and Wheeler: Chapter 3
|
- Taylor and Wheeler: Chapter "L"
|
| Thursday October 29 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Momentum and energy
- Four-momentum
|
- Collision kinematics
- Massless particles: Photons
|
| Textbook reading and reference |
- Taylor and Wheeler: Chapter 7
|
- Taylor and Wheeler: Chapter 8
|
| Tuesday November 3 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- DeBroglie's hypothesis
- Matter waves
- Schrodingers wave equation
|
- Postulates of quantum mechanics
- Operators and eigenvalues
- Expectation values
|
| Textbook reading and reference |
- Nettel: 6.1
- Landshoff: Chapt. 1
|
- Nettel: 6.2
- Landshoff: Chapt. 4
|
| Thursday November 5 |
|
No Homework Due (Exam) |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Stationary states
- Particle in an infinite box
|
- Connection to atmos and nuclei
- Position and momentum uncertainty
- The 3D infinite box
|
| Textbook reading and reference |
| |
- Nettel: 6.2
- Landshoff: Chapt. 3
|
| Tuesday November 10 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Physics from the postulates
|
|
| Textbook reading and reference |
| |
|
| Thursday November 12 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
| |
|
| Textbook reading and reference |
| |
|
| Tuesday November 17 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Solution for a Free Particle
- Tunnelling Through a Barrier
|
- Wave Packets
- The Uncertainty Principle
|
| Textbook reading and reference |
| |
- Nettel: 6.3
- Landshoff: Chapter 4
|
| Thursday November 19 |
|
Homework Assignment Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Quantum Mechanics of Solids
- The Kronig-Penney Potential
|
- Periodic Boundary Conditions
- Energy Bands in Solids
|
| Textbook reading and reference |
- Landshoff: Chapters 10,11
|
- Landshoff: Chapters 10,11
|
| Tuesday November 24 |
|
Homework Assignment Due |
| Special Class: General Relativity |
| Textbook reading and reference |
| Amer. J. Phys. 65(1997)1037-1039 and
Taylor and Wheeler: Chapters 2 and 9 |
| Tuesday December 1 |
|
No Homework Due |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
- Math: Calculus of variations
- Length of a hanging string
- Constraints
|
- Action and the action principle
- Concept of generalized coordinates
- The Lagrangian
|
| Textbook reading and reference |
| |
|
| Thursday December 3 |
|
No Homework Due (Exam) |
| Topics: Period 1 (10:00-10:50) | Topics: Period 2 (11:00-11:50) |
| |
|
Jim Napolitano
Last modified: Mon Dec 7 12:51:56 EST 1998