Skip to content

PHYS225

PHYS225 (Relativity and Math Applications) is a 2-credit hour course that is required for physics majors. It is also required for the physics minor. It counts as a technical elective for both EEs and CEs. It is offered in the fall and spring semesters.

Content Covered

  • Lorentz transformation
  • Time dilation, length contraction
  • Invariant interval
  • Relativistic energy, momentum, and force
  • Relativistic kinematics and dynamics
  • Doppler effect
  • Vector calculus and applications to Maxwell’s equations

PHYS225 begins with an introduction to special relativity and its extensive consequences to the field of physics. Students will learn the Lorentz transformation and use it to derive the phenomena of time dilation and length contraction. The concepts of the invariant interval and timelike and spacelike separation also follow from the Lorentz transformation. The significance of special relativity in the field of mechanics is then covered, including the relativistic forms of energy, momentum, and force, along with the mass-energy equivalence. The relativistic Doppler effect, which has important applications in the field of electromagnetics, is also covered.

The course then moves on to some applications of mathematics to physics. In this part of the course, students will review some vector calculus, including gradient, divergence, curl, line and surface integrals, the divergence theorem, and Stokes's theorem. Using these concepts, they will be able to derive the relationship between the differential and integral forms of Maxwell’s equations. Complex numbers are also reviewed, allowing for the introduction of the Fourier transform, a topic that has many applications in electrical engineering and physics, including in quantum mechanics. Finally, students will then be able to examine the wave equation. Throughout the course, various other math concepts relevant to physics will be covered, namely matrix multiplication, Taylor series, and vector fields.

Prerequisites

The official prerequisite to PHYS225 is credit or concurrent registration in PHYS212. Towards the end, the course will focus on the applications of mathematics to physics, including the use of vector calculus to relate the differential and integral forms of Maxwell’s equations. Thus, for this section, it is very important to be familiar with basic electromagnetics and multivariable calculus from PHYS212 and MATH241.

When to Take It

Physics majors generally take PHYS225 within their first two years to be able to graduate on time. It is important to take this course concurrently with or after MATH241 and PHYS212, as multivariable calculus and basic electricity and magnetism will appear in the last few weeks of the course. This is generally the first course students going for a minor in physics take beyond their previous required courses. For these students, it is recommended to take this course by the first semester of junior year. This is also a good class to take for any student interested in electromagnetics.

Course Structure

PHYS225 holds only one lecture each week. Attendance is required and is a significant portion of a student’s grade. Unlike previous physics courses, PHYS225 does not use iClickers; instead, attendance is recorded with "one-minute papers", or short questions which must be answered at the beginning and end of each lecture. In addition to the lectures, PHYS225 also has required discussion sections, which also meet weekly. Much of the course material is taught in discussion. Each of the discussion units contain reading materials along with several questions, which can be difficult to complete within the allotted time. In discussion, students will derive many of the concepts covered in this course themselves, including the Lorentz factor and Einstein’s most famous equation, the mass-energy equivalence, E = mc²! In lecture, the instructor will go over material that students are having trouble with and any topics that are important, but not covered in discussion.

Homework is assigned every week. The homework problems are hard and require quite a bit of thinking, so office hours can be very helpful, although they are often crowded. It is highly recommended to work on homework in groups to understand the material.

There is only one midterm in this course, which is held in class and is an hour long; working quickly is necessary to finish on time. The final exam is 3 hours long and cumulative.

Instructors

In the past, this course has been taught by Professors Makins, Lamb, Wiss, Hooberman, and Schulte. Recently, this course has been taught by Professor Kahn.

Course Tips

Special relativity has many consequences that are quite odd and unintuitive. Most students find this course to be very difficult conceptually. It is important to work through each discussion section problem set diligently, as this is where much of the material is introduced. Reading and taking notes on the assigned readings from the textbook will also be useful for understanding the material. To complete the homework assignments, it is highly recommended to work in groups and attend office hours.

Life After

Special relativity has broad applications to many different fields of physics; students who have taken this course will be well prepared for future courses in classical mechanics, electromagnetics, quantum physics, and eventually, general relativity. The next step after taking this course is PHYS325 - Classical Mechanics I. Though PHYS325 covers classical, nonrelativistic mechanics, the sections on inertial reference frames and math applications to physics will be quite applicable.

Infamous Topics

  • Lorentz transformation: It can be easy to apply this improperly and get the wrong result. Pay close attention to which reference frame is considered to be fixed and which reference frame is considered to be in motion.
  • Doppler effect: The derivation of the relativistic Doppler effect is difficult and understanding it relies on a good understanding of prior concepts.
  • Math applications to physics: PHYS225 is generally the first physics course students take that relies on an understanding of vector calculus and differential equations, so students generally find this part to be difficult. Pay attention in this section, it will prepare you well for your future courses!

Resources

In addition to the textbook, Albert Einstein’s original paper on special relativity from 1905, On the Electrodynamics of Moving Bodies, is an excellent supplementary resource. It can be found here.

Professor Kudeki has written an excellent document on special relativity, meant specifically for ECE students, which can be found here. In this document, special relativity is derived from the Doppler effect and Maxwell's equations. Many examples relevant to ECE students are also provided.