Physics (B.S.)

Courses

* PHYS 040a / ASTR 040a, Expanding Ideas of Time and Space  C. Megan Urry

Discussions on the nature of time and space. Topics include the shape and contents of the universe, special and general relativity, dark and light matter, and dark energy. Observations and ideas fundamental to astronomers' current model of an expanding and accelerating four-dimensional universe. Enrollment limited to first-year students. Preregistration required; see under First-Year Seminar Program.  SC
TTh 11:35am-12:50pm

* PHYS 050a / APHY 050a, Science of Modern Technology and Public Policy  Daniel Prober

Examination of the science behind selected advances in modern technology and implications for public policy, with focus on the scientific and contextual basis of each advance. Topics are developed by the participants with the instructor and with guest lecturers, and may include nanotechnology, quantum computation and cryptography, renewable energy technologies, optical systems for communication and medical diagnostics, transistors, satellite imaging and global positioning systems, large-scale immunization, and DNA made to order. Enrollment limited to first-year students. Preregistration required; see under First-Year Seminar Program.  SC  RP
MW 2:30pm-3:45pm

* PHYS 100b / APHY 100b / ENAS 100b / EVST 100b / G&G 105b, Energy Technology and Society  Daniel Prober

The technology and use of energy. Impacts on the environment, climate, security, and economy. Application of scientific reasoning and quantitative analysis. Intended for non–science majors with strong backgrounds in math and science.  QR, SC
MW 1pm-2:15pm

* PHYS 107b / EDST 107b / MB&B 107b, Being Human in STEM  Rona Ramos

A collaboratively-designed, project-oriented course that seeks to examine, understand, and disseminate how diversity of gender, race, religion, sexuality, economic circumstances, etc. shape the STEM experience at Yale and nationally, and that seeks to formulate and implement solutions to issues that are identified. Study of relevant peer-reviewed literature and popular-press articles. Implementation of a questionnaire and interviews of STEM participants at Yale. Creation of role-play scenarios for provoking discussions and raising awareness. Design and implementation of group interventions.  SO
F 2:30pm-4:20pm

PHYS 118b / MUSI 200b, The Physics of Music  Sarah Demers

Basic concepts in physics introduced through study of the interplay between physics and music. The mathematics of harmony; tone production by musical instruments; sound propagation through spaces such as concert halls.  QR, SC
MW 1pm-2:15pm

* PHYS 120b, Quantum Physics and Beyond  Helen Caines

Current topics in modern physics, beginning with quantum physics and continuing through subatomic physics, special and general relativity, cosmology, astrophysics, and string theory.  SC
M 3:30pm-5:20pm

PHYS 151b / APHY 151b / ENAS 151b, Multivariable Calculus for Engineers  Beth Anne Bennett

An introduction to multivariable calculus focusing on applications to engineering problems. Topics include vector-valued functions, vector analysis, partial differentiation, multiple integrals, vector calculus, and the theorems of Green, Stokes, and Gauss. Prerequisite: MATH 115 or equivalent.  QR  RP
MW 1pm-2:15pm

PHYS 165La and PHYS 166Lb, General Physics Laboratory  Helen Caines, Sean Barrett, Bonnie Fleming, and Steve Lamoreaux

A variety of individually self-contained experiments are roughly coordinated with the lectures in PHYS 170, 171, and 180, 181 and illustrate and develop physical principles covered in those lectures.  SC  ½ Course cr per term
HTBA

* PHYS 170a and PHYS 171b, University Physics for the Life Sciences  Simon Mochrie

An introduction to classical physics with special emphasis on applications drawn from the life sciences and medicine. Fall-term topics include vectors and kinematics, Newton's laws, momentum, energy, random walks, diffusion, fluid mechanics, mathematical modeling, and statistical mechanics. Spring-term topics include oscillations, waves, sound, electrostatics, circuits, Maxwell's equations, electromagnetic waves, gene circuits, and quantum mechanics. Essential mathematics are introduced and explained as needed. Completion of MATH 112 or equivalent is prerequisite for PHYS 170. Completion of PHYS 170 is a prerequisite for PHYS 171. MATH 116 (or MATH 115) is recommended prior to or concurrently with PHYS 171.  QR, SC
MW 11:35am-12:50pm

PHYS 180a and PHYS 181b, University Physics  Adriane Steinacker

A broad introduction to classical and modern physics for students who have some previous preparation in physics and mathematics. Fall-term topics include Newtonian mechanics, gravitation, waves, and thermodynamics. Spring-term topics include electromagnetism, special relativity, and quantum physics. Concurrently with MATH 115 and 120 or equivalents. See comparison of introductory sequences and laboratories in the YCPS. May not be taken for credit after PHYS 170, 171.  QR, SC
HTBA

PHYS 200a and PHYS 201b, Fundamentals of Physics  Jack Harris

A thorough introduction to the principles and methods of physics for students who have good preparation in physics and mathematics. Emphasis on problem solving and quantitative reasoning. Fall-term topics include Newtonian mechanics, special relativity, gravitation, thermodynamics, and waves. Spring-term topics include electromagnetism, geometrical and physical optics, and elements of quantum mechanics. Prerequisite: MATH 115 or equivalent. MATH 210 and either MATH 225 or MATH 222, are generally taken concurrently. See comparison of introductory sequences and laboratories in the YCPS.  QR, SC
MW 11:35am-12:50pm

PHYS 205La or b and PHYS 206La or b, Modern Physical Measurement  Reina Maruyama and Staff

A two-term sequence of experiments in classical and modern physics for students who plan to major in Physics. In the first term, the basic principles of mechanics, electricity, and magnetism are illustrated in experiments designed to make use of computer data handling and teach error analysis. In the second term, students plan and carry out experiments illustrating aspects of wave and quantum phenomena and of atomic, solid state, and nuclear physics using modern instrumentation. May be begun in either term.  SC  ½ Course cr per term
HTBA

* PHYS 260a and PHYS 261b, Intensive Introductory Physics  Steven Girvin

An introduction to major branches of physics—classical and relativistic mechanics; gravitation; electricity and magnetism; and quantum physics,information, and computation—at a sophisticated level. For students majoring in the physical sciences, mathematics, and philosophy whose high school training included both mechanics and electricity and magnetism at the typical college/AP level and have excellent training in, and a flair for, mathematical methods and quantitative analysis. Concurrently with MATH 120, ENAS 151, PHYS 151, MATH 230 and 231, or PHYS 301, or equivalent.  QR, SC
MW 11:35am-12:50pm

PHYS 293a / APHY 293a, Einstein and the Birth of Modern Physics  A. Douglas Stone

The first twenty-five years of the 20th century represent a turning point in human civilization as for the first time mankind achieved a systematic and predictive understanding of the atomic level constituents of matter and energy, and the mathematical laws which describe the interaction of these constituents. In addition, the General Theory of Relativity opened up for the first time a quantitative study of cosmology, of the history of the universe as a whole. Albert Einstein was at the center of these breakthroughs, and also became an iconic figure beyond physics, representing scientist genius engaged in pure research into the fundamental laws of nature. This course addresses the nature of the transition to modern physics, underpinned by quantum and relativity theory, through study of Einstein’s science, biography, and historical context. It also presents the basic concepts in electromagnetic theory, thermodynamics and statistical mechanics, special theory of relativity, and quantum mechanics which were central to this revolutionary epoch in science. Prerequisites: Two terms of PHYS 170, 171, or PHYS 180, 181, or PHYS 200, 201, or PHYS 260, 261, or one term of any of these course with permission of instructor.  QR, SC
TTh 9am-10:15am

PHYS 295a / ASTR 255a, Research Methods in Astrophysics  Marla Geha

The acquisition and analysis of astrophysical data, including the design and use of ground- and space-based telescopes, computational manipulation of digitized images and spectra, and confrontation of data with theoretical models. Examples taken from current research at Yale and elsewhere. Use of the Python programming language. A background in high school calculus and physics. No previous programming experience required.  QR, SC  RP
MWF 10:30am-11:20am

PHYS 301a, Introduction to Mathematical Methods of Physics  Oliver Baker

Topics include multivariable calculus, linear algebra, complex variables, vector calculus, and differential equations. Designed to give accelerated access to 400-level courses by providing, in one term, the essential background in mathematical methods. Recommended to be taken concurrently with PHYS 401 or 410. Prerequisite: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261, or permission of instructor.  QR
TTh 11:35am-12:50pm

PHYS 341b, Biological Physics  Benjamin Machta

An introduction to the physics of biological structures and life processes, and to the burgeoning field of biological physics. Related concepts from probability theory and statistical physics are developed as needed. Prerequisite: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261, or permission of instructor.  QR, SC
TTh 1pm-2:15pm

PHYS 342a / G&G 342a, Introduction to Earth and Environmental Physics  John Wettlaufer

A broad introduction to the processes that affect the past, present, and future features of the Earth. Examples include climate and climate change and anthropogenic activities underlying them, planetary history, and their relation to our understanding of Earth's present dynamics and thermodynamics. Prerequisite: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261, or permission of instructor. Recommended preparation: familiarity with basic calculus and differential equations.  QR, SC
MW 11:35am-12:50pm

PHYS 343b / ASTR 343b, Gravity, Astrophysics, and Cosmology  Daisuke Nagai

Introduction to frontier areas of research in astrophysics and cosmology exploring ideas and methods. In­-depth discussion of the physics underlying several recent discoveries including extrasolar planets—their discovery, properties, and issues of habitability; black holes—prediction of their properties from GR, observational signatures, and detection; and the accelerating universe—introduction to cosmological models and the discovery of dark energy. Prerequisites: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261, or permission of instructor.  QR, SC
TTh 11:35am-12:50pm

PHYS 353a / BENG 353a, Introduction to Biomechanics  Michael Murrell

An introduction to the biomechanics used in biosolid mechanics, biofluid mechanics, biothermomechanics, and biochemomechanics. Diverse aspects of biomedical engineering, from basic mechanobiology to the design of novel biomaterials, medical devices, and surgical interventions. Prerequisites: PHYS 180, 181, MATH 115, and ENAS 194.  QR
TTh 9am-10:15am

* PHYS 356b / ASTR 356b / ASTR 556b, Astrostatistics and Data Mining  Hector Arce

Introduction to the statistical tools used to analyze and interpret astrophysical data, including common data mining techniques for finding patterns in large data sets and data-based prediction methods. Use of publicly available high-quality astronomical data from large surveys such as SDSS and 2MASS, and from space-based observatories such as Spitzer, Herschel, and WISE. Coding with the Python programming language. Prerequisite: ASTR 255 or equivalent.  QR, SC
TTh 1pm-2:15pm

* PHYS 382Lb, Advanced Physics Laboratory  Steve Lamoreaux and Nir Navon

Laboratory experiments with some discussion of theory and techniques. An advanced course focusing on modern experimental methods and concepts in atomic, optical, nuclear, and condensed matter physics. Intended to prepare students for independent research. For majors in the physical sciences. After or concurrently with PHYS 439 or 440, or with permission of instructor. PHYS 206L  WR, SC
HTBA

PHYS 401a and PHYS 402b, Advanced Classical Physics from Newton to Einstein  Nikhil Padmanabhan

Advanced physics as the field developed from the time of Newton to the age of Einstein. Topics include mechanics, electricity and magnetism, statistical physics, and thermodynamics. The development of classical physics into a "mature" scientific discipline, an idea that was subsequently shaken to the core by the revolutionary discoveries of quantum physics and relativity. Prerequisite: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261. Concurrently with PHYS 301 or other advanced mathematics course.  QR, SC
MW 11:35am-12:50pm

PHYS 410a, Classical Mechanics  Charles Baltay

An advanced treatment of mechanics, with a focus on the methods of Lagrange and Hamilton. Lectures and problems address the mechanics of particles, systems of particles, and rigid bodies, as well as free and forced oscillations. Introduction to chaos and special relativity. Prerequisite: PHYS 170, 171, or 180, 181, or 200, 201, or 260, 261. Concurrently with PHYS 301 or other advanced mathematics course.  QR, SC
MW 11:35am-12:50pm

* PHYS 420a / APHY 420a, Thermodynamics and Statistical Mechanics  Nir Navon

This course is subdivided into two topics. We study thermodynamics from a purely macroscopic point of view and then we devote time to the study of statistical mechanics, the microscopic foundation of thermodynamics. Prerequisites: PHYS 301, 410, and 440 or permission of instructor.  QR, SC
MW 9am-10:15am

PHYS 428a / AMTH 428a / E&EB 428a / G&G 428a, Science of Complex Systems  Jun Korenaga

Introduction to the quantitative analysis of systems with many degrees of freedom. Fundamental components in the science of complex systems, including how to simulate complex systems, how to analyze model behaviors, and how to validate models using observations. Topics include cellular automata, bifurcation theory, deterministic chaos, self-organized criticality, renormalization, and inverse theory. Prerequisite: PHYS 301, MATH 247, or equivalent.  QR, SC
MWF 10:30am-11:20am

PHYS 430b, Electromagnetic Fields and Optics  David Moore

Electrostatics, magnetic fields of steady currents, electromagnetic waves, and relativistic dynamics. Provides a working knowledge of electrodynamics. Prerequisites: PHYS 301 and 410 or equivalents.  QR, SC
MW 11:35am-12:50pm

PHYS 439a / APHY 439a, Basic Quantum Mechanics  Robert Schoelkopf

The basic concepts and techniques of quantum mechanics essential for solid-state physics and quantum electronics. Topics include the Schrödinger treatment of the harmonic oscillator, atoms and molecules and tunneling, matrix methods, and perturbation theory. Prerequisites: PHYS 181 or 201, PHYS 301, or equivalents, or permission of instructor.  QR, SC
TTh 1pm-2:15pm

PHYS 440b, Quantum Mechanics and Natural Phenomena I  Ramamurti Shankar

The first term of a two-term sequence covering principles of quantum mechanics with examples of applications to atomic physics. The solution of bound-state eigenvalue problems, free scattering states, barrier penetration, the hydrogen-atom problem, perturbation theory, transition amplitudes, scattering, and approximation techniques. Prerequisite: PHYS 410 or 401.  QR, SC
MW 11:35am-12:50pm

PHYS 441a, Quantum Mechanics and Natural Phenomena II  Ramamurti Shankar

Continuation of PHYS 440. Prerequisite: PHYS 440.  QR, SC
MW 11:35am-12:50pm

PHYS 442b, Introduction to Nuclear and Elementary Particle Physics  Charles Baltay

. Fundamental concepts in nuclear and particle physics, including the discovery of radioactivity, the Dirac equation, antimatter, Feynman diagrams, hadron resonances, quarks and gluons, fundamental symmetries, the weak interaction, beta decay, quantum chromodynamics, neutrino oscillation, unification, and particle theories for dark matter. Prerequisite: two term courses in quantum mechanics