# Physics (2016 - 2018)

Courses are lectures unless otherwise indicated.

**The Universe: Its Nature and History**

PHYS-UA 7 *Offered every year. 4 points.*

Qualitative introduction to our understanding of the nature and evolution of the universe. Topics include the creation of the cosmos; its explosive evolution, present structure, and ultimate fate; the nature of stars and galaxies; the structure and evolution of our Milky Way; the birth, life, and eventual death of the solar system; our place and role in the universe; and the relationship of modern astronomical ideas to other cultural disciplines.

**Sound and Music**

PHYS-UA 10 *Assumes high school-level mathematics background. 4 points.*

Explores the production of musical sound and how it is perceived by us, dealing mainly with the physical basis of sound. Covers sound waves, resonance, how musical instruments produce sound, the concepts of scales and harmony, physical acoustics, physiological factors of perception, acoustics of auditoria, and sound recording and reproduction. Develops the necessary physics for the course, as needed.

**General Physics I**

PHYS-UA 11 *Prerequisite: Calculus I (MATH-UA 121) with a minimum grade of C or equivalent, or both Mathematics for Economics I and II (MATH-UA 211 and 212) with a C or better, or permission of the instructor. Lecture and laboratory. Not open to students who have completed Physics I (PHYS-UA 91) with a grade of C-minus or better. Offered in the fall. 5 points.*

Begins a two-semester introduction to physics intended primarily for preprofessional students and for those majoring in a science other than physics, although well-prepared students may wish to take the Physics I, II, III three-semester sequence for majors (with corequisite laboratories), below. Topics include kinematics and dynamics of particles; momentum, work, and energy; gravitation; circular, angular, and harmonic motion; mechanical and thermal properties of solids, liquids, and gases.

**General Physics II**

PHYS-UA 12 *Prerequisite: General Physics I (PHYS-UA 11) with a grade of C or better, or permission of the instructor. Lecture and laboratory. Offered in the spring. 5 points.*

Topics include electric charge, field, and potential; magnetic forces and fields; resistive, capacitive, and inductive circuits; electromagnetic induction; wave motion; electromagnetic waves; geometrical optics; interference, diffraction, and polarization of light; relativity; atomic and nuclear structure; elementary particle physics.

**Observational Astronomy**

PHYS-UA 13 *Prerequisite: The Universe: Its Nature and History (PHYS-UA 7) or higher, or permission of the instructor for nonscience majors and minors; no prerequisite for science majors and minors or those who have satisfied the Core Physical Science requirement. Lecture and laboratory. Offered every year. 4 points.*

Introduction to the theory and practice of technical amateur astronomy. The approach is hands-on, with weekly evening laboratory/observing sessions. Topics include astronomical coordinate systems, optics, how to use a telescope, and the phenomena that can be seen in the urban night sky. Observing sessions involve the use of eight-inch telescopes.

**Physics and Astronomy in the Renaissance**

PHYS-UA 14 *Typically offered in the spring. 4 points.*

Moves from ancient Greece and medieval Islam to the Copernican Revolution (16th-17th centuries) of Nicolas Copernicus, Tycho Brahe, Johannes Kepler, and Galileo Galilei that was the beginning of observational science and astronomy. Also included are the universal scientist, engineer, and artist Leonardo da Vinci; the world’s first cosmologist, Giordano Bruno; and Sir Isaac Newton, whose laws of motion and gravitation were the crowning culmination of the Scientific Revolution.

**Introduction to Cosmology**

PHYS-UA 15 *Assumes high-school level mathematics background. Offered every year. Lecture. 4 points.*

A technical but elementary introduction to the modern understanding of cosmology, intended for non-science students. Proficiency with algebra is required. Covers advances in cosmology over the last 100 years, with special emphasis on more recent developments in the field. Explores topics ranging from the early universe to galaxy formation in the present day universe through the lens of the theory of relativity and the expanding universe. Examines the Big Bang, the Cosmic Microwave Background, dark matter, dark energy, and the associated evidence for these phenomena. Mathematically-based; most topics will be explored both qualitatively and quantitatively, and homework and exams will require calculations.

**20th-Century Concepts of Space, Time, and Matter**

PHYS-UA 20 *Assumes high school-level geometry and intermediate algebra background. Not open to students who have completed Physical Science: Einstein’s Universe (CORE-UA 204). Offered every year. 4 points.*

The 20th century witnessed two major revolutions in physics. Einstein’s special and general theories of relativity: implications of the special theory for our understanding of the unity of space and time, and of the general theory for our understanding of the nature of gravity. Quantum mechanics: a new picture of the basic structure and interactions of atoms, molecules, and nuclei. Topics include the uncertainty principle, wave-particle duality, and the continuing search for the fundamental constituents of matter.

**Introductory Experimental Physics I**

PHYS-UA 71 *Laboratory. Typically taken with Physics I (PHYS-UA 91). Offered in the fall. 2 points.*

Introduces essential experimental techniques, including setup and operation of basic laboratory equipment, elementary experimental design, statistics and inference, and computational data analysis. Experimental techniques are introduced in the context of classic physics experiments.

**Introductory Experimental Physics II**

PHYS-UA 72 *Prerequisite: Introductory Experimental Physics I (PHYS-UA 71). Laboratory. Typically taken with Physics II (PHYS-UA 93). Offered in the spring. 2 points.*

Continuation of Introductory Experimental Physics I (PHYS-UA 71).

**Intermediate Experimental Physics I**

PHYS-UA 73 *Prerequisite: Introductory Experimental Physics II (PHYS-UA 72). Laboratory. Typically taken with Physics III (PHYS-UA 95). Offered in the fall. 2 points.*

Develops further the experimental techniques introduced in Introductory Experimental Physics I, II (PHYS-UA 71, 72) in the context of more advanced experiments.

**Intermediate Experimental Physics II**

PHYS-UA 74 *Prerequisite: Intermediate Experimental Physics I (PHYS-UA 73). Laboratory. Typically taken with Classical and Quantum Waves (PHYS-UA 105). Offered in the spring. 2 points.*

Continuation of Intermediate Experimental Physics I (PHYS-UA 73).

**Physics I**

PHYS-UA 91 *Corequisite: Calculus I (MATH-UA 121). Physics majors must also register for Introductory Experimental Physics I (PHYS-UA 71). Offered in the fall. 3 points.*

With PHYS-UA 93 and PHYS-UA 95, forms a three-semester sequence that must be taken in order, starting in the fall semester. Intended for physics majors and other interested science and mathematics majors. Topics include kinematics and dynamics of particles; energy and momentum; rotational kinematics and dynamics; harmonic oscillators; gravitational fields and potentials; special relativity.

**Physics II**

PHYS-UA 93 *Prerequisite: Physics I (PHYS-UA 91) with a grade of C or better, or permission of the department. Corequisite: Calculus II (MATH-UA 122). Physics majors must also register for Introductory Experimental Physics II (PHYS-UA 72). Offered in the spring. 3 points.*

Continuation of Physics I (PHYS-UA 91). Topics include electrostatics; dielectrics; currents and circuits; the magnetic field and magnetic materials; induction; AC circuits; Maxwell’s equations.

**Physics III**

PHYS-UA 95 *Prerequisite: Physics II (PHYS-UA 93) with a grade of C or better, or permission of the department. Corequisite: Calculus III (MATH-UA 123). Physics majors must also register for Intermediate Experimental Physics I (PHYS-UA 73). Offered in the fall. 3 points.*

Continuation of Physics II (PHYS-UA 93). Topics include wave motion; Fourier series; sound; the reflection, refraction, interference, and diffraction of light; polarization; thermodynamics; kinetic theory and statistical physics.

**Classical and Quantum Waves**

PHYS-UA 105 *Prerequisite: Physics III (PHYSUA 95) and Calculus III (MATH-UA 123). Physics majors must also register for Intermediate Experimental Physics II (PHYS-UA 74). Offered in the spring. 3 points.*

Topics include linear and nonlinear oscillators, resonance, coupled oscillators, normal modes, mechanical waves, light, matter waves, Fourier analysis, Fourier optics (diffraction), and an introduction to numerical (computer) methods for solving differential equations.

**Mathematical Physics**

PHYS-UA 106 *Prerequisite: Physics III (PHYSUA 95). Offered in the spring. 3 points.*

Mathematical preparation for further study in physics. Vector analysis, Fourier series and integrals, ordinary differential equations, matrices, partial differential equations, and boundary-value problems.

**Electronics for Scientists**

PHYS-UA 110 *Identical to BIOL-UA 110, CHEM-UA 671. Prerequisite: General Physics II (PHYS-UA 12) or Physics II (PHYS-UA 93) or permission of the instructor. Lecture and laboratory. 5 points.*

Introduction to basic analog and digital electronics used in modern experiments and computers. Basic concepts and devices presented in lecture are studied in the laboratory. Topics include filters, power supplies, transistors, operational amplifiers, digital logic gates, and both combinatorial and sequential digital circuits. Students learn the functions of modern electronic instrumentation and measurement.

**Advanced Experimental Physics**

PHYS-UA 112 *Prerequisites: Intermediate Experimental Physics I, II (PHYS-UA 73, 74) and Quantum Mechanics I (PHYS-UA 123), or permission of the instructor. Laboratory. Offered every year. 3 points.*

Introduces the experiments and techniques of modern physics. Students choose their experiments and may use microcomputers for data analysis. Experimental areas include optical spectroscopy, the Mössbauer effect, cosmic rays, magnetic resonance, condensed matter, and relativistic mass.

**Dynamics**

PHYS-UA 120 *Prerequisites: Physics III (PHYS-UA 95) and Mathematical Physics (PHYS-UA 106). Offered every year. 3 points.*

Emphasis on the formulation of problems and their numerical solution. Topics include conservation laws, central force motion, Lagrange’s and Hamilton’s equations, normal modes and small oscillations, and accelerated reference frames.

**Quantum Mechanics I**

PHYS-UA 123 *Prerequisite: Classical and Quantum Waves (PHYS-UA 105). Offered every year. 3 points.*

Topics include foundational experiments, wave-particle duality, wave functions, the uncertainty principle, the time-independent Schrödinger equation and its applications to one-dimensional problems and the hydrogen atom, angular momentum, and spin; Hilbert Space, operators, and observables; timeindependent perturbation theory; atomic spectra.

**Quantum Mechanics II**

PHYS-UA 124 *Prerequisite: Quantum Mechanics I (PHYS-UA 123). Offered every year. 3 points.*

Continuation of Quantum Mechanics I (PHYSUA 123). Topics include the time-dependent Schrödinger equation, the Schrödinger and Heisenberg description of quantum systems, timedependent perturbation theory, scattering theory, quantum statistics, and applications to atomic, molecular, nuclear, and elementary particle physics.

**Electricity and Magnetism I**

PHYS-UA 131 *Prerequisites: Classical and Quantum Waves (PHYS-UA 105) and Mathematical Physics (PHYS-UA 106). Offered every year. 3 points.*

Introduction to electrodynamics with applications to physical problems. Topics include electrostatics, magnetostatics, Maxwell’s equations, electromagnetic forces, electromagnetic waves, radiation from accelerating charges and currents, and special relativity.

**Electricity and Magnetism II**

PHYS-UA 132 *Prerequisite: Electricity and Magnetism I (PHYS-UA 131). Offered every year. 3 points.*

Continuation of Electricity and Magnetism I (PHYS-UA 131), with greater depth and more complex phenomena and applications. Topics include solutions to the Laplace and Poisson equations, dielectrics and magnetic materials, gauge invariance, plasmas, Fresnel equations, transmission lines, wave guides, and antennas.

**Optics**

PHYS-UA 133 *Prerequisite: Classical and Quantum Waves (PHYS-UA 105) or permission of the instructor. 3 points.*

Introduction to physical and geometrical optics. Wave phenomena including diffraction, interference, first-order and higher-order coherence. Holography, phase contrast and atomic force microscopy, and limits of resolution are some of the subjects included. Topics include atomic energy levels and radiative transitions, and detectors from photon counting to bolometers for infrared radiation.

**Condensed Matter Physics**

PHYS-UA 135 *Prerequisite: Classical and Quantum Waves (PHYS-UA 105) or permission of the instructor. Offered every other year. 3 points.*

Designed as an introduction for students with knowledge of elementary quantum mechanics. Topics include crystal structure, lattice vibrations, and the energy band theory of metals and semiconductors; the electronic, magnetic, and optical properties of solids; and some modern research topics, such as the physics of nanostructures, soft condensed matter physics, and superconductivity.

**Readings in Particle Physics**

PHYS-UA 136 *Prerequisite: Classical and Quantum Waves (PHYS-UA 105). Offered every other year. 3 points.*

The fundamental constituents of matter and the forces between them are microscopic, but also connect to the large-scale realms of astrophysics and cosmology. Close reading of journal articles in which the most important advances in elementary particle physics were first published. Topics include the discovery of elementary particles in cosmic rays, antimatter, symmetries found in nature, and the invention of the Quark model of elementary particles and its experimental verification.

**Quantum Information and Quantum Computing**

PHYS-UA 138 *Prerequisite: Quantum Mechanics I (PHYS-UA 123). Offered every two years. 4 points.*

Quantum mechanical systems can be thought of as information-storing, information-processing, and information-transmitting systems. Topics include density operators, quantum communication, teleportation, quantum cryptography, entanglement and the Bell Inequalities, quantum computing, quantum algorithms, quantum error correction, quantum circuits, and experimental developments.

**Thermal and Statistical Physics**

PHYS-UA 140 *Prerequisites: Classical and Quantum Waves (PHYS-UA 105) and Mathematical Physics (PHYS-UA 106). Offered every year. 3 points.*

Topics include relation of entropy to probability and energy to temperature; the laws of thermodynamics; Maxwell-Boltzmann, Bose-Einstein, and Fermi- Dirac statistics; equations of state for simple gases and chemical and magnetic systems; and elementary theory of phase transitions.

**Astrophysics**

PHYS-UA 150 *Prerequisite: Physics III (PHYS-UA 95) or permission of the instructor. Offered every other year. 4 points.*

Introduction to modern astrophysical problems with an emphasis on the physical concepts involved: radio, optical, and X-ray astronomy; stellar structure and evolution; white dwarfs, pulsars, and black holes; and galaxies, quasars, and cosmology.

**Physics of Biology**

PHYS-UA 160 *Prerequisite: Physics III (PHYSUA 95). 3 points.*

Basic biological processes at all levels of organization (molecular, cellular, organismal, and population) in the light of simple ideas from physics. Topics include self-assembly, molecular motors, low Reynolds fluid dynamics, optical imaging, and single-molecule manipulation.

**General Relativity**

PHYS-UA 170 *Prerequisite: Dynamics (PHYS-UA 120) or permission of the instructor. Offered in the spring. 3 points.*

Provides an introduction to general relativity, stressing physical phenomena and their connection to experiments and observations. Topics include special relativity, gravity as geometry, black holes, gravitational waves, cosmology, Einstein equations.

**Introduction to Fluid Dynamics**

PHYS-UA 180 *Identical to MATH-UA 230. Prerequisite: Calculus III (MATH-UA 123); Mathematical Physics (PHYS-UA 106) is recommended. Offered every year. 4 points.*

Key concepts of fluid dynamics: the formalism of continuum mechanics, the conservation of mass, energy and momentum in a fluid, the Euler and Navier-Stokes equations, and viscosity and vorticity. Concepts are applied to such classic problems as potential flow around a cylinder, the Stokes flow, the propagation of sound and gravity waves, and the onset of instability in shear flow.

**Philosophy of Physics**

PHYS-UA 190 *Identical to PHIL-UA 94. Offered every other year. 4 points.*

Different approaches to understanding space and time, including the debates between Newton and Leibniz and Einstein’s Special and General Theories of Relativity. Mathematics above the level of algebra is neither used nor required.

**Computational Physics**

PHYS-UA 210 *Prerequisites: Mathematical Physics (PHYS-UA 106) or permission of the instructor, and knowledge of a scientific programming language (such as C, C++, Fortran, or Python). Offered every year. 4 points.*

Emphasizes fields of current research interest in which numerical techniques provide unique physical insight. Topics are chosen from various branches of physics, including numerical solution of ordinary and partial differential equations, eigenvalue problems, Monte Carlo methods in statistical mechanics, field theory, dynamical systems, and chaos.

**Special Topics in Physics**

PHYS-UA 800 *Prerequisites vary with the topic. Offered occasionally. 3 points.*

Covers advanced topics or recent developments in physics. Varies by term.

**Special Topics in Physics: A Sneak Peek at the Universe**

PHYS-UA 800 *Usually offered in the fall. 4 points.*

Intended for students who are attracted to the major because of the challenging concepts of contemporary physics and cosmology, whereas the first two years of the major are devoted to classical dynamics and electromagnetism. Topics include quantum entanglement, quantum information, black holes, gravitational radiation, and the big bang. Assumes mastery of basic algebra and is conceptually challenging.

**Independent Study**

PHYS-UA 997, 998 *Prerequisite: permission of the director of undergraduate studies. Offered in the fall and spring respectively. 2 to 4 points per term.*