Physics

PHYS C1001y Physics for Poets 3 pts. This course does not fulfill the physics requirement for admission to medical school. No previous background in physics is expected; high school algebra is required. An introduction to physics taught through the exploration of the scientific method, and the application of physical principles to a wide range of topics from quantum mechanics to cosmology. Science Requirement: Partial Fulfillment.

PHYS F1201x-F1202y General Physics 3 pts. Prerequisites: Prerequisite for PHYS F1202: PHYS F1201 The course will use elementary concepts from calculus. Students should therefore have some background in calculus or should be concurrently taking MATH V1101, Calculus I. The accompanying laboratory is PHYS W1291-W1292. Basic introduction to the study of mechanics, fluids, thermodynamics, electricity, magnetism, optics, special relativity, quantum mechanics, atomic physics, and nuclear physics.

PHYS V1201x-V1202y General Physics 3 pts. Prerequisites: Prerequisite for PHYS V1202: PHYS V1201 The course will use elementary concepts from calculus. Students should therefore have some basic background in calculus or should be concurrently taking MATH V1101, Calculus I. The accompanying laboratory is PHYS W1291-W1292. Basic introduction to the study of mechanics, fluids, thermodynamics, electricity, magnetism, optics, special relativity, quantum mechanics, atomic physics, and nuclear physics. Science Requirement: Partial Fulfillment.

PHYS W1201y General Physics I 3 pts. Same course as PHYS V1201, but given off-sequence. The course will use elementary concepts from calculus. Students should therefore have some basic background in calculus or should be concurrently taking MATH V1101, Calculus I. The accompanying laboratory is PHYS W1291.

PHYS W1291y General Physics Laboratory 1 pt. Same course as PHYS W1291, but given off-sequence. Corequisite: PHYS W1201. This course is the laboratory for the corequisite lecture course and can be taken only during the same term as the corresponding lecture.

PHYS W1291x-W1292y General Physics Laboratory 1 pt. Corequisites: PHYS F1201-F1202 or PHYS V1201-V1202. This course is the laboratory for the corequisite lecture course (PHYS F1201-F1202 or PHYS V1201-V1202) and can be taken only during the same term as the corresponding lecture.

PHYS C1401x Introduction To Mechanics and Thermodynamics 3 pts. Corequisite: MATH V1101, or the equivalent. Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, temperature and heat, gas laws, the first and second laws of thermodynamics.

PHYS C1402y Introduction To Electricity, Magnetism, and Optics 3 pts. Prerequisite: PHYS C1401. Corequisite: MATH V1102, or the equivalent. Electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves, polarization, geometrical optics, interference, and diffraction.

PHYS C1403x Introduction to Classical and Quantum Waves 3 pts. Prerequisite: PHYS C1402. Corequisite: MATH V1201, or the equivalent. Classical waves and the wave equation, Fourier series and integrals, normal modes, wave-particle duality, the uncertainty principle, basic principles of quantum mechanics, energy levels, reflection and transmission coefficients, applications to atomic physics. Science Requirement: Partial Fulfillment.

PHYS C1493x Introduction to Experimental Physics 3 pts. Prerequisite: PHYS C1401 and C1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS C1493 and C1494.

PHYS C1494y Introduction to Experimental Physics 3 pts. Prerequisite: PHYS C1401 and C1402. Laboratory work associated with the two prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics. Note: Students cannot receive credit for both PHYS C1493 and C1494.

PHYS C1601x Physics, I: Mechanics and Relativity 3.5 pts. Corequisite: MATH V1102 or the equivalent. Fundamental laws of mechanics, kinematics and dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, introduction to special relativity and relativistic kinematics. The course is preparatory for advanced work in physics and related fields. Science Requirement: Partial Fulfillment.

PHYS C1602y Physics, II: Thermodynamics, Electricity, and Magnetism 3.5 pts. Prerequisite: PHYS C1601. Corequisite: MATH V1201 or the equivalent. Temperature and heat, gas laws, the first and second laws of thermodynamics, kinetic theory of gases, electric fields, direct currents, magnetic fields, alternating currents, electromagnetic waves. The course is preparatory for advanced work in physics and related fields. Science Requirement: Partial Fulfillment.

ASPH V1900y First-Year Seminar in Contemporary Physics and Astronomy 1 pt. Prerequisite or corequisite: any 1000-level course in the Physics or Astronomy Department. May be taken for Pass/Fail credit only. Lectures on current areas of research with discussions of motivation, techniques, and results, as well as difficulties and unsolved problems. Each student submits a written report on one field of active research.

PHYS C2601x Physics, III: Classical and Quantum Waves 3.5 pts. Prerequisite: PHYS C1402 or C1602. Corequisite: MATH V1202 or the equivalent. Classical waves and the wave equation, geometrical optics, interference and diffraction, Fourier series and integrals, normal modes, wave-particle duality, the uncertainty principle, basic principles of quantum mechanics, energy levels, reflection and transmission coefficients, the harmonic oscillator. The course is preparatory for advanced work in physics and related fields.

PHYS C2699y Experiments in Classical and Modern Physics 3 pts. Prerequisites: PHYS C1601(or C1401), C1602(or C1402), and C2601. Laboratory work associated with the three prerequisite lecture courses. Experiments in mechanics, thermodynamics, electricity, magnetism, optics, wave motion, atomic physics, and nuclear physics.

PHYS C2801x-C2802y Accelerated Physics, I and II 4.5 pts. Prerequisites: Advanced Placement in physics and mathematics, or the equivalent, and the instructor's permission. (A special placement meeting is held during Orientation.) This accelerated two-semester sequence covers the subject matter of PHYS C1601, C1602 and C2601, and is intended for those students who have an exceptionally strong background in both physics and mathematics. The course is preparatory for advanced work in physics and related fields. There is no accompanying laboratory; however, students are encouraged to take the intermediate laboratory, PHYS W3081, in the following year.

PHYS W3002y From Quarks To the Cosmos: Applications of Modern Physics 3.5 pts.Not offered in 2013-2014. Prerequisites: C2601 or C2802 This course reinforces basic ideas of modern physics through applications to nuclear physics, high energy physics, astrophysics and cosmology. The ongoing Columbia research programs in these fields are used as practical examples. The course is preparatory for advanced work in physics and related fields.

PHYS W3003y Mechanics 3 pts. Prerequisites: general physics, and differential and integral calculus. Newtonian mechanics, oscillations and resonance, conservative forces and potential energy, central forces, non-inertial frames of reference, rigid body motion, an introduction to Lagrange's formulation of mechanics, coupled oscillators, and normal modes.

PHYS W3007x Electricity and Magnetism 3 pts. Prerequisites: general physics, and differential and integral calculus. Electrostatics and magnetostatics, Laplace's equation and boundary-value problems, multipole expansions, dielectric and magnetic materials, Faraday's law, AC circuits, Maxwell's equations, Lorentz covariance, and special relativity.

PHYS W3008y Electromagnetic Waves and Optics 3 pts. Prerequisite: PHYS W3007. Maxwell's equations and electromagnetic potentials, the wave equation, propagation of plane waves, reflection and refraction, geometrical optics, transmission lines, wave guides, resonant cavities, radiation, interference of waves, and diffraction.

PHYS W3072y Seminar in Current Research Problems 2 pts. Open only to senior physics majors. May be taken ONLY for Pass/Fail credit, not for letter grade credit. A detailed study of a selected field of active research in physics. The motivation, techniques, and results obtained to the present, as well as the difficulties and unsolved problems.

PHYS W3081x or y Intermediate Laboratory Work 2 pts. Prerequisites: PHYS C2601 or PHYS C2802. Primarily for junior and senior physics majors. Other majors require the instructor's permission. May be repeated for credit by performing different experiments. The laboratory has available fifteen individual experiments, of which two are required per 2 points. Each experiment is chosen by the student in consultation with the instructor. Each section meets one afternoon per week, with registration in each section limited by the laboratory capacity. Experiments (classical and modern) cover topics in electricity, magnetism, optics, atomic physics, and nuclear physics.

PHYS W3083y Electronics Laboratory 3 pts. Registration is limited to the capacity of the laboratory. Corequisite or prerequisite: PHYS W3003 or W3007. A sequence of experiments in solid-state electronics, with introductory lectures.

PHYS V3500x or y Supervised Readings in Physics 3 pts. Prerequisites: the written permission of the faculty member who agrees to act as supervisor, and the permission of the director of undergraduate studies. Readings in a selected field of physics under the supervision of a faculty member. Written reports and periodic conferences with the instructor.

PHYS V3900x or y Supervised Individual Research 1-5 pts. Prerequisites: the written permission of the faculty member who agrees to act as supervisor, and the permission of the director of undergraduate studies. For specially selected physics majors, the opportunity to do a research project in contemporary physics under the supervision of a faculty member. A detailed report on the research is presented by the student when the project is completed.

PHYS G4003y Advanced Mechanics 3 pts. Prerequisites: differential and integral calculus, differential equations, and PHYS W3003 or the equivalent. Lagrange's formulation of mechanics, calculus of variations and the Action Principle, Hamilton's formulation of mechanics, rigid body motion, Euler angles, continuum mechanics, introduction to chaotic dynamics.

PHYS G4011y Particle Physics and Cosmology Prerequisites: PHYS C1403, C2601 or C2802; MATH V1202 or V1208; students are recommended but not required to have taken PHYS W3003 and W3007. An introduction to the basics of particle astrophysics and cosmology. Particle physics - introduction to the Standard Model and supersymmetry/higher dimension theories; Cosmology - Friedmann-Robertson-Walker line element and equation for expansion of universe; time evolution of energy/matter density from the Big Bang; inflationary cosmology; microwave background theory and observation; structure formation; dark energy; observational tests of geometry of universe and expansion; observational evidence for dark matter; motivation for existence of dark matter from particle physics; experimental searches of dark matter; evaporating and primordial black holes; ultra-high energy phenomena (gamma-rays and cosmic-rays).

PHYS G4018y Solid-State Physics 3 pts. Prerequisites: PHYS G4021 and G4023, or the equivalent. Introduction to solid-state physics: crystal structures, properties of periodic lattices, electrons in metals, band structure, transport properties, semiconductors, magnetism, and superconductivity.

PHYS G4019y Mathematical Methods of Physics 3 pts. Prerequisites: Differential and integral calculus; linear algebra; PHYS W3003 and PHYS W3007; or the permission of the instructor. This course will present a wide variety of mathematical ideas and techniques used in the study of physical systems. Topics will include: ordinary and partial differential equations; generalized functions; integral transforms; Green's functions; nonlinear equations, chaos, and solitons; Hilbert space and linear operators; Feynman path integrals; Riemannian manifolds; tensor analysis; probability and statistics. There will also be a discussion of applications to classical mechanics, fluid dynamics, electromagnetism, plasma physics, quantum mechanics, and general relativity.

PHYS G4021x-G4022y Quantum Mechanics, I and II 3 pts. Prerequisite: PHYS C2601 or C2802, or the equivalent. Formulation of quantum mechanics in terms of state vectors and linear operators, three-dimensional spherically symmetric potentials, the theory of angular momentum and spin, time-independent and time-dependent perturbation theory, scattering theory, and identical particles. Selected phenomena from atomic physics, nuclear physics, and elementary particle physics are described and then interpreted using quantum mechanical models.

PHYS G4023x Thermal and Statistical Physics 3 pts. Prerequisite: PHYS G4021 or the equivalent. Thermodynamics, kinetic theory, and methods of statistical mechanics; energy and entropy; Boltzmann, Fermi, and Bose distributions; ideal and real gases; blackbody radiation; chemical equilibrium; phase transitions; ferromagnetism.

PHYS G4040x Introduction to General Relativity 3 pts. Prerequisites: PHYS W3003, PHYS W3007 or the equivalent. Tensor algebra, tensor analysis, introduction to Riemann geometry. Motion of particles, fluid, and fields in curved spacetime. Einstein equation. Schwarzschild solution; test-particle orbits and light bending. Introduction to black holes, gravitational waves, and cosmological models.

PHYS G4050y Introduction to Particle Physics 3 pts.Not offered in 2013-2014. Prerequisites: PHYS C2601 or C2802, or the equivalent. Review of key concepts in quantum mechanics and special relativity. Conservation laws, decays, interactions, oscillations. Atoms, nuclei, hadrons (protons and neutrons) and quarks. Current theoertical and experimental challenges, including physics at the Large Hadron Collider.

PHYS G4075y Biology at Physical Extremes Prerequisites: One year each of introductory physics and biology. This is a combined lecture/seminar course designed for graduate students and advanced undergraduates. The course will cover a series of cases where biological systems take advantage of physical phenomena in counter intuitive and surprising ways to accomplish their functions. In each of these cases, we will discuss different physical mechanisms at work. We will limit our discussions to simple, qualitative arguments. We will also discuss experimental methods enabling the study of these biological systems. Overall, the course will expose students to a wide range of physical concepts involved in biological processes.