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PROGRAMS OF STUDY & COURSE DESCRIPTIONS
Physics (PHY)

Major: Yeshiva College
Thirty-two credits in physics courses. PHY 1041 R&L, 1042 R&L, 1120, 1810 and 17 credits in PHY electives, which must include at least three courses from the following: PHY 1221, 1321, 1510, 1621 and MAT 1412, 1413. MAT 1510 and 2105 are strongly recommended.
Pre-engineering students who wish to fulfill the requirements for a physics major may satisfy up to nine credits with coursework, chosen with the approval of the senior professor, at Columbia University School of Engineering and Applied Science.

Minor: Yeshiva College
Twenty-two credits in physics courses.
All students either majoring or minoring in physics must consult with the senior professor for guidance as to an appropriate program.

1021R The Physical Universe. 2 credits.
Interdisciplinary course for non-science majors, emphasizing the main ideas in astronomy and the physics of motion, light, heat, and electricity. Not open to students who have completed any college course in physics.
Corequisite: PHY 1021L.

1021L The Physical Universe Lab. Two hours. 1 credit.
Laboratory experiments designed to help students master the principles covered in PHY 1021R.
Laboratory fee: $40.
Corequisite: PHY 1021R.

1024C Great Ideas and Experiments in Modern Physics 3 credits.
Oriented toward non-science students, explores the great ideas that shaped physics during the early part of the 20th century: the theory of relativity and the quantum revolution. Hands-on experiments investigate the ideas of particle creation and destruction, nuclear reactions, magnetic resonance, atomic structure, and crystallography.

1026R Introduction to Astronomy: Planets. 2 credits.
History of astronomy; early models of the universe. The Copernican Revolution and the Newtonian Universe. The solar system, from terrestrial and Jovian planets to comets and asteroids. Possibility of organic life elsewhere in the solar system and beyond. Future evolution of our planetary system. Recently discovered planetary systems around other stars.
Corequisite: PHY 1026L.

1026L Introduction to Astronomy: Planets—Laboratory. 1 credit.
Hands-on experiments and computer simulations illustrating concepts introduced in the course. Observations of planets, stars, galaxies, and nebulae with the university’s 12-inch telescope.
Laboratory Fee: $50.
Corequisite: PHY 1026R.

1027R Introduction to Astronomy: Stars. 2 credits.
Birth, life, and death of stars: from protostars, main sequence, red giant stages to white dwarfs, neutron stars, and black holes. The Milky Way galaxy. Evolution of galaxies and their types. Hubble law and expansion of the universe. Big bang and inflation theory.
Corequisite: PHY 1027L.

1027L Introduction to Astronomy: Stars-Laboratory. 1 credit.
Hands-on experiments and computer simulations illustrating concepts introduced in the course. Observations of planets, stars, galaxies, and nebulae with the university’s 12-inch telescope.
Laboratory Fee: $50.
Corequisite PHY 1027R.

1031R, 1032R Introductory Physics-Lectures. Four hours of lecture. One hour of recitation. 4 credits.
Non–calculus-based version of PHY 1041R–1042R.
Corequisite: PHY 1031L, PHY 1032L.

1031L, 1032L Introductory Physics-Laboratory. Two hours of lab. 1 credit.
Non–calculus-based version of PHY 1041L–1042L.
Laboratory fee: $40 per semester.
Corequisite: PHY 1031R, PHY 1032R.

1036 Physics Problems for Pre-Health. 1 credit.
Complement to PHY 1031–1032. Topics include modern physics, optics, fluid mechanics, and other subjects of interest to the health sciences. Emphasis on problem-solving techniques.
Prerequisite: PHY 1031, PHY 1032.

1041R, 1042R General Physics-Lectures. Four hours of lecture. One hour of recitation. 4 credits.
Introduction to Newtonian mechanics for particles, systems of particles, and rigid bodies. Notions of fluid mechanics and elasticity. The physics of waves and geometrical and physical optics. Theory of gravitation. Theory of electricity and magnetism. Direct current and alternating current circuits. The Maxwell’s equations.
Prerequisite or corequisite: MAT 1412, 1413.
Corequisite: PHY 1041L, PHY 1042L.

1041L, 1042L General Physics-Laboratory. Two hours. 1 credit.
Laboratory experiments designed to help students master the principles covered in PHY 1041R–1042R. Covers mechanics, heat, optics, elasticity, electricity, circuits, and magnetism.
Laboratory fee: $40 per semester.
Corequisite: PHY 1041R, PHY 1042R.

1041H, 1042H Honors General Physics. 4 credits.
Complements 1041R, 1042R. Lectures with an honors recitation section and/or honors laboratory section.

1110 Waves and Optics. 3 credits.
Introduction to normal modes in discrete and continuous systems, linearization, basic Fourier analysis, and applications. Traveling waves on strings, sound waves, introduction to electromagnetic waves. Wave reflection, refraction, and partial transmission. Doppler effect. Waves on transmission lines and characteristic impedance. Group velocity, pulses, wave packets, Fourier integral, bandwidth theorem. Elements of geometrical optics. Fermat’s principle. Physical optics: interference, diffraction, limit of resolution, applications.
Prerequisites: PHY 1041, PHY 1042.
Corequisite: MAT 1510.

1120 or 1120H Introduction to Modern Physics. 3 credits.
Introduction to Einstein’s theory of relativity. Time dilation and length contraction. E=MC2. The great experiments that shaped 20th-century physics. The blackbody radiation. The basis of kinetic theory. Quantum theory and Bohr’s model of the atom. Waves of matter, wave-particle duality and the uncertainty principle. Schroedinger’s equation.
Prerequisites: PHY 1041, PHY 1042.

1221 or 1221H Classical Mechanics. 4 credits.
Particle motion in space, time or velocity-dependent potentials. Damped and driven oscillations and resonances. Elements of nonlinearity and chaos. Non-inertial reference systems. Motion relative to the Earth. Central forces. Planetary motion. Orbital dynamics.
Prerequisites: PHY 1041, PHY 1042. Recommended: MAT 1510.

1222 Advanced Mechanics. 4 credits.
Systems of particles. Variable mass. Collision theory. Lagrangian mechanics. Constraints. Variational calculus and Hamilton’s equations. Rotations of rigid bodies in two and three dimensions. Euler’s equations. Tensor analysis. Small coupled oscillations and normal coordinates. Fluid mechanics. Viscosity. Relativistic mechanics.
Prerequisite: PHY 1041, PHY 1042. Recommended: MAT 1510, MAT 2105, PHY 1221.

1222B Mechanics for Engineers II. 4 credits.
Same as PHY 1222 with added material in mechanics designed specifically for pre-engineering majors. Statics. Methods of analysis of trusses. Cables under loads.

1321 Electromagnetic Theory. 3 credits.
Review of vector calculus. Electro- and magnetostatics, multipole expansions, time-dependent fields. Development of Maxwell’s equations. Laplace and Poisson equations, boundary value problems. Electromagnetic wave equation, plane waves in a vacuum. Poynting vector, “blue sky law.” Microscopic and phenomenological theories of dielectric and magnetic materials. Resistors, capacitors, inductors, and their uses in circuits, transformers; generalized forces on charges in electromagnetic fields.
Prerequisite: PHY 1042 (or PHY 1032 with permission of the instructor).
Corequisite: MAT 1510 or equivalent.

1322 Electromagnetic Theory II. 3 credits.
Relativistic transformation of fields and covariance of Maxwell’s equations. Polarizability tensor, electrodynamics in matter. Electromagnetic radiation by accelerating charges; Lienard-Wiechert potentials, multipole radiation, bremsstrahlung, synchrotron radiation, applications to astrophysical sources. Antennas. Electromagnetic wave propagation in matter. Electromagnetic basis of physical optics. Fresnel equations, Kirchoff diffraction theory. Wave-guides and cavity resonators.
Prerequisite: PHY 1321.

1401 Introduction to Solid State Physics. 3 credits.
A survey of the properties of condensed matter. Classification of crystalline lattices. Elements of crystallography. Cohesive forces in solids. Vibrations of crystals. Quantization. Debye and Einstein theories of phonons and thermal conductivity. Free electron theory of metals. Bloch functions and band theory. The Fermi surface. Semiconductors. Survey of advanced topics: excitations in lattices (plasmons and polarons), superconductivity, magnetic materials and models, theory of crystalline defects and alloys.
Prerequisite: PHY 1120.

1510 Elements of Thermodynamics and Statistical Mechanics. 3 credits.
The laws of thermodynamics. Entropy. Equations of state. Phase transitions. Thermodynamic potentials. The third Law. Distribution functions. Theory of ensembles. Statistical formulation of temperature. Quantum and classical ideal gasses. Electronic conductance. Bose-Einstein statistics: phonons, Planck’s Law, Bose condensation.
Prerequisites: PHY 1041, PHY 1042.

1520 Advanced Statistical Mechanics. 4 credits.
Gibbs theory of ensembles. Quantum statistics. Superfluidity. Quantum transport. Virial expansions. Magnetic systems and the Ising model. Theory of phase transitions. Ideas of the renormalization group. Random walks, accretion and percolation phenomena. Complexity and self-organization. Non-equilibrium statistical mechanics. Boltzmann’s equation.

1621 or 1621H Introduction to Quantum Mechanics. 3 credits.
Wave-particle duality; solutions of Schroedinger equation in one dimension for square well and barrier potential, harmonic oscillator, and rigid rotator with fixed axis; observables, expectation values, uncertainty relations; wave packets. Applications to quantum wells and superlattices, molecular beam epitaxy and scanning tunneling microscopy.
Prerequisite: PHY 1120.

1622 Advanced Quantum Theory. 3 credits.
Perturbation theory, approximations; solution of Schroedinger equation for the hydrogen atom; Pauli exclusion principle, electron spin; atomic spectroscopy and second quantization.
Prerequisite: PHY 1621.

1724 Electronics. 2 credits.
Electronic devices and their use in power supplies, audio and radio frequency amplifiers, operational amplifiers, and instrumentation circuits. Electro-chemical and biomedical applications; generation, processing, and analysis of signal waveforms related to speech, music, optical, and biophysical phenomena, and radio and television broadcasting.
Prerequisite: PHY 1032 or 1042 R&L.

1810 or 1810H, 1820 Intermediate Experimental Physics I, II. One hour of lecture. Three hours of lab. 2 credits.
(Formerly PHY 1801L, 1802L). 
Experimental exercises in techniques of modern experimental physics and engineering. Covers the fields of mechanics, analog communication electronics, transmission lines and wave-guides, physical and fiber optics, atomic spectroscopy, nuclear statistics, nuclear spectroscopy, interferometry, and laser physics. Recent examples: impedance divider, gravitational acceleration, thermocouple junction, microwave optics, mechanical phonons, Millikan’s experiment, dielectric constant of water, Stephan-Boltzmann law, radioactivity and Poisson statistics, Michelson interferometer.
Laboratory fee: $50 per semester.
Prerequisites: PHY 1041, PHY 1042 (or PHY 1031, PHY 1032 and permission of the instructor).

1830 Advanced Experimental Physics. Four hours of lab. 2 credits.
(Formerly 1803L). 
A selection of independent projects designed to prepare students for contemporary research in physics. Recent examples: statistics of discharges, temperature dependence of conductivity, Einstein temperature, and the Hall effect.
Laboratory fee: $50 per semester.
Prerequisites: PHY 1810, PHY 1820.

2255R, 2256R Biophysics-Lectures. 2 credits.
Thermodynamics of the body, pressure, hemodynamics, nerve cells, transmission of signals, electrocardiography, transport phenomena, diffusion, osmosis, radiation, production and use of X-rays, nuclear medicine, physics of the eye and ear, exponential growth and decay, measurement, instrumentation.
Prerequisites: PHY 1041, PHY 1042, BIO 1011R, BIO 1012R.

2255L, 2256L Biophysics-Laboratory. Two hours. 1 credit.
Experiments to accompany 2255R, 2256R.
Laboratory fee: $50 per semester.
Corequisite: PHY 2255R, PHY 2256R.

2601, 2602 Special and General Relativity. 3 credits.
Einstein’s special and general theories of relativity; underlying physical and mathematical concepts; formulation of Einstein’s theory of gravitation; mathematical structure, observational tests, exact and approximate methods of solution; problem of gravitational radiation; theory of motion of ponderable bodies.
Prerequisites: PHY 1120, PHY 1221.

3301 or 3301H Computational Methods in the Physical Sciences. 3 credits.
Basic use of symbolic logic software and exploration of different areas of physics through numerical and computational techniques, possibly including random-walk models, accretion phenomena, Monte Carlo methods in statistical physics, cellular automata, complexity, chaos, and planetary motion. Methods of interpolation, rates of convergence, projection methods, boundary problems and singular perturbation methods.

4901, 4902 Independent Study.

4911 Guided Project. (Variable credit).
Independent individual research projects done under the guidance of a physics faculty member.

4991 or 4991H The New Physics and Astronomy. 3 credits.
Review of the new problems and areas that have reshaped physics in the last 30 years: theory of chaos, the quark and the Standard Model, the new cosmology, and the inflationary universe. Physics of scales and the renormalization group. The quantum fluids, and superconductivity and superfluidity. The new theory of complexity, quantum transport.
Prerequisites: PHY 1041, PHY 1042, PHY 1120, or permission of the instructor.