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Applied Physics

MS Degree

The program of study leading to the degree of Master of Science, while emphasizing continued work in basic

physics, permits many options in several applied physics specialties. The program may be considered simply as

additional education in areas beyond the bachelor’s level, or as preparatory to doctoral studies in the applied

physics fields of plasma physics, laser physics, or solid-state physics. All degree requirements must be

completed within five years. A candidate is required to maintain at least a 2.5 grade point average. M.S.

students must complete the Professional Development and Leadership Course, ENGI E4000, as a graduation

requirement.

Core Courses

APPH E4100: Quantum physics of matter (3 pts)

Basic theory of quantum mechanics, well and barrier problems, the harmonic oscillator, angular momentum identical

particles, quantum statistics, perturbation theory and applications to the quantum physics of atoms, molecules, and solids.

APPH E4110: Modern optics (3 pts)

Ray optics, matrix formulation, wave effects, interference, Gaussian beams, Fourier optics, diffraction, image

formation, electromagnetic theory of light, polarization and crystal optics, coherence, guided wave and fiber

optics, optical elements, photons, selected topics in nonlinear optics.

APPH E4112: Laser physics (3 pts)

Optical resonators, interaction of radiation and atomic systems, theory of laser oscillation, specific laser

systems, rate processes, modulation, detection, harmonic generation, and applications.

APPH E4200 : Physics of fluids (3 pts)

An introduction to the physical behavior of fluids for science and engineering students. Derivation of basic

equations of fluid dynamics: conservation of mass, momentum, and energy. Dimensional analysis. Vorticity.

Laminar boundary layers. Potential flow. Effects of compressibility, stratification, and rotation. Waves on a free

surface; shallow water equations. Turbulence.

APPH E4300 : Applied electrodynamics (3 pts)

Overview of properties and interactions of static electric and magnetic fields. Study of phenomena of time

dependent electric and magnetic fields including induction, waves, and radiation as well as special relativity.

Applications are emphasized.

APPH E4301: Introduction to plasma physics (3 pts)

Definition of a plasma. Plasmas in laboratories and nature, plasma production. Motion of charged particles in

electric and magnetic fields, adiabatic invariants. Heuristic treatment of collisions, diffusion, transport, and

resistivity. Plasma as a conducting fluid. Electrostatic and magnetostatic equilibria of plasmas. Waves in cold

plasmas. Demonstration of laboratory plasma behavior, measurement of plasma properties. Illustrative problems

in fusion, space, and nonneutral or beam plasmas.

Applied Mathematics

MS Degree

This 30-point program leads to a Master of Science degree. Students must complete five core courses and five electives. All degree requirements must be completed within five years. A candidate is required to maintain at least a 2.5 grade point average. M.S. students must complete the Professional Development and Leadership Course, ENGI E4000, as a graduation requirement. If a student admitted to the Applied Mathematics M.S. only program is interested in the Ph.D. program, the student must re-apply for admission.

Core Courses

 APMA E4001: Principles of applied mathematics Review of finite-dimensional vector spaces and elementary matrix theory. Linear transformations, change of basis, eigenspaces. Matrix representation of linear operators and diagonalization. Applications to difference equations, Markov processes, ordinary differential equations, and stability of nonlinear dynamical systems..  APMA E4101: Introduction to dynamical systems An introduction to the analytic and geometric theory of dynamical systems; basic existence, uniqueness and parameter dependence of solutions to ordinary differential equations; constant coefficient and parametrically forced systems; Fundamental solutions; resonance; limit points, limit cycles and classification of flows in the plane (Poincare-Bendixson Therem); conservative and dissipative systems; linear and nonlinear stability analysis of equilibria and periodic solutions; stable and unstable manifolds; bifurcations, e.g. Andronov- Hopf; sensitive dependence and chaotic dynamics; selected applications.  APMA E4150: Applied functional analysis Introduction to modern tools in functional analysis that are used in the analysis of deterministic and stochastic partial differential equations and in the analysis of numerical methods: metric and normed spaces.  APMA E4200: Partial differential equations Techniques of solution of partial differential equations. Separation of the variables. Orthogonality and characteristic functions, nonhomogeneous boundary value problems.  APMA E4204: Functions of a complex variable Complex numbers, functions of a complex variable, differentiation and integration in the complex plane. Analytic functions, Cauchy integral theorem and formula, Taylor and Laurent series, poles and residues, branch points, evaluation of contour integrals. Conformal mapping, Schwarz-Christoffel transformation. Applications to physical problems.  APMA E4300: Introduction to numerical methods Introduction to fundamental algorithms and analysis of numerical methods commonly used by scientists, mathematicians and engineers. Designed to give a fundamental understanding of the building blocks of scientific computing that will be used in more advanced courses in scientific computing and numerical methods for PDEs (e.g. APMA E4301, E4302).  APMA E4301: Numerical methods for partial differential equations Numerical solution of differential equations, in particular partial differential equations arising in various fields of application. Presentation emphasizes finite difference approaches to present theory on stability, accuracy, and convergence with minimal coverage of alternate approaches (left for other courses).  APMA E6301: Analytic methods for partial differential equations Introduction to analytic theory of PDEs of fundamental and applied science; wave (hyperbolic), Laplace and Poisson equations (elliptic), heat (parabolic) and Schroedinger (dispersive) equations; fundamental solutions, Green's functions, weak/distribution solutions, maximum principle, energy estimates, variational methods, method of characteristics; elementary functional analysis and applications to PDEs; introduction to nonlinear PDEs, shocks; selected applications.  APMA E6302: Numerical analysis for partial differential equations Numerical analysis of initial and boundary value problems for partial differential equations. Convergence and stability of the finite difference method, the spectral method, the finite element method and applications to elliptic, parabolic, and hyperbolic equations.

Students must also take a required Research Seminar course, APMA E6100 x or y. Students attend at least three

Applied Mathematics research seminars within the Department of Applied Physics and Applied Mathematics

and submit reports on each.

Medical Physics

Medical Physics is an applied branch of physics concerned with the application of the concepts and methods of

physics to the diagnosis and treatment of human disease. Medical Physicists are concerned with clinical service

and consultation, research and development, and teaching. Our CAMPEP-accredited Program is designed to

prepare students for professional careers in the field of Medical Physics. It is registered with the State of New

York, is administered by faculty from the Fu Foundation School of Engineering and Applied Science in

collaboration with faculty from the College of Physicians and Surgeons and the Mailman School of Public

Health, leads to a Master of Science (M.S.) degree, and provides preparation toward certification by the

American Board of Radiology.

Specializations :

Radiation Therapy Physicists perform acceptance testing and commissioning of new equipment, calibrate

radiotherapy units and maintain their clinical information, contribute to the development of therapeutic

techniques, design treatment plans, and assure the safe and effective delivery of radiation as prescribed in

patient care.

Diagnostic Radiology Physicists contribute to the advancement and effectiveness of radiological imaging

exams and procedures by helping to develop improved imaging techniques and using them for the diagnosis of

disease in patients.

Nuclear Medicine Physicists ensure correct and safe application of radioactive molecular-agents used in the

diagnosis and treatment of disease, assist in the introduction of new agents including their dosimetry, assess the

performance of Nuclear Medicine equipment, and contribute to the development of quality assurance programs.

Medical Health Physicists contribute to the protection of patients and the public from excessive radiation by

establishing and monitoring radiation safety procedures and ensuring compliance with applicable federal and

state regulations.

Core Curriculum

The Program consists of a core curriculum of medical and nuclear physics courses, a laboratory course,

anatomy, two practicums, a tutorial, one elective, and a seminar. Specific course requirements are:

APPH E4010 Introduction to nuclear science

APPH E4330 Radiobiology for medical physicists

APPH E4710 Radiation instrumentation lab, I

APPH E4550 Medical physics seminar

APPH E4500 Health physics

APPH E4501 Medical health physics tutorial

APPH E4600 Fundamentals of radiological physics

& radiation dosimetry

APBM E4650 Anatomy for physicists & engineers

APPH E6319 Clinical nuclear medicine physics

APPH E6330 Diagnostic radiology physics

APPH E6335 Radiation therapy physics

Applied Physics and Mathematics Faculty