# Courses

**APAM 1601 Introduction to computational mathematics and physics. ***3 points*.

Lect: 3.

Introduction to computational methods in applied mathematics and physics. Students develop solutions in a small number of subject areas to acquire experience in the practical use of computers to solve mathematics and physics problems. Topics change from year to year. Examples include elementary interpolation of functions, solution of nonlinear algebraic equations, curve-fitting and hypothesis testing, wave propagation, fluid motion, gravitational and celestial mechanics, and chaotic dynamics. Basic requirement for this course is one year of college-level calculus and physics; programming experience is not required.

**APAM 4901 Seminar: Problems in Applied Mathematics. ***0 points*.

0 pts. Lect: 1.

This course is required for, and can be taken only by, all applied mathematics majors in the junior year. Prerequisites or corequisites: APMA E4200 and E4204 or their equivalents. Introductory seminars on problems and techniques in applied mathematics. Typical topics are nonlinear dynamics, scientific computation, economics, operations research, etc.

**APAM E3105 Programming Methods for Scientists and Engineers. ***3 points*.

Lect: 2.5. Lab: 1.**Not offered during 2020-21 academic year.**

Introduction to modern techniques of computer programming for the numerical solutions to familiarity with basic and advanced concepts of modern numerical programming and acquire practical experience solving representative problems in math and physics.

**APAM E3999 UNDERGRADUATE FIELDWORK. ***1.00-2.00 points*.

1-2 pts.

Prerequisites: Obtained internship and approval from faculty advisor.

Prerequisites: Obtained internship and approval from faculty advisor. May be repeated for credit, but no more than 3 total points may be used toward the 128credit degree requirement. Only for APAM undergraduate students who include relevant off-campus work experience as part of their approved program of study. Final report and letter of evaluation required. Fieldwork credits may not count toward any major core, technical, elective, and nontechnical requirements. May not be taken for pass/fail credit or audited

**APAM E4999 Supervised internship. ***1 point*.

1-3 pts.

Only for master's students in the Department of Applied Physics and Applied Mathematics who may need relevant work experience a part of their program of study. Final report required. This course may not be taken for pass/fail or audited.

**APAM E6650 Research project. ***1 point*.

1-6 pts.

Prerequisites: Written permission from instructor and approval from adviser.

Written permission from instructor and approval from adviser. This course may be repeated for credit. A special investigation of a problem in nuclear engineering, medical physics, applied mathematics, applied physics, and/or plasma physics consisting of independent work on the part of the student and embodied in a formal report.

Fall 2020: APAM E6650 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APAM 6650 | 010/12581 | |
Qiang Du | 1 | 1/10 |

APAM 6650 | 011/12582 | |
Alexander Gaeta | 1 | 0/10 |

APAM 6650 | 014/12583 | |
Klaus Hamacher | 1 | 2/10 |

APAM 6650 | 017/12584 | |
Kyle Mandli | 1 | 0/10 |

APAM 6650 | 018/12585 | |
Chris Marianetti | 1 | 0/10 |

APAM 6650 | 020/12586 | |
Gerald Navratil | 1 | 1/10 |

APAM 6650 | 026/12587 | |
Adam Sobel | 1 | 1/10 |

APAM 6650 | 031/12588 | |
Michael Weinstein | 1 | 0/10 |

APAM 6650 | 037/12589 | |
Nanfang Yu | 1 | 0/10 |

APAM 6650 | 038/22280 | |
Kui Ren | 1 | 4/10 |

**APAM E9301 Doctoral research. ***0 points*.

0-15 pts.

Prerequisite: the qualifying examination for the doctorate. Required of doctoral candidates.

Fall 2020: APAM E9301 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APAM 9301 | 005/12560 | |
Allen Boozer | 0 | 1/10 |

APAM 9301 | 009/12561 | |
Qiang Du | 0 | 5/10 |

APAM 9301 | 010/12562 | |
Alexander Gaeta | 0 | 5/10 |

APAM 9301 | 011/12563 | |
Oleg Gang | 0 | 1/10 |

APAM 9301 | 012/12564 | |
Eitan Grinspun | 0 | 0/10 |

APAM 9301 | 013/12565 | |
Irving Herman | 0 | 1/10 |

APAM 9301 | 015/12566 | |
Kyle Mandli | 0 | 3/10 |

APAM 9301 | 016/22306 | |
Chris Marianetti | 0 | 3/10 |

APAM 9301 | 017/12567 | |
Michael Mauel | 0 | 5/10 |

APAM 9301 | 018/12568 | |
Gerald Navratil | 0 | 3/10 |

APAM 9301 | 021/12569 | |
Aron Pinczuk | 0 | 0/10 |

APAM 9301 | 022/12570 | |
Lorenzo Polvani | 0 | 2/10 |

APAM 9301 | 024/12571 | |
Adam Sobel | 0 | 2/10 |

APAM 9301 | 025/12572 | |
Marc Spiegelman | 0 | 1/10 |

APAM 9301 | 026/12573 | |
Latha Venkataraman | 0 | 1/10 |

APAM 9301 | 028/12574 | |
Michael Weinstein | 0 | 1/10 |

APAM 9301 | 030/12575 | |
Chris Wiggins | 0 | 1/10 |

APAM 9301 | 031/12576 | |
Shalom Wind | 0 | 1/10 |

APAM 9301 | 032/12577 | |
Cheng Wuu | 0 | 2/10 |

APAM 9301 | 034/12578 | |
Nanfang Yu | 0 | 5/10 |

APAM 9301 | 035/12579 | |
Kui Ren | 0 | 1/10 |

APAM 9301 | 036/12580 | |
Steven Sabbagh | 0 | 1/10 |

**APAM E9800 Doctoral research instruction. ***3 points*.

3, 6, 9, or 12 pts.

A candidate for the Eng.Sc.D. degree must register for 12 points of doctoral research instruction. Registration for APAM E9800 may not be used to satisfy the minimum residence requirement for the degree.

**APAM E9900 Doctoral dissertation. ***0 points*.

0 pts.

A candidate for the doctorate may be required to register for this course every term after the coursework has been completed, and until the dissertation has been accepted.

**APBM E4650 Anatomy for physicists and engineers. ***3 points*.

Lect: 3.

Prerequisites: Engineering or physics background

Systemic approach to the study of the human body from a medical imaging point of view: skeletal, respiratory, cardiovascular, digestive, and urinary systems, breast and women's issues, head and neck, and central nervous system. Lectures are reinforced by examples from clinical two- and three-dimensional and functional imaging (CT, MRI, PET, SPECT, U/S, etc.).

Fall 2020: APBM E4650 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APBM 4650 | 001/11979 | T Th 4:00pm - 5:20pm Online Only |
Monique Katz, Anna Rozenshtein, Matthew Moy | 3 | 15/24 |

**APCH E Soft Condensed Matter. ***0 points*.

Prerequisites: (MSAE E3111) and (CHEN E3010) or (CHEN E3120) or

**APMA E Multivariable Calculus for Engineers and Applied Scientists. ***0 points*.

**APMA E2000 MULTV. CALC. FOR ENGI ＆ APP SCI. ***4.00 points*.

Lect: 3.

Differential and integral calculus of multiple variables. Topics include partial differentiation; optimization of functions of several variables; line, area, volume, and surface integrals; vector functions and vector calculus; theorems of Green, Gauss, and Stokes; applications to selected problems in engineering and applied science

Fall 2020: APMA E2000 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 2000 | 001/12591 | T Th 8:40am - 9:55am Online Only |
Amir Sagiv | 4.00 | 67/96 |

APMA 2000 | 002/12592 | T Th 1:10pm - 2:25pm Online Only |
Drew Youngren | 4.00 | 121/110 |

APMA 2000 | 003/12593 | T Th 5:40pm - 6:55pm Online Only |
Drew Youngren | 4.00 | 60/96 |

**APMA E2101 Introduction to Applied Mathematics. ***3 points*.

Lect: 3.

Prerequisites: Calculus III.

A unified, single-semester introduction to differential equations and linear algebra with emphases on (1) elementary analytical and numerical technique and (2) discovering the analogs on the continuous and discrete sides of the mathematics of linear operators: superposition, diagonalization, fundamental solutions. Concepts are illustrated with applications using the language of engineering, the natural sciences, and the social sciences. Students execute scripts in Mathematica and MATLAB (or the like) to illustrate and visualize course concepts (programming not required).

**APMA E3101 Linear Algebra. ***3 points*.

Lect: 3.

Matrix algebra, elementary matrices, inverses, rank, determinants. Computational aspects of solving systems of linear equations: existence-uniqueness of solutions, Gaussian elimination, scaling, ill-conditioned systems, iterative techniques. Vector spaces, bases, dimension. Eigenvalue problems, diagonalization, inner products, unitary matrices.

Fall 2020: APMA E3101 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 3101 | 001/12605 | T Th 10:10am - 11:25am Online Only |
Yuan He | 3 | 29/52 |

**APMA E3102 Partial Differential Equations. ***3 points*.

Lect: 3.

Prerequisites: (MATH UN2030) or the equivalent

Introduction to partial differential equations; integral theorems of vector calculus. Partial differential equations of engineering in rectangular, cylindrical, and spherical coordinates. Separation of the variables. Characteristic-value problems. Bessel functions, Legendre polynomials, other orthogonal functions; their use in boundary value problems. Illustrative examples from the fields of electromagnetic theory, vibrations, heat flow, and fluid mechanics.

**APMA E3900 Undergraduate Research in Applied Mathematics. ***0 points*.

0-4 pts.

Prerequisites: Written permission from instructor and approval from adviser.

This course may be repeated for credit, but no more than 6 points of this course may be counted toward the satisfaction of the B.S. degree requirements. Candidates for the B.S. degree may conduct an investigation in applied mathematics or carry out a special project under the supervision of the staff. Credit for the course is contingent upon the submission of an acceptable thesis or final report.

Fall 2020: APMA E3900 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 3900 | 005/22253 | |
Kyle Mandli | 0 | 4/10 |

**APMA E4001 Principles of Applied Mathematics. ***3 points*.

Lect: 3.

Prerequisites: Introductory Linear Algebra required. Ordinary Differential Equations recommended.

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. Inner product spaces, projection operators, orthogonal bases, Gram-Schmidt orthogonalization. Least squares method, pseudo-inverses, singular value decomposition. Adjoint operators, Hermitian and unitary operators, Fredholm Alternative Theorem. Fourier series and eigenfunction expansions. Introduction to the theory of distributions and the Fourier Integral Transform. Green's functions. Application to Partial Differential Equations.

**APMA E4101 Introduction to Dynamical Systems. ***3 points*.

Lect: 3.

Prerequisites: (APMA E2101) and (APMA E3101)

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. ***3 points*.

Prerequisites: Advanced calculus and course in basic analysis, or instructor's permission.

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. Banach space of continuous functions, measurable spaces, the contraction mapping theorem, Banach and Hilbert spaces bounded linear operators on Hilbert spaces and their spectral decomposition, and time permitting distributions and Fourier transforms.

**APMA E4200 Partial Differential Equations. ***3 points*.

Prerequisites: Course in ordinary differential equations.

Techniques of solution of partial differential equations. Separation of the variables. Orthogonality and characteristic functions, nonhomogeneous boundary value problems. Solutions in orthogonal curvilinear coordinate systems. Applications of Fourier integrals, Fourier and Laplace transforms. Problems from the fields of vibrations, heat conduction, electricity, fluid dynamics, and wave propagation are considered.

Fall 2020: APMA E4200 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4200 | 001/12607 | T Th 1:10pm - 2:25pm Online Only |
Qiang Du | 3 | 93/200 |

**APMA E4204 Functions of a Complex Variable. ***3 points*.

Prerequisites: (MATH UN1202) or the equivalent.

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.

Fall 2020: APMA E4204 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4204 | 001/12610 | M W 10:10am - 11:25am 412 Schapiro Cepser |
Kui Ren | 3 | 79/80 |

**APMA E4300 Computational Math: Introduction to Numerical Methods. ***3 points*.

Lect: 3.

Prerequisites: (MATH UN1201) and (MATH UN2030) and (APMA E3101) and (ENGI E1006) or their equivalents. Programming experience in Python extremely useful.

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). Topics include numerical solutions of algebraic systems, linear least-squares, eigenvalue problems, solution of non-linear systems, optimization, interpolation, numerical integration and differentiation, initial value problems and boundary value problems for systems of ODE's. All programming exercises will be in Python.

Fall 2020: APMA E4300 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4300 | 001/12612 | T Th 2:40pm - 3:55pm Online Only |
Marc Spiegelman | 3 | 122/150 |

**APMA E4301 Numerical Methods for Partial Differential Equations. ***3 points*.

Lect: 3.

Prerequisites: (APMA E4300) and (APMA E3102) or (APMA E4200) or or equivalents.

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). Method coverage includes explicit and implicit time-stepping methods, direct and iterative solvers for boundary-value problems.

**APMA E4302 Methods in Computational Science. ***3 points*.

Lect: 3.

Prerequisites: (APMA E4300) and application and knowledge in C, Fortran or similar complied language.

Introduction to the key concepts and issues in computational science aimed at getting students to a basic level of understanding where they can run simulations on machines aimed at a range of applications and sizes from a single workstation to modern super-computer hardware. Topics include but are not limited to basic knowledge of UNIX shells, version control systems, reproducibility, Open MP, MPI, and many-core technologies. Applications will be used throughout to demonstrate the various use cases and pitfalls of using the latest computing hardware.

Fall 2020: APMA E4302 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4302 | 001/12613 | T Th 1:10pm - 2:25pm 303 Seeley W. Mudd Building |
Kyle Mandli | 3 | 23/35 |

**APMA E4400 Introduction to Biophysical Modeling. ***3 points*.

Lect: 3.

Prerequisites: (PHYS UN1401) and (APMA E2101) or (MATH UN2030) or or equivalent.

Introduction to physical and mathematical models of cellular and molecular biology. Physics at the cellular scale (viscosity, heat, diffusion, statistical mechanics). RNA transcription and regulation of genetic expression. Genetic and biochemical networks. Bioinformatics as applied to reverse-engineering of naturally-occurring networks and to forward-engineering of synthetic biological networks. Mathematical and physical aspects of functional genomics.

**APMA E4901 Seminar: Problem in Applied Mathematics. ***0 points*.

Lect: 1.

This course is required for, and can be taken only by, all applied mathematics majors in the junior year. Introductory seminars on problems and techniques in applied mathematics. Typical topics are nonlinear dynamics, scientific computation, economics, operation research, etc.

Fall 2020: APMA E4901 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4901 | 001/13441 | W 11:40am - 12:55pm Online Only |
Chris Wiggins | 0 | 58/60 |

**APMA E4903 Seminar: Problems in Applied Mathematics. ***3 points*.

3-4 pts. Lect: 1

For 4 pts. credit, term paper required. This course is required for all applied mathematics majors in the senior year. Examples of problem areas are nonlinear dynamics, asymptotics, approximation theory, numerical methods, etc. Approximately three problem areas are studies per term.

Fall 2020: APMA E4903 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APMA 4903 | 001/13442 | M W 11:40am - 12:55pm Online Only |
Chris Wiggins | 3 | 50/60 |

**APMA E4990 Special Topics in Applied Mathematics. ***1 point*.

1-3 pts. Lect: 3.

Prerequisites: Advanced calculus and junior year applied mathematics, or their equivalents.

This course may be repeated for credit. Topics and instructors from the Applied Mathematics Committee and the staff change from year to year. For advanced undergraduate students and graduate students in engineering, physical sciences, biological sciences, and other fields.

**APMA E6100 Research Seminar. ***0 points*.

Lect: 3. **Not offered during 2020-21 academic year.**

Prerequisites: (MATH UN3027) or (APMA E4101) or (MATH UN3028) or (APMA E4200) or (MATH UN2010) or (APMA E3101) or their equivalents.

Corequisites: MATH UN3027

APMA E4101

MATH UN3028

APMA E4200

MATH UN2010

APMA E3101

This course is an M.S. degree requirement. Students attend at least three Applied Mathematics research seminars within the Department of Applied Physics and Applied Mathematics and submit reports on each.

**APMA E6209 Approximation Theory. ***3 points*.

Lect: 2.**Not offered during 2020-21 academic year.**

Prerequisites: (MATH GU4061) or or some knowledge of modern analysis.

Theory and application of approximate methods of analysis from the viewpoint of functional analysis. Approximate numerical and analytical treatment of linear and nonlinear algebraic, differential, and integral equations. Topics include function spaces, operators in normed and metric spaces, fixed point theorems and their applications.

**APMA E6301 Analytic methods for partial differential equations. ***3 points*.

Lect: 2.

Prerequisites: (APMA E3101) and (APMA E4200) or their equivalents, Advanced calculus, basic concepts in analysis, or instructor's permission.

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 of partial differential equations. ***3 points*.

Lect: 2.

Prerequisites: (APMA E3102) or (APMA E4200)

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.

**APMA E6304 Integral transforms. ***3 points*.

Lect: 2.**Not offered during 2020-21 academic year.**

Prerequisites: (APMA E4204) and (MATH UN2030) or their equivalents.

Laplace, Fourier, Hankel, and Mellin transforms. Selection of suitable transform for a given partial differential equation boundary value problem. Operational properties of transforms. Inversion theorems. Approximate evaluation of inversion integrals for small and large values of parameter. Application to the solution of integral equations.

**APMA E6901 Special topics in applied mathematics. ***3 points*.

Lect: 3.

Prerequisites: Advanced calculus and junior year applied mathematics, or their equivalents.

This course may be repeated for credit. Topics and instructors from the Applied Mathematics Committee and the staff change from year to year. For students in engineering, physical sciences, biological sciences, and other fields.

**APMA E8308 Asymptotic methods in applied mathematics. ***3 points*.

Lect: 2. Not offered in 2016-2017.**Not offered during 2020-21 academic year.**

Prerequisites: (APMA E4204) or or the equivalent.

Asymptotic treatment of ordinary and partial differential equations in problems arising in applied mathematics. Asymptotic series. Asymptotic evaluation of integrals. Expansion of solutions of ordinary differential equations: connection problem and turning points. Stoke's phenomenon. Differential equations with a parameter: "boundary layer" phenomenon. Application to partial differential equations: problems from fluid dynamics, wave propagation theory, electromagnetic theory.

**APMA E9101 Research. ***1 point*.

1-4 pts.

Prerequisites: Prerequisite: the permission of the supervising faculty member.

This course may be repeated. Advanced study in a special area.

**APMA E9102 Research. ***1 point*.

1-4 pts.

Prerequisites: Prerequisite: the permission of the supervising faculty member.

This course may be repeated. Advanced study in a special area.

**APMA E9810 SEAS colloquium in climate science. ***0 points*.

0 pts. Lect: 1.

Prerequisites: Instructor's permission.

Current research in problems at the interface between applied mathematics and earth and environmental sciences.

**APMA E9815 Geophysical fluid dynamics seminar. ***1-3 points*.

May be repeated for up to 10 points of credit. **Not offered during 2020-21 academic year.**

Prerequisites: Instructor's permission.

Problems in the dynamics of geophysical fluid flows.

**APPH E3100 Introduction to quantum mechanics. ***3 points*.

Lect: 3.

Prerequisites: (PHYS UN1403) or the equivalent, and differential and integral calculus.

Corequisites: APMA E3101

Basic concepts and assumptions of quantum mechanics, Schrodinger's equation, solutions for one-dimensional problems including square wells, barriers and the harmonic oscillator, introduction to the hydrogen atom, atomic physics and x-rays, electron spin.

**APPH E3200 Mechanics: fundamentals and applications. ***3 points*.

Lect: 3

Prerequisites: (PHYS UN1402) and (MATH UN2030) or or equivalent.

Basic non-Euclidean coordinate systems, Newtonian Mechanics, oscillations, Green's functions, Newtonian graviation, Lagrangian mechanics, central force motion, two-body collisions, noninertial reference frames, rigid body dynamics. Applications, including GPS and feedback control systems, are emphasized throughout.

Fall 2020: APPH E3200 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 3200 | 001/13552 | M W 10:10am - 11:25am Online Only |
Michael Mauel | 3 | 8/35 |

**APPH E3300 Applied electromagnetism. ***3 points*.

Lect: 3.

Corequisites: APMA E3102

Vector analysis, electrostatic fields, Laplace's equation, multipole expansions, electric fields in matter: dielectrics, magnetostatic fields, magnetic materials, and superconductors. Applications of electromagnetism to devices and research areas in applied physics.

**APPH E3400 Physics of the human body. ***3 points*.

Lect: 3.

Prerequisites: (PHYS UN1201) or (PHYS UN1401) and (MATH UN1101)

Corequisites: PHYS UN1202,PHYS UN1402,MATH UN1102

This introductory course analyzes the human body from the basic principles of physics. Topics covered include the energy balance in the body, the mechanics of motion, fluid dynamics of the heart and circulation, vibrations in speaking and hearing, muscle mechanics, gas exchange and transport in the lungs, vision, structural properties and limits, electrical properties and the development and sensing of magnetic fields, and the basics of equilibrium and regulatory control. In each case, a simple model of the body organ, property, or function will be derived and then applied.

**APPH E3900 Undergraduate research in applied physics. ***0 points*.

0-4 pts.

Prerequisites: Written permission from instructor and approval from adviser.

This course may be repeated for credit, but no more than 6 points of this course may be counted toward the satisfaction of the B.S. degree requirements. Candidates for the B.S. degree may conduct an investigation in applied physics or carry out a special project under the supervision of the staff. Credit for the course is contingent upon the submission of an acceptable thesis or final report.

Fall 2020: APPH E3900 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 3900 | 005/22392 | |
Irving Herman | 0 | 0/10 |

APPH 3900 | 006/22391 | |
Michael Mauel | 0 | 1/10 |

**APPH E4008 Introduction to atmospheric science. ***3 points*.

Lect: 3

Prerequisites: Advanced calculus and general physics, or instructor's permission.

Basic physical processes controlling atmospheric structure: thermodynamics; radiation physics and radiative transfer; principles of atmospheric dynamics; cloud processes; applications to Earth's atmospheric general circulation, climatic variations, and the atmosphere of the other planets.

**APPH E4010 INTRODUCTN TO NUCLEAR SCIENCE. ***3.00 points*.

Prerequisites: (MATH UN1202) and (MATH UN2030) and (PHYS UN1403) or or equivalents. This introductory course is for individuals with an interest in medical physics and other branches of radiation science. Topics covered include: basic concepts, nuclear models, semi-empirical mass formula, interaction of radiation with matter, nuclear detectors, nuclear structure and instability, radioactive decay process and radiation, particle accelerators, and fission and fusion processes and technologies

Fall 2020: APPH E4010 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4010 | 001/11812 | T 6:30pm - 9:00pm Online Only |
Stephen Ostrow | 3.00 | 13/35 |

**APPH E4018 Applied physics laboratory. ***2 points*.

Lab: 4.

Prerequisites: (ELEN E3401) or or equivalent.

Typical experiments are in the areas of plasma physics, microwaves, laser applications, optical spectroscopy physics, and superconductivity.

**APPH E4090 Nanotechnology. ***3 points*.

Lect: 3.

Prerequisites: (APPH E3100) and (MSAE E3103) or or their equivalents with instructor's permission.

The science and engineering of creating materials, functional structures and devices on the nanometer scale. Carbon nanotubes, nanocrystals, quantum dots, size dependent properties, self-assembly, nanostructured materials. Devices and applications, nanofabrication. Molecular engineering, bionanotechnology. Imaging and manipulating at the atomic scale. Nanotechnology in society and industry.

**APPH E4100 Quantum physics of matter. ***3 points*.

Lect: 3.

Prerequisites: (APPH E3100)

Corequisites: APMA E3102

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.

Fall 2020: APPH E4100 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4100 | 001/13556 | T Th 10:10am - 11:25am 1024 Seeley W. Mudd Building |
Latha Venkataraman | 3 | 24/35 |

**APPH E4110 Modern optics. ***3 points*.

Lect: 3.

Prerequisites: (APPH E3300)

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 points*.

Lect: 3.

Prerequisites: Recommended but not required: APPH E3100 and APPH E3300 or their equivalents.

Optical resonators, interaction of radiation and atomic systems, theory of laser oscillation, specific laser systems, rate processes, modulation, detection, harmonic generation, and applications.

Fall 2020: APPH E4112 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4112 | 001/13557 | T Th 11:40am - 12:55pm 1127 Seeley W. Mudd Building |
Nanfang Yu | 3 | 14/35 |

**APPH E4130 Physics of solar energy. ***3 points*.

Lect: 3.

Prerequisites: (PHYS UN1403) or (PHYS UN1602) and (MATH UN1202) or (MATH UN2030) or instructor's permission.

The physics of solar energy including solar radiation, the analemma, atmospheric efforts, thermodynamics of solar energy, physics of solar cells, energy storage and transmission, and physics and economics in the solar era.

Fall 2020: APPH E4130 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4130 | 001/13558 | M W 1:10pm - 2:25pm Online Only |
Chengjun Chen | 3 | 7/35 |

**APPH E4200 Physics of fluids. ***3 points*.

Lect: 3.

Prerequisites: (APMA E3102) or (PHYS UN1401) or (PHYS UN1601) or or equivalent.

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 E4210 Geophysical fluid dynamics. ***3 points*.

Lect: 3.

Prerequisites: (APMA E3101) and (APMA E3102) and (APPH E4200) or equivalents or permission from instructor.

Fundamental concepts in the dynamics of rotating, stratified flows. Geostrophic and hydrostatic balances, potential vorticity, f and beta plane approximations, gravity and Rossby waves, geostrophic adjustment and quasigeostrophy, baroclinic and barotropic instabilities, Sverdrup balance, boundary currents, Ekman layers.

**APPH E4300 Applied electrodynamics. ***3 points*.

Lect: 3.

Prerequisites: (APPH E3300)

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.

Fall 2020: APPH E4300 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4300 | 001/13559 | M W 2:40pm - 3:55pm Online Only |
Alexander Gaeta | 3 | 23/35 |

**APPH E4301 Introduction to plasma physics. ***3 points*.

Lect: 3.

Prerequisites: (PHYS UN3008) or (APPH E3300)

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.

**APPH E4330 Radiobiology for medical physicists. ***3 points*.

Lect: 3.

Prerequisites: (APPH E4010) or equivalent or

Corequisites: APPH E4010

Interface between clinical practice and quantitative radiation biology. Microdosimetry, dose-rate effects and biological effectiveness thereof; radiation biology data, radiation action at the cellular and tissue level; radiation effects on human populations, carcinogenesis, genetic effects; radiation protection; tumor control, normal-tissue complication probabilities; treatment plan optimization.

**APPH E4500 Health physics. ***3 points*.

Lect: 3.

Prerequisites: (APPH E4600) or

Corequisites: APPH E4600

Fundamental principles and objectives of health physics (radiation protection), the quantities of radiation dosimetry (the absorbed dose, equivalent dose, and effective dose) used to evaluate human radiation risks, elementary shielding calculations and protection measures for clinical environments, characterization and proper use of health physics instrumentation, and regulatory and administrative requirements of health physics programs in general and as applied to clinical activities.

**APPH E4550 Medical physics seminar. ***0 points*.

0 pts. Lect: 1.

Required for all graduate students in the medical physics program. Practicing professionals and faculty in the field present selected topics in medical physics.

**APPH E4600 Fundamentals of radiological physics and radiation dosimetry. ***3 points*.

Lect: 3.

Prerequisites: (APPH E4010) or or equivalent

Corequisites: APPH E4010

Basic radiation physics: radioactive decay, radiation producing devices, characteristics of the different types of radiation (photons, charged and uncharged particles) and mechanisms of their interactions with materials. Essentials of the determination, by measurement and calculation, of absorbed doses from ionizing radiation sources used in medical physics (clinical) situations and for health physics purposes.

Fall 2020: APPH E4600 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4600 | 001/11816 | W 3:00pm - 6:00pm Online Only |
Jerome Meli | 3 | 4/35 |

**APPH E4710 Radiation instrumentation and measurement laboratory, I. ***3 points*.

Lect: 1. Lab: 4.

Prerequisites: (APPH E4010) or

Corequisites: APPH E4010

Lab fee: $50. Theory and use of alpha, beta, gamma, and X-ray detectors and associated electronics for counting, energy spectroscopy, and dosimetry; radiation safety; counting statistics and error propagation; mechanisms of radiation emission and interaction. (Topic coverage may be revised.)

Fall 2020: APPH E4710 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4710 | 001/11823 | M 5:00pm - 10:00pm 214 Seeley W. Mudd Building |
Stephen Ostrow, Marco Zaider | 3 | 4/20 |

**APPH E4711 Radiation instrumentation and measurement laboratory, II. ***3 points*.

Lect: 1. Lab: 4.

Prerequisites: (APPH E4010) or

Corequisites: APPH E4010

Lab fee: $50. Additional detector types; applications and systems including coincidence, low-level, and liquid scintillation counting; neutron activation; TLD dosimetry; gamma camera imaging. (Topic coverage may be revised.)

**APPH E4901 Seminar: problems in applied physics. ***1 point*.

Lect: 1.

This course is required for, and can be taken only by, all applied physics majors and minors in the junior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Topics change yearly.

Fall 2020: APPH E4901 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4901 | 001/13563 | M W 11:40am - 12:55pm Online Only |
Michael Mauel | 1 | 17/35 |

**APPH E4903 Seminar: problems in applied physics. ***2 points*.

Lect: 1. Tutorial:1.

This course is required for, and can be taken only by, all applied physics majors in the senior year. Discussion of specific and self-contained problems in areas such as applied electrodynamics, physics of solids, and plasma physics. Formal presentation of a term paper required. Topics change yearly.

Fall 2020: APPH E4903 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 4903 | 001/13564 | M W 11:40am - 12:55pm Online Only |
Michael Mauel | 2 | 12/35 |

**APPH E4990 Special topics in applied physics. ***1-3 points*.

**Not offered during 2020-21 academic year.**

Prerequisites: Instructor's permission.

This course may be repeated for credit. Topics and instructors change from year to year. For advanced undergraduate students and graduate students in engineering, physical sciences, and other fields.

**APPH E6081 Solid state physics, I. ***3 points*.

Lect: 3.

Prerequisites: (APPH E3100) or the equivalent. Knowledge of statistical physics on the level of MSAE E3111 or PHYS GU4023 strongly recommended.

Crystal structure, reciprocal lattices, classification of solids, lattice dynamics, anharmonic effects in crystals, classical electron models of metals, electron band structure, and low-dimensional electron structures.

**APPH E6082 Solid state physics, II. ***3 points*.

Lect: 3.**Not offered during 2020-21 academic year.**

Prerequisites: (APPH E6081) or the instructor's permission.

Semiclassical and quantum mechanical electron dynamics and conduction, dielectric properties of insulators, semiconductors, defects, magnetism, superconductivity, low-dimensional structures, and soft matter.

**APPH E6085 Computing the electronic structure of complex materials. ***3 points*.

Lect: 3**Not offered during 2020-21 academic year.**

Prerequisites: (APPH E3100) or equivalent.

Basics of density functional theory (DFT) and its application to complex materials. Computation of electronics and mechanical properties of materials. Group theory, numerical methods, basis sets, computing, and running open source DFT codes. Problem sets and a small project.

**APPH E6091 Magnetism and magnetic materials. ***3 points*.

Lect. 3. **Not offered during 2020-21 academic year.**

Prerequisites: (MSAE E4206) or (APPH E6081) or equivalent.

Types of magnetism. Band theory of ferromagnetism. Magnetic metals, insulators, and semiconductors. Magnetic nanostructures: ultrathin films, superlattices, and particles. Surface magnetism and spectroscopies. High speed magnetization dynamics. Spin electronics.

**APPH E6101 Plasma physics, I. ***3 points*.

Lect: 3.

Prerequisites: (APPH E4300)

Debye screening. Motion of charged particles in space- and time-varying electromagnetic fields. Two-fluid description of plasmas. Linear electrostatic and electromagnetic waves in unmagnetized and magnetized plasmas. The magnetohydrodynamic (MHD) model, including MHD equilibrium, stability, and MHD waves in simple geometries.

Fall 2020: APPH E6101 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6101 | 001/13569 | M W 1:10pm - 2:25pm 406 Hamilton Hall |
Gerald Navratil | 3 | 3/35 |

**APPH E6102 Plasma physics, II. ***3 points*.

Lect: 3.

Prerequisites: (APPH E6101)

Magnetic coordinates. Equilibrium, stability, and transport of torodial plasmas. Ballooning and tearing instabilities. Kinetic theory, including Vlasov equation, Fokker-Planck equation, Landau damping, kinetic transport theory. Drift instabilities.

**APPH E6110 Laser interactions with matter. ***3 points*.

Lect: 3.

Prerequisites: (APPH E4112) or equivalent, and quantum mechanics.

Principles and applications of laser-matter coupling, non-linear optics, three- and four-wave mixing, harmonic generation, laser processing of surfaces, laser probing of materials, spontaneous and stimulated light scattering, saturation spectroscopy, multiphoton excitation, laser isotope separation, transient optical effects.

**APPH E6319 Clinical nuclear medicine physics. ***3 points*.

Lect: 3.

Prerequisites: (APPH E4010) or equivalent.

Introduction to the instrumentation and physics used in clinical nuclear medicine and PET with an emphasis on detector systems, tomography and quality control. Problem sets, papers and term project.

**APPH E6330 Diagnostic radiology physics. ***3 points*.

Lect: 3.

Prerequisites: (APPH E4600)

Physics of medical imaging. Imaging techniques: radiography, fluoroscopy, computed tomography, mammography, ultrasound, magnetic resonance. Includes conceptual, mathematical/theoretical, and practical clinical physics aspects.

**APPH E6333 Radiation therapy physics practicum. ***3 points*.

Prerequisites: Grade of B+ or better in APPH E6335 and instructor's permission.

Students spend two to four days per week studying the clinical aspects of radiation therapy physics. Projects on the application of medical physics in cancer therapy within a hospital environment are assigned; each entails one or two weeks of work and requires a laboratory report. Two areas are emphasized: 1. computer-assisted treatment planning (design of typical treatment plans for various treatment sites including prostate, breast, head and neck, lung, brain, esophagus, and cervix) and 2. clinical dosimetry and calibrations (radiation measurements for both photon and electron beams, as well as daily, monthly, and part of annual QA).

Fall 2020: APPH E6333 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6333 | 001/11981 | |
Cheng Wuu | 3 | 7/10 |

**APPH E6335 Radiation therapy physics. ***3 points*.

Lect: 3.

Prerequisites: (APPH E4600) APPH E4330 recommended.

Review of X-ray production and fundamentals of nuclear physics and radioactivity. Detailed analysis of radiation absorption and interactions in biological materials as specifically related to radiation therapy and radiation therapy dosimetry. Surveys of use of teletherapy isotopes and X-ray generators in radiation therapy plus the clinical use of interstitial and intracavitary isotopes. Principles of radiation therapy treatment planning and isodose calculations. Problem sets taken from actual clinical examples are assigned.

**APPH E6336 Advanced Topics in Radiation Therapy. ***3 points*.

Lect: 3.

Prerequisites: (APPH E6335)

Advanced technology applications in radiation therapy physics, including intensity modulated, image guided, stereotactic, and hypofractionated radiation therapy. Emphasis on advanced technological, engineering, clinical, and quality assurance issues associated with high technology radiation therapy and the special role of the medical physicist in the safe clinical application of these tools.

Fall 2020: APPH E6336 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6336 | 001/11985 | W 6:00pm - 8:30pm Online Only |
Cheng Wuu | 3 | 3/15 |

**APPH E6340 Diagnostic radiology practicum. ***3 points*.

Lab: 6.

Prerequisites: Grade of B+ or better in APPH E6330 and instructor's permission.

Practical applications of diagnostic radiology for various measurements and equipment assessments. Instruction and supervised practice in radiation safety procedures, image quality assessments, regulatory compliance, radiation dose evaluations and calibration of equipment. Students participate in clinical QC of the following imaging equipment: radiologic units (mobile and fixed), fluoroscopy units (mobile and fixed), angiography units, mammography units, CT scanners, MRI units and ultrasound units. The objective is familiarization in routine operation of test instrumentation and QC measurements utilized in diagnostic medical physics. Students are required to submit QC forms with data on three different types of radiology imaging equipment.

Fall 2020: APPH E6340 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6340 | 001/11982 | |
Sachin Jambawalikar | 3 | 2/10 |

**APPH E6365 Nuclear medicine practicum. ***3 points*.

Lab: 6.

Prerequisites: Grade of B+ or better in APPH E6319 and instructor's permission.

Practical applications of nuclear medicine theory and application for processing and analysis of clinical images and radiation safety and quality assurance programs. Topics may include tomography, instrumentation, and functional imaging. Reports.

Fall 2020: APPH E6365 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6365 | 001/11983 | |
Klaus Hamacher | 3 | 2/3 |

**APPH E6380 Health physics practicum. ***3 points*.

Lab: 6.

Prerequisites: Grade of B+ or better in APPH E4500 and permission of the instructor, or

Corequisites: APPH E4500

Radiation protection practices and procedures for clinical and biomedical research environments. Includes design, radiation safety surveys of diagnostic and therapeutic machine source facilities, the design and radiation protection protocols for facilities using unsealed sources of radioactivity – nuclear medicine suites and sealed sources – brachytherapy suites. Also includes radiation protection procedures for biomedical research facilities and the administration of programs for compliance to professional health physics standards and federal and state regulatory requirements for the possession and use of radioactive materials and machine sources of ionizing and non ionizing radiations in clinical situations. Individual topics are decided by the student and the collaborating Clinical Radiation Safety Officer.

Fall 2020: APPH E6380 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

APPH 6380 | 001/11984 | |
Peter Caracappa | 3 | 3/10 |

**APPH E9142 Applied physics seminar. ***3 points*.

Sem: 3.**Not offered during 2020-21 academic year.**

These courses may be repeated for credit. Selected topics in applied physics. Topics and instructors change from year to year.

**APPH E9143 Applied physics seminar. ***3 points*.

Sem: 3.**Not offered during 2020-21 academic year.**

These courses may be repeated for credit. Selected topics in applied physics. Topics and instructors change from year to year.

**CHAP E4120 Statistical mechanics. ***3 points*.

Lect: 3.

Prerequisites: (CHEN E3210) or equivalent thermodynamics course, or instructor's permission.

Fundamental principles and underlying assumptions of statistical mechanics. Boltzmann's entropy hypothesis and its restatement in terms of Helmholtz and Gibbs free energies and for open systems. Correlation times and lengths. Exploration of phase space and observation timescale. Correlation functions. Fermi-Dirac and Bose-Einstein statistics. Fluctuation-response theory. Applications to ideal gases, interfaces, liquid crystals, microemulsions and other complex fluids, polymers, Coulomb gas, interactions between charged polymers and charged interfaces, ordering transitions.

Fall 2020: CHAP E4120 | |||||

Course Number | Section/Call Number | Times/Location | Instructor | Points | Enrollment |
---|---|---|---|---|---|

CHAP 4120 | 001/10124 | T 7:00pm - 9:30pm Online Only |
Ben O'Shaughnessy | 3 | 52/65 |

**HSAM UN2901 Data: Past, Present, and Future. ***3 points*.

Lect: 1.5. Lab: 1.5.

Data-empowered algorithms are reshaping our professional, personal, and political realities, for good--and for bad. "Data: Past, Present, and Future" moves from the birth of statistics in the 18th century to the surveillance capitalism of the present day, covering racist eugenics, World War II cryptography, and creepy personalized advertising along the way. Rather than looking at ethics and history as separate from the science and engineering, the course integrates the teaching of algorithms and data manipulation with the political whirlwinds and ethical controversies from which those techniques emerged. We pair the introduction of technical developments with the shifting political and economic powers that encouraged and benefited from new capabilities. We couple primary and secondary readings on the history and ethics of data with computational work done largely with user-friendly Jupyter notebooks in Python.