MULTV. CALC. FOR ENGI & APP SCI
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.
- TR 8:40 a.m.-9:55 a.m.
- TR 1:10 p.m.-2:25 p.m.
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Instructor:
Drew C Youngren
CULPA: 10
Info
- 4 points
MULTV. CALC. FOR ENGI & APP SCI
Required recitation session for students enrolled in APMA E2000.
- F 2:40 p.m.-3:30 p.m.
- R 4:10 p.m.-5 p.m.
- F 10:10 a.m.-11 a.m.
- R 4:10 p.m.-5 p.m.
- R 5:10 p.m.-6 p.m.
- R 11:40 a.m.-12:30 p.m.
- 0 points
INTRO TO APPLIED MATHEMATICS
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).
LABORATORY IN MATERIALS SCI II
Metallographic sample preparation, optical microscopy, quantitative metallography, hardness and tensile testing, plastic deformation, annealing, phase diagrams, brittle fracture of glass, temperature and strain-rate dependent deformation of polymers; written and oral reports. This is the second of a two-semester sequence materials laboratory course.
- M 1 p.m.-5 p.m.
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Instructor:
Ismail C Noyan
CULPA: 7
Info
- 3 points
INTRO TO QUANTUM MECHANICS
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.
- MW 1:10 p.m.-2:25 p.m.
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Instructor:
Aravind Devarakonda
Info - 3 points
APPLIED MATHEMATICS II: PDE'S
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.
- TR 1:10 p.m.-2:25 p.m.
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Instructor:
Michael K Tippett
CULPA: 8 h-index: 43 Info - 3 points
DESIGN PROJECT
E3156: a design problem in materials science or metallurgical engineering selected jointly by the student and a professor in the department. The project requires research by the student, directed reading, and regular conferences with the professor in charge. E3157: completion of the research, directed reading, and conferences, culminating in a written report and an oral presentation to the department.
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Instructor:
Simon Billinge
CULPA: 3 h-index: 75 Info - 3 points
Materials Thermodynamics and Phase Diagr
Mat Thermo and Phase Diag
Review of laws of thermodynamics, thermodynamic variables and relations, free energies and equilibrium in thermodynamic systems. Unary, binary, and ternary phase diagrams, compounds and intermediate phases, solid solutions and Hume-Rothery rules, relationship between phase diagrams and metastability, defects in crystals. Thermodynamics of surfaces and interfaces, effect of particle size on phase equilibria, adsorption isotherms, grain boundaries, surface energy, electrochemistry. Note: MSAE E4201 shares lectures and meeting times with E3201 and therefore, may not be taken in other semesters.
- TR 11:40 a.m.-12:55 p.m.
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Instructor:
Renata M Wentzcovitch
Info - 3 points
APPLIED ELECTROMAGNETISM
Vector analysis, electrostatic fields, Laplaces 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.
- MW 10:10 a.m.-11:25 a.m.
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Instructor:
Sherry Zhang
Info - 3 points
UNDERGRAD RES IN MATERIALS SCI
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 materials science 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.
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Instructor:
Katayun Barmak
CULPA: 1 h-index: 49 Info - 0-4 points
Advanced and Applied Linear Algebra
Advanced Linear Algebra
Advanced topics in linear algebra with applications to data analysis, algorithms, dynamics and differential equations, and more. (1) General vector spaces, linear transformations, spaces isomorphisms; (2) spectral theory - normal matrices and their spectral properties, Rayleigh quotient, Courant-Fischer Theorem, Jordan forms, eigenvalue perturbations; (3) least squares problem and the Gauss-Markov Theorem; (4) singular value decomposition, its approximation properties, matrix norms, PCA and CCA.
APPLIED PHYSICS LABORATORY
Typical experiments are in the areas of plasma physics, microwaves, laser applications, optical spectroscopy physics, and superconductivity.
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Instructor:
Michael E Mauel
CULPA: 9
Info
- 2 points
NANOTECHNOLOGY
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. Offered in alternate years.
- MW 2:40 p.m.-3:55 p.m.
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Instructor:
Yuan Yang
h-index: 49 Info - 3 points
APPL MATH III:DYNAMICAL SYSTMS
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.
SYNTHESIS & PROCESSING OF MATERIALS
A course on synthesis and processing of engineering materials. Established and novel methods to produce all types of materials (including metals, semiconductors, ceramics, polymers, and composites). Fundamental and applied topics relevant to optimizing the microstructure of the materials with desired properties. Synthesis and processing of bulk, thin-film, and nano materials for various mechanical and electronic applications.
MODERN OPTICS
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.
- TR 11:40 a.m.-12:55 p.m.
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Instructor:
Nanfang Yu
h-index: 48 Info - 3 points
Quantum and Nonlinear Photonics
Quantum & Nonlinear Photo
Advanced senior-level/MS/PhD course covering interaction of laser light with matter in both classical and quantum domains. First half introduces microscopic origin of optical nonlinearities through formal derivation of nonlinear susceptibilities, emphasis on second- and third-order optical processes. Topics include Maxwell's wave equation, and nonlinear optical processes such as second-harmonic, difference frequency generation, four-wave mixing, and self-phase modulation, including various applications of processes such as frequency conversion, and optical parametric amplifiers and oscillators. Second half describes two-level atomic systems and quantization of electromagnetic field. Descriptions of coherent, Fock, and squeezed states of light discussed and techniques to generate such states outlined.
- W 1:10 p.m.-3:40 p.m.
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Instructor:
Alexander Gaeta
Wikipedia h-index: 89 Info - 3 points
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. 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.
- MW 2:40 p.m.-3:55 p.m.
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Instructor:
Michael I Weinstein
CULPA: 2 h-index: 47 Info - 3 points
PARTIAL 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.
- TR 1:10 p.m.-2:25 p.m.
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Instructor:
Liliana Borcea
Info - 3 points
MATERIALS THERMODYN/PHASE DIAG
Review of laws of thermodynamics, thermodynamic variables and relations, free energies and equilibrium in thermodynamic system. Statistical thermodynamics. Unary, binary, and ternary phase diagrams, compounds and intermediate phases, solid solutions and Hume-Rothery rules, relationship between phase diagrams and metastability, defects in crystals. Thermodynamics of surfaces and interfaces, effect of particle size on phase equilibria, adsorption isotherms, grain boundaries, surface energy, electrochemistry, statistical mechanics.
- TR 11:40 a.m.-12:55 p.m.
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Instructor:
Renata M Wentzcovitch
Info - 3 points
KINETICS OF TRANSFORMATIONS
Review of thermodynamics, irreversible thermodynamics, diffusion in crystals and noncrystalline materials, phase transformations via nucleation and growth, overall transformation analysis and time-temperature-transformation (TTT) diagrams, precipitation, grain growth, solidification, spinodal and order-disorder transformations, martensitic transformation.
THEORY CRYSTALL MAT: ELECTRONS
Phenomenological theoretical understanding of electrons in crystalline materials. Both translational and point symmetry employed to block diagonalize the Schrödinger equation and compute observables related to electrons. Topics include nearly free electrons, tight-binding, electron-electron interactions, transport, magnetism, optical properties, topological insulators, spin-orbit coupling, and superconductivity. Illustrated using both minimal model Hamiltonians in addition to accurate Hamiltonians for real materials.
- TR 1:10 p.m.-2:25 p.m.
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Instructor:
Chris A Marianetti
Info - 3 points
ELEC & MAGNETIC PROP OF SOLIDS
A survey course on the electronic and magnetic properties of materials, oriented towards materials for solid state devices. Dielectric and magnetic properties, ferroelectrics and ferromagnets. Conductivity and superconductivity. Electronic band theory of solids: classification of metals, insulators, and semiconductors. Materials in devices: examples from semiconductor lasers, cellular telephones, integrated circuits, and magnetic storage devices. Topics from physics are introduced as necessary.
- MW 11:40 a.m.-12:55 p.m.
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Instructor:
William Bailey
CULPA: 12 Info - 3 points
COMPUT MATH:INTRO-NUMERCL METH
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 ODEs. All programming exercises will be in Python.
NUMERICAL METHODS/PDE'S
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.
- TR 11:40 a.m.-12:55 p.m.
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Instructor:
Pierre Amenoagbadji
Info - 3 points
Applied Stochastic Analysis
Provides elementary introduction to fundamental ideas in stochastic analysis for applied mathematics. Core material includes: (i) review of probability theory (including limit theorems), and introduction to discrete Markov chains and Monte Carlo methods; (ii) elementary theory of stochastic process, Ito's stochastic calculus and stochastic differential equations; (iii) introductions to probabilistic representation of elliptic partial differential equations (the Fokker-Planck equation theory); (iv) stochastic approximation algorithms; and (v) asymptotic analysis of SDEs.
- MW 10:10 a.m.-11:25 a.m.
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Instructor:
Shanyin Tong
Info - 3 points
HEALTH PHYSICS
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.
- M 5:30 p.m.-8 p.m.
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Instructor:
Peter Caracappa
h-index: 12 Info - 3 points
MEDICAL PHYSICS SEMINAR
Required for all graduate students in the Medical Physics Program. Practicing professionals and faculty in the field present selected topics in medical physics.
- M 9 a.m.-10:15 a.m.
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Instructor:
Cheng S Wuu
CULPA: 1 Info - 0 points
SPEC TOPICS IN APPLIED MATH
Calculus of Variations
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. Examples of topics include multi-scale analysis and Applied Harmonic Analysis.
- MW 11:40 a.m.-12:55 p.m.
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Instructor:
James M Scott
h-index: 2 Info - 3 points
SPEC TOPICS IN APPLIED MATH
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. Examples of topics include multi-scale analysis and Applied Harmonic Analysis.
- MW 11:40 a.m.-12:55 p.m.
- 3 points
SPEC TOPICS IN APPLIED PHYSICS
FUSION HISTORY
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.
- M 4:10 p.m.-6:40 p.m.
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Instructor:
Carlos Paz Soldan
h-index: 28 Info - 3 points
SPEC TOPICS:MATERIAL SCI & ENGIN
ML/AI for Materials
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.
- MW 10:10 a.m.-11:25 a.m.
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Instructor:
Simon Billinge
CULPA: 3 h-index: 75 Info - 3 points
PLASMA PHYSICS II
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.
- MW 1:10 p.m.-2:25 p.m.
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Instructor:
Carlos Paz Soldan
h-index: 28 Info - 3 points
CLIN NUCLEAR MEDICINE PHYSICS
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.
- T 6 p.m.-8:30 p.m.
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Instructor:
Pat Zanzonico
Info - 3 points
DIAGNOSTIC RADIOLOGY PHYSICS
Physics of medical imaging. Imaging techniques: radiography, fluoroscopy, computed tomography, mammography, ultrasound, magnetic resonance. Includes conceptual, mathematical/theoretical, and practical clinical physics aspects.
RADIATION THERAPY PHYSICS
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.
- R 5 p.m.-8 p.m.
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Instructor:
Cheng S Wuu
CULPA: 1 Info - 3 points
APPLIED PHYSICS SEMINAR
KINETIC THEORY
May be repeated for credit. Selected topics in applied physics. Topics and instructors change from year to year.
- TR 2:40 p.m.-3:55 p.m.
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Instructor:
Elizabeth Paul
Info - 3 points