Graduate Program

Physical phenomena in a wide range of areas such as fluid and solid mechanics, electromagnetism, quantum mechanics, chemical diffusion, and acoustics are governed by Partial Differential Equations (PDEs). In this course, you will learn how to solve a variety of BVPs, each of which is defined by a PDE, boundary conditions, and possibly initial conditions. We will cover the classical PDEs of mathematical physics: 1) diffusion equation, 2) Laplace equations, 3) wave equation. You will learn different techniques to solve these equations. Topics include separation of variables, Fourier analysis, Sturm-Liouville theory, spherical coordinates and Legendre’s equation, cylindrical coordinates and Bessel’s equation, method of characteristics, and Green's functions. You will also learn the basics of how to discretize linear and nonlinear PDEs and solve them numerically. Emphasis will be on physical understanding of the governing equations and the resulting solutions. You will learn to use software and write code (Python, Matlab, Mathematica) to solve PDEs and visualize the solutions. Prior knowledge of any of these languages/software, although helpful, is not required.

Location

(MWF 11:50AM - 12:40PM)

This course covers the classical partial differential equations of mathematical physics: the heat equation, the Laplace equation, and the wave equation. The primary technique covered in the course is separation of variables, which leads to solutions in the form of eigenfunction expansions. The topics include Fourier series, separation of variables, Sturm-Liouville theory, unbounded domains and the Fourier transform, spherical coordinates and Legendres equation, cylindrical coordinates and Bessels equation. The software package Mathematica will be used extensively. Prior knowledge of Mathematica is helpful but not essential. In the last two weeks of the course, there will be a project on an assigned topic. The course will include applications in heat conduction, electrostatics, fluid flow, and acoustics.

Location

(F 3:25PM - 4:40PM)

The course deals with computational methods to analytically intractable mathematical problems in biological research. For the first half of the course, general numerical analysis topics are reviewed such as linear algebra, ODE and PDE. Through homework assignments, students write their own computer code. Sufficient sample solutions are given to practice various numerical methods within limited time. The rest of the course is comprised of case studies and projects. Examples of computational analyses are drawn from life science problems such as biodynamics of human loco motion, ion channel kinetics, ionic diffusion, and finite element analysis of cells/tissues. For final project, students bring their own research problems, express them in mathematical equations, solve them using custom written computer programs and interpret the solutions.

Location

(MW 4:50PM - 6:05PM)

This course focuses on the multidisciplinary aspects of designing complex optical systems. Aspects from mechanics, optics, design for manufacturing, design for assembly, design for alignment, and design for metrology & qualification must be considered to design, build, and demonstrate a successful optical system. Students will gain a fundamental understanding of the requirements and specifications for designing, building, tolerancing, and verifying optical systems through iterative design work.

Location

(MW 6:15PM - 7:30PM)

Basic plasma parameters; quasi-neutrality, Debye length, plasma frequency, plasma parameter, Charged particle motion: orbit theory. Basic plasma equations; derivation of fluid equations from the Vlasov equation. Waves in plasmas. MHD theory. Energy balance.

Location

(TR 3:25PM - 4:40PM)

The study of incompressible flow covers fluid motions which are gentle enough that the density of the fluid changes little or none. Topics: Conservation equations. Bernoullis equation, the Navier-Stokes equations. Inviscid flows; vorticity; potential flows; stream functions; complex potentials. Viscosity and Reynolds number; some exact solutions with viscosity; boundary layers; low Reynolds number flows. Waves.

Location

(MW 3:25PM - 4:40PM)

This course provides a thorough grounding on the theory and application of linear finite element analysis in solid mechanics and related disciplines. Topics: structural matrix analysis concepts and computational procedures; shape functions and element formulation methods for 1-D, 2-D problems; variational methods, weighted residual methods and Galerkin techniques; isoparametric elements; error estimation and convergence; global analysis aspects. Term project and homework require computer implementation of 1-D and 2-D finite element procedures using Matlab. Term project not required for ME254

Location

(MW 10:25AM - 11:40AM)

This course introduces the theory and application of characterization techniques for examining the atomic structure of materials. Student will learn about widely used materials in both academic and industrial research, including X-ray diffraction, electron microscopy, and spectroscopy. The fundamentals of these techniques will be demonstrated, along with their applications for analyzing nanostructures in a wide range of materials, such as catalysts, semiconductors, ceramics, and metals.

Location

(MW 2:00PM - 3:15PM)

Continuum mechanics may be the topic that best defines and unifies mechanical engineering. The topic considers motion, deformation, flow, stresses, forces, and heat transfer as determined by the laws of mechanics. Those phenomena may occur in any materials — solids, fluids, or things in-between — that can be well-modeled as continuous, not discrete (meaning quantization effects are negligible). To handle this wide variety of phenomena and materials, we use the language of tensor mathematics, which we will build up at the beginning of the course. Applications to ongoing research of the instructor and students will be incorporated wherever possible. The course will include indicial notation and tensor analysis, concepts of stress, both Eulerian and Lagrangian descriptions of deformation and strain, conservation of mass, momentum, energy, angular momentum, and constitutive equations to describe material response.

Location

(MW 4:50PM - 6:05PM)

This course focuses teaching the multidisciplinary aspects of designing complex, precise systems. In these systems, aspects from mechanics, optics, electronics, design for manufacturing/assembly, and metrology/qualification must all be considered to design, build, and demonstrate a successful precisionsystem. The goal of this class is to develop a fundamental understanding of multidisciplinary design for designing the next generation of advanced instrumentation.

Location

(TR 4:50PM - 6:05PM)

In this course, we will survey the role of mechanics in cells, tissues, organs and organisms. A particular emphasis will be placed on the mechanics of the musculoskeletal system, the circulatory system and the eye. Engineering concepts will be used to understand how physical forces contribute to biological processes, especially disease and healing. Experimental and modeling techniques for characterizing the complex mechanical response of biosolids will be discussed in detail, and the continuum mechanics approach will highlighted.

Location

(TR 11:05AM - 12:20PM)

In this course, we will survey the role of mechanics in cells, tissues, organs and organisms. A particular emphasis will be placed on the mechanics of the musculoskeletal system, the circulatory system and the eye. Engineering concepts will be used to understand how physical forces contribute to biological processes, especially disease and healing. Experimental and modeling techniques for characterizing the complex mechanical response of biosolids will be discussed in detail, and the continuum mechanics approach will highlighted.

Location

(R 12:30PM - 1:45PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course provides master’s students with the opportunity to conduct, develop, and refine their research projects. Students will engage in research relevant to their field of study and make progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

No description

Location

( 7:00PM - 7:00PM)

No description

Location

( 7:00PM - 7:00PM)

This course will survey the field of high-energy-density science (HEDS), extending from ultra-dense matter to the radiation-dominated regime. Topics include: experimental and computational methods for the productions, manipulation, and diagnosis of HED matter, thermodynamic equations-of-state; dynamic transitions between equilibrium phases; and radiative and other transport properties. Throughout the course, we will make connections with key HEDS applications in astrophysics, laboratory fusion, and new quantum states of matter

Location

(TR 2:00PM - 3:15PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides PhD students with fewer than 90 credits the opportunity to conduct, develop, and refine their doctoral research projects. Students will engage in research relevant to their field of study and make progress toward completing their dissertations.

Location

( 7:00PM - 7:00PM)

This course provides master's students who are currently completing their final required coursework, or with special circumstances like an approved reduced courseload, with the opportunity to work full-time on their degrees. Students will make significant progress toward completing their degrees.

Location

( 7:00PM - 7:00PM)

This course affords graduate students visiting the University of Rochester full-time student status. Visiting students will engage in research, discussion, and/or professional training in partnership with an academic department or faculty member.

Location

( 7:00PM - 7:00PM)

This course provides PhD students the opportunity to work full-time on their dissertation. Students will make significant progress toward completing degree requirements.

Location

( 7:00PM - 7:00PM)