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ENGR 50: Introduction to Materials Science, Nanotechnology Emphasis

The structure, bonding, and atomic arrangements in materials leading to their properties and applications. Topics include electronic and mechanical behavior, emphasizing nanotechnology, solid state devices, and advanced structural and composite materials.
Terms: Spr | Units: 4 | UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-SMA | Grading: Letter or Credit/No Credit
Instructors: ; Sinclair, R. (PI)

ENGR 50E: Introduction to Materials Science, Energy Emphasis

Materials structure, bonding and atomic arrangements leading to their properties and applications. Topics include electronic, thermal and mechanical behavior; emphasizing energy related materials and challenges.
Terms: Aut | Units: 4 | UG Reqs: WAY-SMA | Grading: Letter or Credit/No Credit

ENGR 50M: Introduction to Materials Science, Biomaterials Emphasis

Topics include: the relationship between atomic structure and macroscopic properties of man-made and natural materials; mechanical and thermodynamic behavior of surgical implants including alloys, ceramics, and polymers; and materials selection for biotechnology applications such as contact lenses, artificial joints, and cardiovascular stents. No prerequisite.
Terms: Win | Units: 4 | UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-SMA | Grading: Letter or Credit/No Credit

ENGR 240: Introduction to Micro and Nano Electromechanical Systems

Miniaturization technologies now have important roles in materials, mechanical, and biomedical engineering practice, in addition to being the foundation for information technology. This course will target an audience of first-year engineering graduate students and motivated senior-level undergraduates, with the goal of providing an introduction to M/NEMS fabrication techniques, selected device applications, and the design tradeoffs in developing systems. The course has no specific prerequisites, other than graduate or senior standing in engineering; otherwise, students will require permission of the instructors.
Terms: Aut | Units: 3 | Grading: Letter or Credit/No Credit

ME 1: Introduction to Mechanical Engineering

This course is intended to be the starting point for Mechanical Engineering majors. It will cover the concepts, engineering methods, and common tools used by mechanical engineers while introducing the students to a few interesting devices. We will discuss how each device was conceived, design challenges that arose, application of analytical tools to the design, and production methods. Main class sections will include lectures, demonstrations, and in-class group exercises. Lab sections will develop specific skills in freehand sketching and computational modeling of engineering systems. Prerequisites: Physics: Mechanics, and first quarter Calculus.
Terms: Aut, Win | Units: 3 | Grading: Letter or Credit/No Credit

ME 17: The Science of Flames

This course is about what causes flames to look like they do and about what causes them to propagate. The physical and chemical phenomena that govern behaviors of flames will constitute the topics for discussion. The basic principles that govern flame phenomena include the conservation of mass, the first law of thermodynamics, and the momentum principle. Since flame processes are controlled by the rates of chemical reactions, these basic principles will be applied when account is made for the chemical transformations that occur when reactant bonds are broken and new bonds are formed, producing combustion products. In essence, this course serves as an introduction to combustion science.
Terms: Sum | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Mitchell, R. (PI)

ME 80: Mechanics of Materials

Mechanics of materials and deformation of structural members. Topics include stress and deformation analysis under axial loading, torsion and bending, column buckling and pressure vessels. Introduction to stress transformation and multiaxial loading. Prerequisite: ENGR 14.
Terms: Aut, Win, Spr | Units: 3 | UG Reqs: GER:DB-EngrAppSci | Grading: Letter (ABCD/NP)

ME 103: Product Realization: Design and Making

Students will build on the foundation created in ME102. ME103 includes structured labs in machining, casting, forming and welding; carrying a single project through the entire design process from conceptualization through presentation of a customer ready prototype, creation of a project based portfolio, and an introduction to manufacturing processes.
Terms: Aut, Win, Spr | Units: 4 | Grading: Letter (ABCD/NP)

ME 115A: Introduction to Human Values in Design

An intensive project-based class that introduces the central philosophy of the product design program. Students learn how to use the lens of human needs to innovate at the intersection of technical factors (feasibility), business factors (viability), and human values (desirability). Students work toward mastery of the human-centered design methodology through several real-world, team-based projects. Students gain fluency in designing solutions ranging from physical products, to digital interfaces, to services and experiences. Students are immersed in building their individual and team capacities around core design process and methods, and emerge with a strong foundation in needfinding, synthesis, ideation, rapid prototyping, user testing, iteration, and storytelling.
Terms: Aut | Units: 3 | Grading: Letter (ABCD/NP)

ME 123: Computational Engineering

The design of wind turbines, biomedical devices, jet engines, electronic units, and almost every other engineering system, require the analysis of its flow and thermal characteristics to ensure optimal performance and safety. The continuing growth ofcomputer power and the emergence of general-purpose engineering software has fostered the use of computational analysis as a complement to experimental testing. Virtual prototyping is a staple of modern engineering practice. This course is an introduction to Computational Engineering using commercial analysis codes, covering both theory and applications. Assuming limited knowledge of computational methods, the course starts with introductory training on the software, using a nseries of lectures and hands-on tutorials. We utilize the ANSYS software suite, which is used across a variety of engineering fields. Herein, the emphasis is on geometry modeling, mesh generation, solution strategy and post-processing for diverse applications. Using classical flow/thermal problems, the course develops the essential concepts of Verification and Validation for engineering simulations, nproviding the basis for assessing the accuracy of the results. Advanced concepts such as the use of turbulence models, user programming and automation for design are also introduced. The course is concluded by a project, in which the students apply the software to solve a industry-inspired problem.
Terms: Spr | Units: 4 | Grading: Letter or Credit/No Credit
Instructors: ; Iaccarino, G. (PI)

ME 133: Intermediate Fluid Mechanics

This course expands on the introduction to fluid mechanics provided by ME70. Topics include the conservation equations and finite volume approaches to flow quantification; engineering applications of the Navier-Stokes equations for viscous fluid flows; flow instability and transition to turbulence, and basic concepts in turbulent flows, including Reynolds averaging; boundary layers, including the governing equations, the integral method, thermal transport, and boundary layer separation; fundamentals of computational fluid dynamics (CFD); basic ideas of one-dimensional compressible flows.
Terms: Spr | Units: 3 | Grading: Letter (ABCD/NP)
Instructors: ; Lele, S. (PI)

ME 151: Introduction to Computational Mechanics

In modern engineering design of structural systems, computer analysis is often used at every stage, from initial prototyping through final design. This course will introduce students to computational modeling and prototyping applied to solids and structures. The course reviews the basic theory of linear solid mechanics, introduces the finite element method for numerical modeling of mechanics-based problems, and provides practical experience in computer modeling using a commercial finite element code.
Terms: Win | Units: 4 | Repeatable for credit | Grading: Letter or Credit/No Credit
Instructors: ; Pinsky, P. (PI); Gude, G. (TA)

ME 171E: Aerial Robot Design (AA 248E, ME 271E)

(Graduate students only enroll in ME 271e or AA 248e) A result-focused introduction to the design of winged aerial robots capable of vertical takeoff and landing for a wide range of applications. Students will learn how to ideate specific aerial robot applications and make an appropriate design from scratch that meets mission requirements. Design skill outcomes include: robot need identification based on mission requirements; system ideation and sizing; making design performance tradeoffs; aerodynamic wing design; CAD assembly; communicating the design and its application. The hands-on lab experience includes prototyping the aerial robot mission, to inform system design, by building and flying quadcopters. Prerequisites: intro level undergraduate fluid mechanics or aerodynamics (e.g. ME 70 or AA 100) or equivalent; Intro level undergraduate electronics or Arduino experience; MATLAB experience.
Terms: not given this year | Units: 4 | Grading: Letter (ABCD/NP)
Instructors: ; Lentink, D. (PI)

ME 210: Introduction to Mechatronics (EE 118)

Technologies involved in mechatronics (intelligent electro-mechanical systems), and techniques to apply this technology to mecatronic system design. Topics include: electronics (A/D, D/A converters, op-amps, filters, power devices); software program design, event-driven programming; hardware and DC stepper motors, solenoids, and robust sensing. Large, open-ended team project. Prerequisites: ENGR 40, CS 106, or equivalents.
Terms: Win | Units: 4 | Grading: Letter (ABCD/NP)

ME 215C: Analytical Product Design (APD)

Analytical design experience for consumer product. Integration of models of engineering function, manufacturing costs, and market conditions. Introduction to modeling micro economics, market models, and consumer surveying as applied in product design. Introduction to consumer product cost modeling. Draw from other coursework to build engineering function model. Student teams build and link these models in an optimization framework to maximize profitability. Build prototypes for engineering function and form expression.
Terms: Spr | Units: 4 | Grading: Letter (ABCD/NP)
Instructors: ; MacDonald, E. (PI)

ME 216M: Introduction to the Design of Smart Products (CS 377N)

This course will focus on the technical mechatronic skills as well as the human factors and interaction design considerations required for the design of smart products and devices. Students will learn techniques for rapid prototyping of smart devices, best practices for physical interaction design, fundamentals of affordances and signifiers, and interaction across networked devices. Students will be introduced to design guidelines for integrating electrical components such as PCBs into mechanical assemblies and consider the physical form of devices, not just as enclosures but also as a central component of the smart product. Prerequisites include: CS106A and E40 highly recommended, or instructor approval.
Terms: Spr | Units: 3-4 | Grading: Letter or Credit/No Credit
Instructors: ; Follmer, S. (PI)

ME 220: Introduction to Sensors

Sensors are widely used in scientific research and as an integral part of commercial products and automated systems. The basic principles for sensing displacement, force, pressure, acceleration, temperature, optical radiation, nuclear radiation, and other physical parameters. Performance, cost, and operating requirements of available sensors. Elementary electronic circuits which are typically used with sensors. Lecture demonstration of a representative sensor from each category elucidates operating principles and typical performance. Lab experiments with off-the-shelf devices. Recommended Pre-requisites or equivalent knowledge: Physics 43 electromagnetism, Physics 41 mechanics, Math 53 Taylor series approximation, 2nd order Ordinary Diff Eqns, ENGR40A/Engr40 or ME210, i.e. some exposure to building basic circuits
Terms: Spr | Units: 3-4 | Grading: Letter or Credit/No Credit

ME 234: Introduction to Neuromechanics

Understanding the role of mechanics in brain development, physiology, and pathology. Mechanics of brain cells: neurons, mechanobiology, mechanotransduction. Mechanics of brain tissue: experimental testing, constitutive modeling, computational modeling. Mechanics of brain development: gyrification, cortical folding, axon elongation, lissencephaly, polymicrogyria. Mechanics of traumatic brain injury: high impact loading, neural injury. Mechanics of brain tumors, brain cancer, tumor growth, altered cytoskeletal mechanics. Mechanics of neurological disorders: autism, dementia, schizophrenia. Mechanics of brain surgery.
Terms: Win | Units: 3 | Grading: Letter or Credit/No Credit

ME 265: Technology Licensing and Commercialization

Course focuses on how to bridge the gap between creation and commercialization with new ideas, inventions, and technology (not limited to mechanical engineering). Comprehensive introduction to patents, copyrights, trademarks, and trade secrets. Covers business strategies and legal aspects of determining what can be owned and licensed, how to determine commercial value, and what agreements and other paperwork is necessary. Discussion includes aspects of Contract and Intellectual Property law as well as provisions of license agreements, NDAs, and their negotiation. All materials provided including many sample documents.
Terms: Spr | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Hustein, J. (PI)

ME 271E: Aerial Robot Design (AA 248E, ME 171E)

(Graduate students only enroll in ME 271e or AA 248e) A result-focused introduction to the design of winged aerial robots capable of vertical takeoff and landing for a wide range of applications. Students will learn how to ideate specific aerial robot applications and make an appropriate design from scratch that meets mission requirements. Design skill outcomes include: robot need identification based on mission requirements; system ideation and sizing; making design performance tradeoffs; aerodynamic wing design; CAD assembly; communicating the design and its application. The hands-on lab experience includes prototyping the aerial robot mission, to inform system design, by building and flying quadcopters. Prerequisites: intro level undergraduate fluid mechanics or aerodynamics (e.g. ME 70 or AA 100) or equivalent; Intro level undergraduate electronics or Arduino experience; MATLAB experience.
Terms: not given this year | Units: 4 | Grading: Letter (ABCD/NP)
Instructors: ; Lentink, D. (PI)

ME 283: Introduction to Biomechanics and Mechanobiology

Introduction to the mechanical analysis of tissues (biomechanics), and how mechanical cues play a role in regulating tissue development, adaptation, regeneration, and aging (mechanobiology). Topics include tissue viscoelasticity, cardiovascular biomechanics, blood rheology, interstitial flow, bone mechanics, muscle contraction and mechanics, and mechanobiology of the musculoskeletal system. Undergraduates should have taken ME70 and ME80, or equivalent courses.
Terms: Spr | Units: 3 | Grading: Letter (ABCD/NP)
Instructors: ; Chaudhuri, O. (PI)

ME 287: Mechanics of Biological Tissues

Introduction to the mechanical behaviors of biological tissues in health and disease. Overview of experimental approaches to evaluating tissue properties and mathematical constitutive models. Elastic behaviors of hard tissues, nonlinear elastic and viscoelastic models for soft tissues.
Terms: Aut | Units: 4 | Grading: Letter (ABCD/NP)

ME 300C: Introduction to Numerical Methods for Engineering (CME 206)

Numerical methods from a user's point of view. Lagrange interpolation, splines. Integration: trapezoid, Romberg, Gauss, adaptive quadrature; numerical solution of ordinary differential equations: explicit and implicit methods, multistep methods, Runge-Kutta and predictor-corrector methods, boundary value problems, eigenvalue problems; systems of differential equations, stiffness. Emphasis is on analysis of numerical methods for accuracy, stability, and convergence. Introduction to numerical solutions of partial differential equations; Von Neumann stability analysis; alternating direction implicit methods and nonlinear equations. Prerequisites: CME 200/ME 300A, CME 204/ME 300B.
Terms: Spr | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Mani, A. (PI)

ME 302B: The Future of the Automobile- Driver Assistance and Automated Driving

This course provides a holistic overview over the field of vehicle automation. The course starts with the history of vehicle automation and then introduces key terminology and taxonomy. Guest lecturers present the legal and policy aspects of vehicle automation both on the federal and state level. Then, the state of the art in vehicle automation is provided. This includes sensor and actuator technology as well as the driver assistance technology in cars today. Finally, the technology currently being developed for future highly and fully automated vehicles is described, including a high-level introduction of the software and algorithms used as well as HMI and system aspects. Students are asking to work in groups on a current topic related to vehicle automation and present their findings in the final two classes in a short presentation.
Terms: Win | Units: 1 | Repeatable for credit | Grading: Satisfactory/No Credit
Instructors: ; Becker, J. (PI)

ME 304D: Designing Your Life

The course employs a design thinking approach to help fellows develop a point of view about their life and career. The course focuses on an introduction to design thinking, the integration of work and worldview, and practices that support vocation formation. Includes seminar-style discussions, role-playing, short writing assignments, guest speakers, and individual mentoring and coaching. Open to DCI (Distinguished Career Institute) Fellows only. Additional course information at http://www.designingyourlife.org.
Terms: Aut, Win, Spr | Units: 1 | Repeatable for credit | Grading: Satisfactory/No Credit
Instructors: ; Evans, D. (PI)

ME 313: Human Values and Innovation in Design

Introduction to the philosophy and practice of the Design Impact program. Hands-on design projects are used as vehicles for learning design thinking's tools and methodology. The relationships among technical, human, aesthetic, and business concerns, and drawing, prototyping, and story-telling a will be explored. The focus is on design thinking process and mindsets including: empathy, point of view, ideation, prototyping and testing. For master's students in the Design Impact program only. For a general introduction to design thinking, see ME 377: Design Thinking Studio, taught Autumn and Winter quarters.
Terms: Aut | Units: 3 | Grading: Letter (ABCD/NP)
Instructors: ; Burnett, W. (PI)

ME 320: Introduction to Robotics (CS 223A)

Robotics foundations in modeling, design, planning, and control. Class covers relevant results from geometry, kinematics, statics, dynamics, motion planning, and control, providing the basic methodologies and tools in robotics research and applications. Concepts and models are illustrated through physical robot platforms, interactive robot simulations, and video segments relevant to historical research developments or to emerging application areas in the field. Recommended: matrix algebra.
Terms: Win | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Khatib, O. (PI)

ME 336: Discontinuous Galerkin Methods for Fluid-Flow Simulations

This course is designed to provide an introduction to discontinuous Galerkin (DG) methods and related high-order discontinuous solution techniques for solving partial differential equations with application to fluid flows. The course covers mathematical and theoretical concepts of the DG-methods and connections to finite-element and finite-volume methods. Computational aspects on the discretization, stabilization methods, flux-evaluations, and integration techniques will be discussed. Problems and examples will be drawn from advection-reaction-diffusion equations, non-linear Euler and Navier-Stokes systems, and related fluid-dynamics problems. As part of a series of homework assignments and projects, students will develop their own DG-method for solving the compressible flow equations in complex two-dimensional geometries.
Terms: Aut | Units: 3 | Grading: Letter (ABCD/NP)
Instructors: ; Ihme, M. (PI)

ME 338: Continuum Mechanics (CEE 312)

Introduction to vectors and tensors: kinematics, deformation, forces, and stress concept of continua; balance principles; aspects of objectivity; hyperelastic materials; thermodynamics of materials; variational principles. Prerequisite: CEE 291 or equivalent.
Terms: Spr | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Linder, C. (PI)

ME 339: Introduction to parallel computing using MPI, openMP, and CUDA (CME 213)

This class will give hands-on experience with programming multicore processors, graphics processing units (GPU), and parallel computers. The focus will be on the message passing interface (MPI, parallel clusters) and the compute unified device architecture (CUDA, GPU). Topics will include multithreaded programs, GPU computing, computer cluster programming, C++ threads, OpenMP, CUDA, and MPI. Pre-requisites include C++, templates, debugging, UNIX, makefile, numerical algorithms (differential equations, linear algebra).
Terms: Win | Units: 3 | Grading: Letter or Credit/No Credit

ME 340: Mechanics - Elasticity and Inelasticity

Introduction to the theories of elasticity, plasticity and fracture and their applications. Elasticity: Definition of stress, strain, and elastic energy; equilibrium and compatibility conditions; and formulation of boundary value problems. Stress function approach to solve 2D elasticity problems and Green’s function approach in 3D. Applications to contact and crack. Plasticity: Yield surface, associative flow rule, strain hardening models, crystal plasticity models. Applications to plastic bending, torsion and pressure vessels. Fracture: Linear elastic fracture mechanics, J-integral, Dugdale-Barrenblatt crack model. Applications to brittle fracture and fatigue crack growth. Computer programming in Matlab is used to aid analytic derivation and numerical solutions.
Terms: Aut | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Gu, W. (PI)

ME 344: Introduction to High Performance Computing

ME 344 is an introductory course on High Performance Computing Systems, providing a solid foundation in parallel computer architectures, cluster operating systems, and resource management. This course will discuss fundamentals of what an HPC cluster consists of, and how we can take advantage of such systems to solve large scare problems in wide ranging applications like computational fluid dynamics, image processing, machine learning and analytics. You will learn how to take advantage of Open HPC, Intel Parallel Studio, Environment Modules, Containers, Spack, and Cloud-based architectures via lectures, practical hands-on homework assignments, and hands-on laboratory work. While we provide software and supporting libraries to complete homework, you are welcome to bring you own application to learn how to build and make use of it in an HPC, Container, or Cloud-based compute environment. There are no prerequisites for computer programming languages. Many of the tasks involve scripting languages, knowledge of bash, python, or similar is helpful. Group work and collaboration on projects is both allowed and encouraged.
Terms: Sum | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Jones, S. (PI)

ME 346A: Introduction to Statistical Mechanics

The main purpose of this course is to provide students with enough statistical mechanics background to the Molecular Simulations classes (ME 346B,C), including the fundamental concepts such as ensemble, entropy, and free energy, etc. The main theme of this course is how the laws at the macroscale (thermodynamics) can be obtained by analyzing the spontaneous fluctuations at the microscale (dynamics of molecules). Topics include thermodynamics, probability theory, information entropy, statistical ensembles, phase transition and phase equilibrium. Recommended: PHYSICS 110 or equivalent.
Terms: Spr | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Cai, W. (PI)

ME 351B: Fluid Mechanics

Laminar viscous fluid flow. Governing equations, boundary conditions, and constitutive laws. Exact solutions for parallel flows. Creeping flow limit, lubrication theory, and boundary layer theory including free-shear layers and approximate methods of solution; boundary layer separation. Introduction to stability theory and transition to turbulence, and turbulent boundary layers. Prerequisite: 351A.
Terms: Win | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Mani, A. (PI); Balaji, R. (TA)

ME 352B: Fundamentals of Heat Conduction

Physical description of heat conduction in solids, liquids, and gases. The heat diffusion equation and its solution using analytical and numerical techniques. Data and microscopic models for the thermal conductivity of solids, liquids, and gases, and for the thermal resistance at solid-solid and solid-liquid boundaries. Introduction to the kinetic theory of heat transport, focusing on applications for composite materials, semiconductor devices, micromachined sensors and actuators, and rarefied gases. Prerequisite: consent of instructor.
Terms: Win | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Goodson, K. (PI)

ME 352C: Convective Heat Transfer

Prediction of heat and mass transfer rates based on analytical and numerical solutions of the governing partial differential equations. Heat transfer in fully developed pipe and channel flow, pipe entrance flow, laminar boundary layers, and turbulent boundary layers. Superposition methods for handling non-uniform wall boundary conditions. Approximate models for turbulent flows. Comparison of exact and approximate analyses to modern experimental results. General introduction to heat transfer in complex flows. Prerequisite: 351B or equivalent.
Terms: Spr | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Eaton, J. (PI)

ME 373: Nanomaterials Synthesis and Applications for Mechanical Engineers

This course provides an introduction to both combustion synthesis of functional nanomaterials and nanotechnology. The first part of the course will introduce basic principles, synthesis/fabrication techniques and application of nanoscience and nanotechnology. The second part of the course will discuss combustion synthesis of nanostructures in zero-, one- two- and three- dimensions, their characterization methods, physical and chemical properties, and applications in energy conversion systems.
Terms: Win | Units: 3 | Grading: Letter (ABCD/NP)
Instructors: ; Zheng, X. (PI)

ME 374: Dynamics and Kinetics of Nanoparticles

Part 1: Thermodynamics, transport theories and properties, aerosol dynamics and reaction kinetics of nanoparticles in fluids. Nucleation, gas kinetic theory of nanoparticles, the Smoluchowski equation, gas-surface reactions, diffusion, thermophoresis, conservation equations and useful solutions. Part 2: Introduction to soot formation, nanoparticles in reacting flows, particle transport and kinetics in flames, atmospheric heterogenous reactions, and nanocatalysis.
Terms: Win | Units: 3 | Grading: Letter or Credit/No Credit
Instructors: ; Wang, H. (PI)

ME 377: Design Thinking Studio

Design Thinking Studio is an immersive introduction to design thinking. You will engage in the real world with your heart, hands and mind to learn and apply the tools and attitudes of design. The class is project-based and emphasizes adopting new behaviors of work. Fieldwork and collaboration with teammates are required and are a critical component of the class. Application required, see dschool.stanford.edu/classes for more information.
Terms: Aut, Win, Spr | Units: 4 | Grading: Letter (ABCD/NP)

ME 405: Asymptotic Methods in Computational Engineering

This course is not a standard teaching of asymptotic methods as thought in the applied math programs. Nor does it involve such elaborate algebra and analytical derivations. Instead, the class relies on students' numerical programming skills and introduces improvements on numerical methods using standard asymptotic and scaling ideas. The main objective of the course is to bring physical insight into numerical programming. The majority of the problems to be explored involve one- and two-dimensional transient partial differential equations inspired by thermal-fluid and transport engineering applications. Topics include: 1-Review of numerical discretization and numerical stability, 2-Implicit versus explicit methods, 3-Introduction to regular and singular perturbation problems, 4-Method of matched asymptotic expansions, 5-Stationary thin interfaces: boundary layers, Debye layers, 6-Moving thin interfaces: shocks, phase-interfaces, 7-Reaction-diffusion problems, 8-Directional equilibrium and lubrication theory.
Terms: not given this year | Units: 3 | Grading: Letter or Credit/No Credit
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