High resolution schemes for capturing shock waves and contact discontinuities; upwinding and artificial diffusion; LED and TVD concepts; alternative flow splittings; numerical shock structure. Applications in heat and mass transport, mechanical vibration and acoustic waves, transmission lines, and fluid mechanics. Same as: ENGR 155A. 5 Units. Introduction to Scientific Python. 3 Units. Approval is valid until June 10, 2021. Numerous applications in engineering, manufacturing, reliability and quality assurance, medicine, biology, and other fields. An estimated 10 new activities will be available online this year. 1 Unit. Introduction to Computational Mechanics. Markov chains and processes, random walks, basic ergodic theory and its application to parameter estimation. It includes a 2-page cheatsheet dedicated to Probability as well as another 2-page cheasheet to Statistics , so that you can review the material of the class in a concise format! Introduction to MATLAB. 3 Units. Same as: ME 300A. Same as: ENGR 155C. Back testing, stress testing and Monte Carlo methods. Lagrange interpolation, splines. Introduction to Scientific Computing. Teams of students use techniques in applied and computational mathematics to tackle problems with real world data sets. Same as: BIOE 279, BIOMEDIN 279, BIOPHYS 279, CS 279. Formulation of supervised and unsupervised learning problems. Computation and visualization using MATLAB. Regularization and its role in controlling complexity. Same as: BIOE 285, ME 285. Computer representation of integer and floating point numbers, and interoperability between C/C++ and Fortran is described. Computation and visualization using MATLAB. Lectures will be interactive with a focus on real world applications of scientific computing. Topics include tail bounds, the probabilistic method, Markov chains, and martingales, with applications to analyzing random graphs, metric embeddings, random walks, and a host of powerful and elegant randomized algorithms. CME 100. Emphasis is on theoretical foundations, though we will apply this theory broadly, discussing applications in machine learning and data analysis, networking, and systems. CME 262. Automatic design; inverse problems and aerodynamic shape optimization via adjoint methods. 3 Units. Prerequisites: 302 or 200 (ME 300A), 213 or equivalent, or consent of instructor. Educational opportunities in high technology research and development labs in applied mathematics. Earn 100 Case Interpretation certificate; 20 hours of Category 1 CME credits; Tuition includes a case-based on-line cardiac training module with 50 additional cases housed at www.CardiacTraining.com (with an option for an additional 10 CME credits) Physician Course Highlights This short course runs for the first four weeks of the quarter. Prerequisite: Basic coursework in multivariable calculus and ordinary differential equations, and some prior experience with a proof-based treatment of the material as in MATH 171 or MATH 61CM.nnNOTE: Undergraduates require instructor permission to enroll. Same as: EE 364B. Same as: ME 332. Covers the fundamentals of accelerating applications with GPUs (Graphics Processing Units); GPU programming with CUDA and OpenACC, debugging, thrust/CUB, profiling, optimization, debugging, and other CUDA tools. Discretization of Euler and Navier Stokes equations on unstructured meshes; the relationship between finite volume and finite element methods. The basics of convex analysis and theory of convex programming: optimality conditions, duality theory, theorems of alternative, and applications. Introduction to Machine Learning. Bayesian inference methods are used to combine data and quantify uncertainty in the estimate. Topics will include multithreaded programs, GPU computing, computer cluster programming, C++ threads, OpenMP, CUDA, and MPI. 3 Units. Evidence-Based Medicine Glossary. 3 Units. Basic Probability and Stochastic Processes with Engineering Applications. The rudiments of computational topology and persistent homology on sampled spaces. Weekly briefings with faculty adviser and associated faculty to discuss ongoing consultancy projects and evaluate solutions. Computational Modeling in the Cardiovascular System. 3 Units. This course will offer skills in support of the teams working toward the Big Earth Hackathon Wildland Fire challenge (CEE 265H, EARTH 165H, EARTH 265H). Same as: EE 104. CME 323. Numerous examples and applications drawn from classical mechanics, fluid dynamics and electromagnetism. Prerequisites: ENGR 108; EE 178 or CS 109; CS106A or equivalent. An introduction to computer architecture covering processors, memory hierarchy, storage, and networking provides a foundation for understanding software performance. Python, Matlab and other software will be used for weekly assignments and projects.nPrerequisites: MATH 51, 52, 53; prior programming experience (Matlab or other language at level of CS 106A or higher). Experiments on data from a wide variety of engineering and other disciplines. Computational Consulting. Differential vector calculus: analytic geometry in space, functions of several variables, partial derivatives, gradient, unconstrained maxima and minima, Lagrange multipliers. Same as: MATH 301. 3 Units. Prerequisites: CME 200/ME 300A, CME 204/ME 300B. Topics in this course include analytical and computational methods for solutions of flow in deformable vessels, one-dimensional equations of blood flow, cardiovascular anatomy, lumped parameter models, vascular trees, scaling laws, biomechanics of the circulatory system, and 3D patient specific modeling with finite elements; course will provide an overview of the diagnosis and treatment of adult and congenital cardiovascular diseases and review recent research in the literature in a journal club format. Technologies covered include Numpy, SciPy, Pandas, Scikit-learn, and others. Time discretization; explicit and implicit schemes; acceleration of steady state calculations; residual averaging; math grid preconditioning. Same as: CEE 362G. Departmental Seminar. CME 214. These computational methods play an increasingly important role in drug discovery, medicine, bioengineering, and molecular biology. Mathematical solution methods via applied problems including chemical reaction sequences, mass and heat transfer in chemical reactors, quantum mechanics, fluid mechanics of reacting systems, and chromatography. Same as: ENGR 154. Basic usage of the Python and C/C++ programming languages are introduced and used to solve representative computational problems from various science and engineering disciplines. Analytical and numerical methods for solving ordinary differential equations arising in engineering applications are presented. We will discuss a framework for reasoning about when to apply various machine learning techniques, emphasizing questions of over-fitting/under-fitting, regularization, interpretability, supervised/unsupervised methods, and handling of missing data. CME with gift card offers are popular with clinicians who need to spend their remaining CME allowance before it expires at the end of December 2020. 1 Unit. Educational opportunities in high technology research and development labs in applied mathematics. With online CME that comes with a complimentary Amazon gift card, you can easily meet your annual CME and MOC requirements while earning a … 3 Units. CME 206. Short course running first four weeks of the quarter (8 lectures) with interactive online lectures and application based assignment. 16 pages. Students will work collaboratively in problem solving through a supportive community of mathematics learners. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc. CME 303. CME 444. Application at: https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers. This course has three goals ¿ to give you a different mathematics experience that could reshape your relationship with mathematics, to provide you with a basis for success in future courses at Stanford, and to teach you the important ideas that pervade calculus. Same as: MS&E 346. This is a multidisciplinary graduate level course designed to give students hands-on experience working in teams through real-world project-based research and experiential classroom activities. Applications to signal processing, communications, control, analog and digital circuit design, computational geometry, statistics, machine learning, and mechanical engineering. Placement diagnostic (recommendation non-binding) at: https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext. Students will be invited to think about what calculus is all about and why it matters. The class will be based on short workshops and a final project. Approval is valid until October 30, 2021. Differential vector calculus: vector-valued functions, analytic geometry in space, functions of several variables, partial derivatives, gradient, linearization, unconstrained maxima and minima, Lagrange multipliers and applications to trajectory simulation, least squares, and numerical optimization. It is highly recommended for students with no prior programming experience who are expected to use MATLAB in math, science, or engineering courses. Applied Fourier Analysis and Elements of Modern Signal Processing. CME 285. Same as: EE 364A. Same as: ME 343. 3 Units. Examples and applications drawn from a variety of engineering fields. CME 302. Solution of linear systems, accuracy, stability, LU, Cholesky, QR, least squares problems, singular value decomposition, eigenvalue computation, iterative methods, Krylov subspace, Lanczos and Arnoldi processes, conjugate gradient, GMRES, direct methods for sparse matrices. Presentations about research at Stanford by faculty and researchers from Engineering, H&S, and organizations external to Stanford. Students work in dynamic teams with the support of course faculty and mentors, researching preselected topics focused on COVID-19 during fall 2020 with the option to continue into winter 2021. Students will use SimVascular software to do clinically-oriented projects in patient specific blood flow simulations. This course covers the key tools of probabilistic analysis, and application of these tools to understand the behaviors of random processes and algorithms. Applications include Fourier imaging (the theory of diffraction, computed tomography, and magnetic resonance imaging) and the theory of compressive sensing. CME 106. CME 330. Linear Algebra with Application to Engineering Computations. CME 300. 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