printer friendly pageCME 200: Linear Algebra with Application to Engineering Computations (ME 300A)
Computer based solution of systems of algebraic equations obtained from engineering problems and eigen-system analysis, Gaussian elimination, effect of round-off error, operation counts, banded matrices arising from discretization of differential equations, ill-conditioned matrices, matrix theory, least square solution of unsolvable systems, solution of non-linear algebraic equations, eigenvalues and eigenvectors, similar matrices, unitary and Hermitian matrices, positive definiteness, Cayley-Hamilton theory and function of a matrix and iterative methods. Prerequisite: familiarity with computer programming, and
MATH51.
Terms: Aut
| Units: 3
Instructors:
Aboumrad, G. (PI)
;
Iaccarino, G. (PI)
;
AKULI, N. (TA)
...
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Instructors:
Aboumrad, G. (PI)
;
Iaccarino, G. (PI)
;
AKULI, N. (TA)
;
Benjamin, M. (TA)
;
Kloker, L. (TA)
;
Madden, I. (TA)
;
Zainana, S. (TA)
CME 204: Partial Differential Equations in Engineering (ME 300B)
Geometric interpretation of partial differential equation (PDE) characteristics; solution of first order PDEs and classification of second-order PDEs; self-similarity; separation of variables as applied to parabolic, hyperbolic, and elliptic PDEs; special functions; eigenfunction expansions; the method of characteristics. If time permits, Fourier integrals and transforms, Laplace transforms. Prerequisite:
CME 200/
ME 300A, equivalent, or consent of instructor.
Terms: Win
| Units: 3
Instructors:
Khanwale, M. (PI)
;
Mirjalili, S. (PI)
;
AKULI, N. (TA)
...
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Instructors:
Khanwale, M. (PI)
;
Mirjalili, S. (PI)
;
AKULI, N. (TA)
;
Brown, R. (TA)
;
Goel, P. (TA)
CME 206: Introduction to Numerical Methods for Engineering (ME 300C)
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
CME 209: Mathematical Modeling of Biological Systems (BIOE 209)
The course covers mathematical and computational techniques needed to solve advanced problems encountered in applied bioengineering. Fundamental concepts are presented in the context of their application to biological and physiological problems including cancer, cardiovascular disease, infectious disease, and systems biology. Topics include Taylor's Series expansions, parameter estimation, regression, nonlinear equations, linear systems, optimization, numerical differentiation and integration, stochastic methods, ordinary differential equations and Fourier series. Python, Matlab and other software will be used for weekly assignments and projects.Prerequisites:
Math 51, 52, 53; prior programming experience (Matlab or other language at level of
CS 106a or higher)
Terms: Aut
| Units: 3
Instructors:
Marsden, A. (PI)
;
Papamanolis, L. (TA)
CME 211: Software Development for Scientists and Engineers
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. Software design principles including time and space complexity analysis, data structures, object-oriented design, decomposition, encapsulation, and modularity are emphasized. Usage of campus wide Linux compute resources: login, file system navigation, editing files, compiling and linking, file transfer, etc. Versioning and revision control, software build utilities, and the LaTeX typesetting software are introduced and used to help complete programming assignments. Prerequisite: introductory programming course equivalent to
CS 106A or instructor consent.
Last offered: Autumn 2022
CME 213: Introduction to parallel computing using MPI, openMP, and CUDA (ME 339)
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: Spr
| Units: 3
CME 214: Software Design in Modern Fortran for Scientists and Engineers
This course introduces software design and development in modern Fortran. Course covers the functional, object-oriented-, and parallel programming features introduced in the Fortran 95, 2003, and 2008 standards, respectively, in the context of numerical approximations to ordinary and partial differential equations; introduces object-oriented design and design schematics based on the Unified Modeling Language (UML) structure, behavior, and interaction diagrams; cover the basic use of several open-source tools for software building, testing, documentation generation, and revision control. Recommended: Familiarity with programming in Fortran 90, basic numerical analysis and linear algebra, or instructor approval
Last offered: Autumn 2017
CME 215: Machine Learning and the Physical Sciences (GEOPHYS 148, GEOPHYS 248)
This course provides a survey of the rapidly growing field of machine learning in the physical sciences. It covers various areas such as inverse problems, emulating physical processes, model discovery given data, and solution discovery given equations. It both introduces the background knowledge required to implement physics-informed deep learning and provides practical in-class coding exercises. Students have the opportunity to apply this emerging methodology to their own research interests across all fields of the physical sciences, including geophysics, climate, fluids, or other systems where the same technique applies. Students develop individual projects throughout the semester. Recommended Prerequisite: Calculus (e.g.
Math 21), Differential Equations (e.g.
MATH 53 or
PHYSICS 111) or equivalents.
Terms: Spr
| Units: 3
Instructors:
Lai, C. (PI)
CME 216: Machine Learning for Computational Engineering. (ME 343)
Linear and kernel support vector machines, deep learning, deep neural networks, generative adversarial networks, physics-based machine learning, forward and reverse mode automatic differentiation, optimization algorithms for machine learning, TensorFlow, PyTorch.
Terms: Win
| Units: 3
Instructors:
Patel, D. (PI)
;
Woringer, P. (TA)
CME 217: Analytics Accelerator (BIODS 217)
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. Students work in dynamic teams with the support of course faculty and mentors, researching preselected topics. Students apply a computational and data analytics lens and use design thinking methodology. The course exposes students to ethics, unintended consequences and team building exercises supported by relevant lectures on data science and subject matter topics. Pre-requisites: none. Enrollment by application only. Graduate students only. The course application closes November 30, 2021. Application and more information:
https://forms.gle/VW6KKWN4AUV6cPzZA
Last offered: Winter 2022
| Repeatable
2 times
(up to 6 units total)
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