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CME 100: Vector Calculus for Engineers (ENGR 154)

Computation and visualization using MATLAB. Differential vector calculus: analytic geometry in space, functions of several variables, partial derivatives, gradient, unconstrained maxima and minima, Lagrange multipliers. Introduction to linear algebra: matrix operations, systems of algebraic equations, methods of solution and applications. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green¿s, divergence, and Stokes¿ theorems. Examples and applications drawn from various engineering fields. Prerequisites: MATH 41 and 42, or 10 units AP credit. Note: Students enrolled in section 100-02 and 100A-02 are required to attend the discussion sections on Thursdays 5:15-6:45.
Terms: Aut, Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

CME 100A: Vector Calculus for Engineers, ACE

Students attend CME100/ENGR154 lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Enrollment by department permission only. Prerequisite: application at:http://soe.stanford.edu/current_students/edp/programs/ace.html
Terms: Aut, Spr | Units: 6 | UG Reqs: GER:DB-Math, WAY-FR

CME 102: Ordinary Differential Equations for Engineers (ENGR 155A)

Analytical and numerical methods for solving ordinary differential equations arising in engineering applications: Solution of initial and boundary value problems, series solutions, Laplace transforms, and nonlinear equations; numerical methods for solving ordinary differential equations, accuracy of numerical methods, linear stability theory, finite differences. Introduction to MATLAB programming as a basic tool kit for computations. Problems from various engineering fields. Prerequisite: CME 100/ENGR 154 or MATH 51.
Terms: Aut, Win, Spr, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

CME 102A: Ordinary Differential Equations for Engineers, ACE

Students attend CME102/ENGR155A lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Prerequisite: application at:http://soe.stanford.edu/current_students/edp/programs/ace.html
Terms: Aut, Win, Spr | Units: 6 | UG Reqs: GER:DB-Math, WAY-FR

CME 103: Introduction to Matrix Methods (EE 103)

Introduction to applied linear algebra with emphasis on applications. Vectors, norm, and angle; linear independence and orthonormal sets. Matrices, left and right inverses, QR factorization. Least- squares and model fitting, regularization and cross-validation, time-series prediction, and other examples. Constrained least-squares; applications to least-norm reconstruction, optimal control, and portfolio optimization. Newton methods and nonlinear least-squares. Prerequisites: MATH 51 or CME 100.
Terms: Aut | Units: 4-5 | UG Reqs: GER:DB-Math, WAY-FR

CME 192: Introduction to MATLAB

This short course runs for the first eight weeks of the quarter and is offered each quarter during the academic year. It is highly recommended for students with no prior programming experience who are expected to use MATLAB in math, science, or engineering courses. It will consist of interactive lectures and application-based assignments.nThe goal of the short course is to make students fluent in MATLAB and to provide familiarity with its wide array of features. The course covers an introduction of basic programming concepts, data structures, and control/flow; and an introduction to scientific computing in MATLAB, scripts, functions, visualization, simulation, efficient algorithm implementation, toolboxes, and more.
Terms: Aut, Win, Spr | Units: 1

CME 193: Introduction to Scientific Python

This short course runs for the first eight weeks of the quarter and is offered each quarter during the academic year. It is recommended for students who want to use Python in math, science, or engineering courses and for students who want to learn the basics of Python programming. The goal of the short course is to familiarize students with Python¿s tools for scientific computing. Lectures will be interactive with a focus on learning by example, and assignments will be application-driven. Some prior programming experience is highly recommended.nTopics covered include control flow, basic data structures, File I/O, and an introduction to NumPy/SciPy.
Terms: Aut, Win, Spr | Units: 1

CME 195: Introduction to R (STATS 195)

This short course runs for the first four weeks of the quarter and is offered in fall and spring. It is recommended for students who want to use R in statistics, science, or engineering courses and for students who want to learn the basics of R programming. The goal of the short course is to familiarize students with R's tools for scientific computing. Lectures will be interactive with a focus on learning by example, and assignments will be application-driven. No prior programming experience is needed. Topics covered include basic data structures, File I/O, graphs, control structures, etc, and some useful packages in R.
Terms: Aut, Spr | Units: 1
Instructors: ; Michael, H. (PI); Suo, X. (PI)

CME 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: ; Iaccarino, G. (PI)

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: Aut, Win | Units: 3
Instructors: ; Lele, S. (PI)

CME 206: Introduction to Numerical Methods for Engineering (AA 214A, 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: Aut, Spr | Units: 3

CME 211: Introduction to Programming for Scientists and Engineers (EARTHSCI 211)

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 individual programming assignments and a final project. Prerequisite: Some previous experience with programming (does not need to be a formal course in programming).
Terms: Aut | Units: 3

CME 242: Mathematical and Computational Finance Seminar (STATS 239)

| Units: 1 | Repeatable for credit
Instructors: ; Jain, K. (PI)

CME 244: Project Course in Mathematical and Computational Finance

For graduate students in the MCF track; students will work individually or in groups on research projects.
| Units: 1-6
Instructors: ; Jain, K. (PI)

CME 245: Topics in Mathematical and Computational Finance

Current topics for enrolled students in the MCF program; can be repeated up to three times.
Terms: Aut, Win, Spr, Sum | Units: 1 | Repeatable 3 times (up to 3 units total)
Instructors: ; Jain, K. (PI)

CME 263: Introduction to Linear Dynamical Systems (EE 263)

Applied linear algebra and linear dynamical systems with application to circuits, signal processing, communications, and control systems. Topics: least-squares approximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm, and singular value decomposition. Eigenvalues, left and right eigenvectors, with dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input/multi-output systems, impulse and step matrices; convolution and transfer matrix descriptions. Control, reachability, and state transfer; observability and least-squares state estimation. Prerequisites: linear algebra and matrices as in MATH 103; differential equations and Laplace transforms as in EE 102A.
Terms: Aut, Sum | Units: 3
Instructors: ; Lall, S. (PI); Lemon, A. (PI)

CME 292: Advanced MATLAB for Scientific Computing

Short course running first four weeks of the quarter (8 lectures) with interactive lectures and application based assignment. Students will be introduced to advanced MATLAB features, syntaxes, and toolboxes not traditionally found in introductory courses. Material will be reinforced with in-class examples, demos, and homework assignment involving topics from scientific computing. MATLAB topics will be drawn from: advanced graphics (2D/3D plotting, graphics handles, publication quality graphics, animation), MATLAB tools (debugger, profiler), code optimization (vectorization, memory management), object-oriented programming, compiled MATLAB (MEX files and MATLAB coder), interfacing with external programs, toolboxes (optimization, parallel computing, symbolic math, PDEs). Scientific computing topics will include: numerical linear algebra, numerical optimization, ODEs, and PDEs.
Terms: Aut, Win, Spr | Units: 1
Instructors: ; Zahr, M. (PI)

CME 300: First Year Seminar Series

Required for first-year ICME Ph.D. students; recommended for first-year ICME M.S. students. Presentations about research at Stanford by faculty and researchers from Engineering, H&S, and organizations external to Stanford. May be repeated for credit.
Terms: Aut, Win, Spr | Units: 1 | Repeatable for credit
Instructors: ; Gerritsen, M. (PI)

CME 302: Numerical Linear Algebra

First in a three quarter graduate sequence. Solution of systems of linear equations: direct methods, error analysis, structured matrices; iterative methods and least squares. Parallel techniques. Prerequisites: CME 108, MATH 103 or 113.
Terms: Aut | Units: 3
Instructors: ; Darve, E. (PI)

CME 303: Partial Differential Equations of Applied Mathematics (MATH 220)

First-order partial differential equations; method of characteristics; weak solutions; elliptic, parabolic, and hyperbolic equations; Fourier transform; Fourier series; and eigenvalue problems. Prerequisite: foundation in multivariable calculus and ordinary differential equations.
Terms: Aut | Units: 3
Instructors: ; Ryzhik, L. (PI)

CME 309: Randomized Algorithms and Probabilistic Analysis (CS 265)

Randomness pervades the natural processes around us, from the formation of networks, to genetic recombination, to quantum physics. Randomness is also a powerful tool that can be leveraged to create algorithms and data structures which, in many cases, are more efficient and simpler than their deterministic counterparts. This course covers the key tools of probabilistic analysis, and application of these tools to understand the behaviors of random processes and algorithms. Emphasis is on theoretical foundations, though we will apply this theory broadly, discussing applications in machine learning and data analysis, networking, and systems. 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. Prerequisites: CS 161 and STAT 116, or equivalents and instructor consent.
Terms: Aut | Units: 3
Instructors: ; Valiant, G. (PI)

CME 330: Applied Mathematics in the Chemical and Biological Sciences (CHEMENG 300)

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. Topics include generalized vector space theory, linear operator theory with eigenvalue methods, phase plane methods, perturbation theory (regular and singular), solution of parabolic and elliptic partial differential equations, and transform methods (Laplace and Fourier). Prerequisites: CME 102/ENGR 155A and CME 104/ENGR 155B, or equivalents.
Terms: Aut | Units: 3
Instructors: ; Shaqfeh, E. (PI)

CME 334: Advanced Methods in Numerical Optimization (MS&E 312)

Topics include interior-point methods, relaxation methods for nonlinear discrete optimization, sequential quadratic programming methods, optimal control and decomposition methods. Topic chosen in first class; different topics for individuals or groups possible. Individual or team projects. May be repeated for credit.
Terms: Aut | Units: 3 | Repeatable for credit

CME 362: An Introduction to Compressed Sensing (STATS 330)

Compressed sensing is a new data acquisition theory asserting that one can design nonadaptive sampling techniques that condense the information in a compressible signal into a small amount of data. This revelation may change the way engineers think about signal acquisition. Course covers fundamental theoretical ideas, numerical methods in large-scale convex optimization, hardware implementations, connections with statistical estimation in high dimensions, and extensions such as recovery of data matrices from few entries (famous Netflix Prize).
Terms: Aut | Units: 3
Instructors: ; Donoho, D. (PI)

CME 390: Curricular Practical Training

May be repeated three times for credit.
Terms: Aut, Win, Spr, Sum | Units: 1 | Repeatable 3 times (up to 3 units total)
Instructors: ; Jain, K. (PI); Murray, W. (PI)

CME 399: Special Research Topics in Computational and Mathematical Engineering

Graduate-level research work not related to report, thesis, or dissertation. May be repeated for credit.
Terms: Aut, Win, Spr, Sum | Units: 1-15 | Repeatable 6 times (up to 30 units total)

CME 444: Computational Consulting

Advice by graduate students under supervision of ICME faculty. Weekly briefings with faculty adviser and associated faculty to discuss ongoing consultancy projects and evaluate solutions. May be repeated for credit.
Terms: Aut, Win, Spr | Units: 1-3 | Repeatable for credit
Instructors: ; Gerritsen, M. (PI)

CME 500: Departmental Seminar

Weekly research lectures by experts from academia, national laboratories, industry, and doctoral students. May be repeated for credit. In autumn and winter 2014-15, this seminar will predominantly feature current graduate students talking about their research.
Terms: Aut, Win, Spr | Units: 1 | Repeatable for credit
Instructors: ; Gerritsen, M. (PI)

CME 510: Linear Algebra and Optimization Seminar

Recent developments in numerical linear algebra and numerical optimization. Guest speakers from other institutions and local industry. Goal is to bring together scientists from different theoretical and application fields to solve complex scientific computing problems. May be repeated for credit.
Terms: Aut, Win, Spr | Units: 1 | Repeatable for credit
Instructors: ; Saunders, M. (PI)

CME 214: Software Design in Modern Fortran for Scientists and Engineers (EARTHSCI 214)

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
| Units: 3
Instructors: ; Rouson, D. (PI)
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