printer friendly pageCME 100: Vector Calculus for Engineers (ENGR 154)
Computation and visualization using MATLAB. 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. Introduction to linear algebra: matrix operations, systems of algebraic equations with applications to coordinate transformations and equilibrium problems. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green's, divergence, and Stokes' theorems. Numerous examples and applications drawn from classical mechanics, fluid dynamics and electromagnetism. Prerequisites: knowledge of single-variable calculus equivalent to the content of
Math 19-21 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math 21). Placement diagnostic (recommendation non-binding) at:
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext.
Terms: Aut, Spr
| Units: 5
| UG Reqs: WAY-FR, GER:DB-Math
CME 100ACE: 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: must be concurrently enrolled in
CME100-01 or 02. Application at:
https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers
Terms: Aut, Spr
| Units: 1
Instructors:
Chian, S. (PI)
;
Hall-Zazueta, R. (PI)
CME 104: Linear Algebra and Partial Differential Equations for Engineers (ENGR 155B)
Linear algebra: systems of algebraic equations, Gaussian elimination, undetermined and overdetermined systems, coupled systems of ordinary differential equations, LU factorization, eigensystem analysis, normal modes. Linear independence, vector spaces, subspaces and basis. Numerical analysis applied to structural equilibrium problems, electrical networks, and dynamic systems. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Applications in heat and mass transport, mechanical vibration and acoustic waves, transmission lines, and fluid mechanics. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications drawn from a variety of engineering fields. Prerequisite:
CME102/
ENGR155A.
Terms: Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
CME 107: Introduction to Machine Learning (EE 104)
Introduction to machine learning. Formulation of supervised and unsupervised learning problems. Regression and classification. Data standardization and feature engineering. Loss function selection and its effect on learning. Regularization and its role in controlling complexity. Validation and overfitting. Robustness to outliers. Simple numerical implementation. Experiments on data from a wide variety of engineering and other disciplines. Undergraduate students should enroll for 5 units, and graduate students should enroll for 3 units. Prerequisites:
ENGR 108;
EE 178 or
CS 109; CS106A or equivalent.
Terms: Spr
| Units: 3-5
Instructors:
Boyd, S. (PI)
;
Devanathan, N. (TA)
CME 192: Introduction to MATLAB
This short course runs for the first four weeks/eight lectures 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. The 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
Instructors:
Wei, Z. (PI)
CME 193: Introduction to Scientific Python
It is recommended for students who are familiar with programming at least at the level of CS106A and want to translate their programming knowledge to Python with the goal of becoming proficient in the scientific computing and data science stack. Lectures will be interactive with a focus on real world applications of scientific computing. Technologies covered include Numpy, SciPy, Pandas, Scikit-learn, and others. Topics will be chosen from Linear Algebra, Optimization, Machine Learning, and Data Science. Prior knowledge of programming will be assumed, and some familiarity with Python is helpful, but not mandatory.
Terms: Aut, Win, Spr
| Units: 1
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 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 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 243: Risk Analytics and Management in Finance and Insurance (STATS 243)
Market risk and credit risk, credit markets. Back testing, stress testing and Monte Carlo methods. Logistic regression, generalized linear models and generalized mixed models. Loan prepayment and default as competing risks. Survival and hazard functions, correlated default intensities, frailty and contagion. Risk surveillance, early warning and adaptive control methodologies. Banking and bank regulation, asset and liability management. Prerequisite:
STATS 240 or equivalent.
Terms: Spr
| Units: 3
Filter Results: