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 102: Ordinary Differential Equations for Engineers (ENGR 155A)
Analytical and numerical methods for solving ordinary differential equations arising in engineering applications are presented. For analytical methods students learn to solve linear and non-linear first order ODEs; linear second order ODEs; and Laplace transforms. Numerical methods using MATLAB programming tool kit are also introduced to solve various types of ODEs including: first and second order ODEs, higher order ODEs, systems of ODEs, initial and boundary value problems, finite differences, and multi-step methods. This also includes accuracy and linear stability analyses of various numerical algorithms which are essential tools for the modern engineer. This class is foundational for professional careers in engineering and as a preparation for more advanced classes at the undergraduate and graduate levels. 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, Win
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Darve, E. (PI)
;
Le, H. (PI)
;
Ankeney, G. (TA)
;
Ayala Bellido, C. (TA)
;
Chen, C. (TA)
;
Diller, E. (TA)
;
Nzia Yotchoum, H. (TA)
CME 102ACE: 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. Enrollment by department permission only. Prerequisite: must be concurrently enrolled in
CME102. Application at:
https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers
Terms: Aut, Win
| Units: 1
Instructors:
Jose, A. (PI)
CME 108: Introduction to Scientific Computing
Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites:
CME 100, 102 or
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).
Terms: Aut
| Units: 3
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR
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 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 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 218: Applied Data Science (MS&E 218)
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 important techniques in applied data science as well as to the soft skills necessary for success in applied data science, such as ethics, unintended consequences and team building. Enrollment by application only. Graduate students only. The course application closes Sept 25, 2023. Application and more information:
https://forms.gle/gzGXkJmGMVYuJabK7
Terms: Aut
| Units: 3
| Repeatable
2 times
(up to 6 units total)
Instructors:
Hanson, K. (PI)
;
Udell, M. (PI)
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