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: must be enrolled in the regular
CME100-01 or 02. Application at:
https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers
Terms: Aut, Win, Spr
| Units: 6
| UG Reqs: WAY-FR, GER:DB-Math
Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
;
Aboumrad, G. (TA)
;
Bhargava, P. (TA)
;
DePaul, G. (TA)
;
Fadavi, D. (TA)
;
Fournier-Bidoz, E. (TA)
;
Gao, P. (TA)
;
Genin, M. (TA)
;
Hegde, V. (TA)
;
Krason, M. (TA)
;
Lakshman, V. (TA)
;
Lenain, R. (TA)
;
Sanchez, S. (TA)
;
Storchan, V. (TA)
;
Suresh, S. (TA)
;
Westhoff, P. (TA)
;
Yang, F. (TA)
;
shirian, y. (TA)
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: 10 units of AP credit (Calc BC with 4 or 5, or Calc AB with 5), or
Math 41 and 42. Recommended:
CME100.
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: students must be enrolled in the regular section (
CME102) prior to submitting application at:n
https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers
Terms: Aut, Win, Spr
| Units: 6
| UG Reqs: WAY-FR, GER:DB-Math
CME 106: Introduction to Probability and Statistics for Engineers (ENGR 155C)
Probability: random variables, independence, and conditional probability; discrete and continuous distributions, moments, distributions of several random variables. Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, non-parametric tests, regression and correlation analyses; applications in engineering, industrial manufacturing, medicine, biology, and other fields. Prerequisite:
CME 100/ENGR154 or
MATH 51 or 52.
Terms: Win, Sum
| Units: 4
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR
Instructors:
Khayms, V. (PI)
;
An, J. (TA)
;
Ayoul, T. (TA)
;
Fournier-Bidoz, E. (TA)
;
Gao, P. (TA)
;
Genin, M. (TA)
;
Krason, M. (TA)
;
Lakshman, V. (TA)
;
Slottje, A. (TA)
CME 108: Introduction to Scientific Computing (MATH 114)
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:
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).
Terms: Win, Sum
| Units: 3-4
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR
Instructors:
Le, H. (PI)
;
Ying, L. (PI)
;
Aboumrad, G. (TA)
;
Horel, E. (TA)
;
Li, Y. (TA)
;
Lyman, L. (TA)
CME 193: Introduction to Scientific Python
This short course runs for the first four weeks of the quarter. 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 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
CME 212: Advanced Software Development for Scientists and Engineers
Advanced topics in software development, debugging, and performance optimization are covered. The capabilities and usage of common libraries and frameworks such as BLAS, LAPACK, FFT, PETSc, and MKL/ACML are reviewed. Computer representation of integer and floating point numbers, and interoperability between C/C++ and Fortran is described. More advanced software engineering topics including: representing data in files, signals, unit and regression testing, and build automation. The use of debugging tools including static analysis, gdb, and Valgrind are introduced. An introduction to computer architecture covering processors, memory hierarchy, storage, and networking provides a foundation for understanding software performance. Profiles generated using gprof and perf are used to help guide the performance optimization process. Computational problems from various science and engineering disciplines will be used in assignments. Prerequisites:
CME 200 /
ME 300A and
CME 211. The
CME 211 requirement may be satisfied by passing a placement test administered by ICME.
Terms: Win
| Units: 3
Instructors:
Cecka, C. (PI)
;
Henderson, N. (PI)
;
Chen, Y. (TA)
;
Kasera, R. (TA)
;
Shoemaker, A. (TA)
CME 215A: Advanced Computational Fluid Dynamics (AA 215A)
High resolution schemes for capturing shock waves and contact discontinuities; upwinding and artificial diffusion; LED and TVD concepts; alternative flow splittings; numerical shock structure. Discretization of Euler and Navier Stokes equations on unstructured meshes; the relationship between finite volume and finite element methods. Time discretization; explicit and implicit schemes; acceleration of steady state calculations; residual averaging; math grid preconditioning. Automatic design; inverse problems and aerodynamic shape optimization via adjoint methods. Pre- or corequisite: 214B or equivalent.
Terms: Win
| Units: 3
Instructors:
Jameson, A. (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.
Terms: Aut, Win, Spr, Sum
| Units: 1-6
Instructors:
Jain, K. (PI)
;
Horel, E. (TA)
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