## 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, 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: GER:DB-Math, WAY-FR

Instructors:
Le, H. (PI)

## 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. Numerical simulation using Monte Carlo techniques. Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, non-parametric tests, regression and correlation analyses. Numerous applications in engineering, manufacturing, reliability and quality assurance, medicine, biology, and other fields. Prerequisite:
CME100/ENGR154 or
Math 51 or 52.

Terms: Win
| Units: 4
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

Instructors:
Khayms, V. (PI)
;
Chen, G. (TA)
;
Cote de Soux, P. (TA)
...
more instructors for CME 106 »

Instructors:
Khayms, V. (PI)
;
Chen, G. (TA)
;
Cote de Soux, P. (TA)
;
Deshpande, S. (TA)
;
Rowley, J. (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
| Units: 3
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

Instructors:
Dunham, E. (PI)
;
Saad, N. (TA)

## CME 187: Mathematical Population Biology (BIO 187)

Mathematical models in population biology, in biological areas including demography, ecology, epidemiology, evolution, and genetics. Mathematical approaches include techniques in areas such as combinatorics, differential equations, dynamical systems, linear algebra, probability, and stochastic processes. Math 50 or 60 series is required, and at least two of (
Bio 81,
Bio 82,
Bio 85) are strongly recommended.

Terms: Win
| Units: 3

Instructors:
Rosenberg, N. (PI)

## 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

Instructors:
Jambulapati, A. (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: Win
| Units: 3

Instructors:
Lele, S. (PI)
;
Maeda, K. (PI)

## 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.nPrerequisites:
Math 51, 52, 53; prior programming experience (Matlab or other language at level of
CS 106a or higher)

Terms: Win
| Units: 3

Instructors:
Marsden, A. (PI)

## 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.

Terms: Win
| Units: 3

## 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 focused on COVID-19 during fall 2020 with the option to continue into winter 2021. Students apply a computational and data analytics lens and will use design thinking methodology. The course exposes students to ethics, emotional intelligence, unintended consequences of their work and team building supported by relevant lectures on data science and med/bio topics. Pre-requisites: none.nThe course application generally opens 5-6 weeks before registration for each quarter. If you missed the application for the quarter, please submit your application anyway to be added to the waitlist and to receive information regarding upcoming quarters.
https://forms.gle/oLtUe7dMKGy8bb2Z9

Terms: Aut, Win
| Units: 3
| Repeatable
2 times
(up to 6 units total)

Instructors:
Hanson, K. (PI)
;
Iaccarino, G. (PI)
;
Ioannidis, A. (PI)
...
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Instructors:
Hanson, K. (PI)
;
Iaccarino, G. (PI)
;
Ioannidis, A. (PI)
;
Rivas, M. (PI)
;
Pendo, L. (TA)

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