## CME 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:
Math 21 (preferred), or equivalent (5 on the AP Calculus BC test or suitable score on certain international exams:
https://studentservices.stanford.edu/my-academics/earn-my-degree/undergraduate-degree-progress/test-transfer-credit/external-test-2)

Terms: Aut, Spr
| Units: 5
| UG Reqs: WAY-FR, GER:DB-Math

Instructors:
Khayms, V. (PI)
;
Le, H. (PI)
;
Goel, P. (TA)
;
Muneton Gallego, J. (TA)
;
Ramanantsoa, R. (TA)

## 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)

## 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:
Math 21 (preferred), or equivalent (5 on the AP Calculus BC test or suitable score on certain international exams:
https://studentservices.stanford.edu/my-academics/earn-my-degree/undergraduate-degree-progress/test-transfer-credit/external-test-2)

Terms: Aut, Win
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

## 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 with machine learning applications

Numerical computation for engineering and machine learning applications: error analysis, floating-point arithmetic, numerical solution of linear and nonlinear equations, optimization, gradient descent, polynomial interpolation, numerical differentiation and integration, supervised learning, numerical solution of ordinary differential equations, numerical stability, unsupervised learning, sampling (Monte Carlo algorithms). Implementation of numerical methods in programming assignments (Python or Matlab). 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: WAY-AQR, WAY-FR, GER:DB-EngrAppSci

Instructors:
Ying, L. (PI)
;
Chen, H. (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

## 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

Instructors:
Nzia Yotchoum, H. (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

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

Applied linear algebra and linear dynamical systems with applications 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
ENGR 108 or
MATH 104; ordinary differential equations and Laplace transforms as in
EE 102B or
CME 102.

Terms: Aut
| Units: 3

Instructors:
Rajagopal, R. (PI)

## CME 279: Computational Biology: Structure and Organization of Biomolecules and Cells (BIOE 279, BIOMEDIN 279, BIOPHYS 279, CS 279)

Computational techniques for investigating and designing the three-dimensional structure and dynamics of biomolecules and cells. These computational methods play an increasingly important role in drug discovery, medicine, bioengineering, and molecular biology. Course topics include protein structure prediction, protein design, drug screening, molecular simulation, cellular-level simulation, image analysis for microscopy, and methods for solving structures from crystallography and electron microscopy data. Prerequisites: elementary programming background (
CS 106A or equivalent) and an introductory course in biology or biochemistry.

Terms: Aut
| Units: 3

Instructors:
Dror, R. (PI)

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