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ENGR 10: Introduction to Engineering Analysis

Integrated approach to the fundamental scientific principles that are the cornerstones of engineering analysis: conservation of mass, atomic species, charge, momentum, angular momentum, energy, production of entropy expressed in the form of balance equations on carefully defined systems, and incorporating simple physical models. Emphasis is on setting up analysis problems arising in engineering. Topics: simple analytical solutions, numerical solutions of linear algebraic equations, and laboratory experiences. Provides the foundation and tools for subsequent engineering courses. Prerequisite: AP Physics and AP Calculus or equivalent.
Terms: Sum | Units: 4 | UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR
Instructors: Cappelli, M. (PI)

ENGR 76: Information Science and Engineering

What is information? How can we measure and efficiently represent it? How can we reliably communicate and store it over media prone to noise and errors? How can we make sound decisions based on partial and noisy information? This course introduces the basic notions required to address these questions, as well as the principles and techniques underlying the design of modern information, communication, and decision-making systems with relations to and applications in machine-learning, through genomics, to neuroscience. Students will get a hands-on appreciation of the concepts via projects in small groups, where they will develop their own systems for streaming of multi-media data under human-centric performance criteria. Prerequisite: CS 106A.
Terms: Spr | Units: 5 | UG Reqs: WAY-AQR, WAY-FR

ENGR 80: Introduction to Bioengineering (Engineering Living Matter) (BIOE 80)

Students completing BIOE 80 should have a working understanding for how to approach the systematic engineering of living systems to benefit all people and the planet. Our main goals are (1) to help students learn ways of thinking about engineering living matter and (2) to empower students to explore the broader ramifications of engineering life. Specific concepts and skills covered include but are not limited to: capacities of natural life on Earth; scope of the existing human-directed bioeconomy; deconstructing complicated problems; reaction & diffusion systems; microbial human anatomy; conceptualizing the engineering of biology; how atoms can be organized to make molecules; how to print DNA from scratch; programming genetic sensors, logic, & actuators; biology beyond molecules (photons, electrons, etc.); constraints limiting what life can do; and possible health challenges in 2030. And we explore questions like, how does what we want shape bioengineering, and who should choose and realize various competing bioengineering futures?
Terms: Spr | Units: 4 | UG Reqs: GER:DB-EngrAppSci, WAY-FR

ENGR 108: Introduction to Matrix Methods

Formerly EE 103/ CME 103. Introduction to applied linear algebra with emphasis on applications. Vectors, norm, and angle; linear independence and orthonormal sets; applications to document analysis. Clustering and the k-means algorithm. Matrices, left and right inverses, QR factorization. Least-squares and model fitting, regularization and cross-validation. Constrained and nonlinear least-squares. Applications include time-series prediction, tomography, optimal control, and portfolio optimization. Undergraduate students should enroll for 5 units, and graduate students should enroll for 3 units. Prerequisites: MATH 51 or CME 100, and basic knowledge of computing ( CS 106A is more than enough, and can be taken concurrently). ENGR 108 and Math 104 cover complementary topics in applied linear algebra. The focus of ENGR 108 is on a few linear algebra concepts, and many applications; the focus of Math 104 is on algorithms and concepts.
Terms: Aut, Sum | Units: 3-5 | UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

ENGR 120: Mass and Energy Transport in Porous Media (ENERGY 120)

Engineering topics in mass and energy transport in porous media relevant to energy systems. Mass, momentum and energy conservation equations in porous structures. Single phase and multiphase flow through porous media. Gas laws. Introduction to thermodynamics. Chemical, physical, and thermodynamic properties of liquids and gases in the subsurface.
Terms: Win | Units: 3 | UG Reqs: GER:DB-EngrAppSci, WAY-FR, WAY-SMA

ENGR 154: Vector Calculus for Engineers (CME 100)

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: GER:DB-Math, WAY-FR

ENGR 155A: Ordinary Differential Equations for Engineers (CME 102)

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, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

ENGR 155B: Linear Algebra and Partial Differential Equations for Engineers (CME 104)

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: WAY-FR, GER:DB-Math

ENGR 155C: Introduction to Probability and Statistics for Engineers (CME 106)

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

GEOPHYS 120: Geophysical Mechanics and Dynamics (GEOPHYS 220)

Introductory application of continuum mechanics to ice sheets and glaciers, water waves and tsunamis, and volcanoes. Emphasis on physical processes and mathematical description using balance of mass and momentum, combined with constitutive equations for fluids and solids. Designed for undergraduates with no prior geophysics background; also appropriate for beginning graduate students. Prerequisites: CME 100 or MATH 52 and PHYSICS 41 (or equivalent).
Terms: Win | Units: 3-5 | UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA
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