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## ENGR 154:Vector Calculus for Engineers (CME 100)

Computation and visualization using MATLAB. Differential vector calculus: analytic geometry in space, functions of several variables, partial derivatives, gradient, unconstrained maxima and minima, Lagrange multipliers. Introduction to linear algebra: matrix operations, systems of algebraic equations, methods of solution and applications. Integral vector calculus: multiple integrals in Cartesian, cylindrical, and spherical coordinates, line integrals, scalar potential, surface integrals, Green¿s, divergence, and Stokes¿ theorems. Examples and applications drawn from various engineering fields. Prerequisites: 10 units of AP credit (Calc BC with 5, or Calc AB with 5 or placing out of the single variable math placement test: https://exploredegrees-nextyear.stanford.edu/undergraduatedegreesandprograms/#aptextt), or Math 19-21.
Terms: Aut, Win, Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

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

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 5, or Calc AB with 5 or placing out of the single variable math placement test: https://exploredegreesnextyear.stanford.edu/undergraduatedegreesandprograms/#aptextt),), or Math 19-21. Recommended: CME100.
Terms: Aut, Win, Spr, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

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

Linear algebra: matrix operations, systems of algebraic equations, Gaussian elimination, undetermined and overdetermined systems, coupled systems of ordinary differential equations, eigensystem analysis, normal modes. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications from various engineering fields. Prerequisite: CME 102/ ENGR 155A.
Terms: Spr | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR | Grading: Letter or Credit/No Credit

## 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. 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 | Grading: Letter or Credit/No Credit

## GEOPHYS 120:Ice, Water, Fire (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: given next year, last offered Winter 2017 | Units: 3-5 | UG Reqs: GER: DB-NatSci, WAY-FR, WAY-SMA | Grading: Letter or Credit/No Credit

## GS 111:Fundamentals of Structural Geology (CEE 195)

Techniques for mapping using GPS and differential geometry to characterize structures; dimensional analysis and scaling relations; kinematics of deformation and flow; measurement and analysis of stress; elastic deformation and properties of rock; brittle deformation including fracture and faulting; linear viscous flow including folding and magma dynamics; model development and methodology. Models of tectonic processes are constructed and solutions visualized using MATLAB. Prerequisites: GS 1, MATH 51
Terms: not given this year, last offered Winter 2016 | Units: 3 | UG Reqs: WAY-FR, WAY-SMA | Grading: Letter or Credit/No Credit

## LINGUIST 35:Minds and Machines (PHIL 99, PSYCH 35, SYMSYS 1)

(Formerly SYMSYS 100). An overview of the interdisciplinary study of cognition, information, communication, and language, with an emphasis on foundational issues: What are minds? What is computation? What are rationality and intelligence? Can we predict human behavior? Can computers be truly intelligent? How do people and technology interact, and how might they do so in the future? Lectures focus on how the methods of philosophy, mathematics, empirical research, and computational modeling are used to study minds and machines. Undergraduates considering a major in symbolic systems should take this course as early as possible in their program of study.
Terms: Aut | Units: 4 | UG Reqs: GER:DB-SocSci, WAY-FR | Grading: Letter or Credit/No Credit

## LINGUIST 110:Introduction to Phonology

Introduction to the sound systems of the world's languages, their similarities and differences. Theories that account for the tacit generalizations that govern the sound patterns of languages.
Terms: Aut | Units: 4 | UG Reqs: GER:DB-SocSci, WAY-FR | Grading: Letter or Credit/No Credit

## LINGUIST 120:Introduction to Syntax

Grammatical constructions, primarily English, and their consequences for a general theory of language. Practical experience in forming and testing linguistic hypotheses, reading, and constructing rules.
Terms: not given this year, last offered Autumn 2015 | Units: 4 | UG Reqs: GER:DB-SocSci, WAY-FR | Grading: Letter or Credit/No Credit

## LINGUIST 121A:The Syntax of English

A data-driven introduction to the study of generative syntax through an in-depth investigation of the sentence structure of English. Emphasis is on central aspects of English syntax, but the principles of theory and analysis extend to the study of the syntax of other languages. The course focuses on building up syntactic argumentation skills via the collective development of a partial formal theory of sentence structure, which attempts to model native speaker knowledge. Satisfies the WIM requirement for Linguistics and the WAY-FR requirement. Prerequisites: none (can be taken before or after Linguistics 121B). The discussion section is mandatory.
Terms: Aut | Units: 4 | UG Reqs: WAY-FR | Grading: Letter or Credit/No Credit
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