1.010 Uncertainty in Engineering () Prereq.: 18.01, 18.02 Units: 3-2-7 Quantitative uncertainty analysis with emphasis on engineering applications. Events and their probability, univariate and multivariate distributions, uncertainty propagation through linear and nonlinear functions, conditional analysis for extrapolation and prediction, second-moment uncertainty characterization and analysis. Poisson processes. Bayes theory and risk-based decision. Descriptive statistics, point and interval estimation of distribution parameters, hypothesis testing, and simple linear regression. Computer applications using MATLAB. 3 Engineering Design Points. D. Veneziano

1.060 Fluid Mechanics () Prereq.: 8.01, 18.03 Units: 3-2-7 Lecture: MWF11 (48-316) Recitation: WF2 (48-316) +final Introduction to the mechanics of incompressible fluid flow. Fluid properties. Hydrostatics. Conservation of mass and momentum using differential and integral balances. The Bernoulli equation. Shear stresses and velocity profiles in laminar and turbulent flows. Flow in porous media. Dynamic similarity. First law of thermodynamics and the energy equation. Applications to steady flow in conduits and open channels, pumps, turbines, drag, and lift on immersed objects. Subject has laboratory exercises and demonstrations. 3 Engineering Design Points. O. S. Madsen

10.301 Fluid Mechanics () Prereq.: 18.03, 10.001 Units: 3-0-9 URL: http://web.mit.edu/10.301/www/welcome.html Lecture: WF11 (66-110) Recitation: M10 (66-148) or M11 (56-154) or M11 (26-210) or M12 (66-156) +final Introduces the mechanical principles governing fluid flow. Stress in a fluid. Conservation of mass and momentum, using differential and integral balances. Elementary constitutive equations. Hydrostatics. Exact solutions of the Navier-Stokes equations. Approximate solutions using control volume analysis. Mechanical energy balances and Bernoulli's equation. Dimensional analysis and dynamic similarity. Introduces boundary-layer theory and turbulence. H. Brenner, P. S. Virk

12.800 Fluid Dynamics of the Atmosphere and Ocean () (Subject meets with 12.331) Prereq.: 8.03, 18.04 Units: 3-0-9 Introductory subject for first-year graduate students in meteorology, climate, and oceanography. Eulerian and Lagrangian kinematics. Equations of mass, momentum, and energy in Eulerian form in rotating frame of reference. Vorticity and divergence. Scaling and geostrophic approximation. Potential vorticity. Rossby waves. Ekman layers. Wave motion and instability. Vortex motion. J. Marshall

13.015 Mathematical Methods in Ocean Engineering () Prereq.: 18.03 Units: 3-0-9 Lecture: TR11-12:30 (1-136) Mathematical methods are developed to solve deterministic and stochastic problems in ocean engineering. Formulation and solution of model problems from wave propagation, vibrations, signal processing, hydrodynamics and structural mechanics using the theory of ordinary differential equations, complex variables, Laplace and Fourier transforms, convolution and impulse response functions. Random variables, stationary random processes and spectral techniques are then introduced to represent stochastic signals and environmental forcing functions arising from wind, current and sea-wave action. Linear system response to random excitation. Application of statistical inference theory to estimate physical parameters from random data. N. C. Makris

8.01 Physics I (, ) Prereq.: -- Units: 5-0-7 Credit cannot also be received for 8.012 or 8.01X URL: http://web.mit.edu/8.01/www/ Lab: F10 (2-190) Lecture: MTW10 (REC BEGINS FEB 2) (26-328) or MTW11 (REC BEGINS FEB 2) (26-328) or MTW2 (REC BEGINS FEB 2) (1-246) or MTW3 (REC BEGINS FEB 2) (1-246) or MTW10 (REC BEGINS FEB 2) (1-246) Recitation: R12 (1-375) or R1 (1-375) or R2 (1-371) or R2 (1-246) or R3 (1-246) or R4 (1-246) or R EVE (7 PM) (8-302) or R EVE (8 PM) (8-302) or R4 (1-132) +final Introduces classical mechanics. Space and time: straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics. Fall Term: A. Guth, Staff Spring Term: B. Wyslouch

8.02 Physics II (, ) Prereq.: 8.01 or 8.01X or 8.01L or 8.012; 18.01 Units: 5-0-7 Credit cannot also be received for 8.022 URL: http://web.mit.edu/8.02/www/ RECITATION SCHEDULED REG DAY Lecture: MWF10 (26-100) or MWF11 (26-100) +final Introduction to electromagnetism and electrostatics: electric charge, Coulomb's law, electric structure of matter; conductors and dielectrics. Concepts of electrostatic field and potential, electrostatic energy. Electric currents, magnetic fields and Ampere's law. Magnetic materials. Time-varying fields and Faraday's law of induction. Basic electric circuits. Electromagnetic waves and Maxwell's equations. Credit cannot also be received for 8.02X. Fall Term: S. Mochrie Spring Term: U. Becker, E. Bertschinger

8.03 Physics III (, ) Prereq.: 8.02 or 8.022 or 8.02X; 18.02 Units: 5-0-7 URL: http://web.mit.edu/8.03/Kaspi/ Lecture: MW2-3:30 (6-120) Recitation: TR10 (REC BEGINS FEB 4) (26-210) or TR11 (REC BEGINS FEB 4) (26-210) or TR2 (REC BEGINS FEB 4) (26-302) +final Mechanical vibrations and waves; simple harmonic motion, superposition, forced vibrations and resonance, coupled oscillations and normal modes; vibrations of continuous systems; reflection and refraction; phase and group velocity. Optics; wave solutions to Maxwell's equations; polarization; Snell's Law, interference, Huygens's principle, Fraunhofer diffraction, gratings. V. Kaspi

10.001 Introduction to Computer Methods (, ) Prereq.: -- Units: 2-0-4 URL: http://web.mit.edu/10.001/Web/10_001homepage.html Introduction to the use of computers, programming, software tools, and problem solving using Athena. Emphasis on the development of algorithms, programming in C, and symbolic computing, with applications in elementary numerical analysis and data visualization for science and engineering. G. C. Rutledge, W. H. Green

13.017 Design of Ocean Systems I (Revised Units) () Prereq.: 2.001, 6.071, 13.016, 13.012, or permission of instructor Units: 2-4-6 URL: http://albacore.mit.edu/~jleonard/13017.html Lab: TR2:30-4:30 (5-028) Lecture: MF11 (5-231) 13.018 Design of Ocean Systems II () Prereq.: 13.017 Units: 2-4-6 A two-semester subject sequence that demonstrates the design process through application to small-scale ocean systems. Emphasis on carrying out the design and implementation of a system, including demonstration of its operation in the marine environment. Fall Term: Introduction to the design process and its application in the marine environment. Design project with students developing system definition and completing its preliminary design. Students are instructed in the use of the machine shop and are required to implement mechanical, electrical, and electronic components of the systems. Spring Term: Students work in small groups to design and implement system defined in 13.017, including demonstration of its operation in the laboratory or marine environment. Students design, plan, construct, and operate a small-scale ocean system, or plan, develop experimental apparatus, acquire data, and report the analysis of an experiment in the ocean or the laboratory. Subject varies from year to year. The specific topic is made available to students during IAP before the first term of the subject sequence. Each of these subjects satisfies six units of the General Institute Laboratory Requirement. J. Leonard, T. Consi

13.021 Marine Hydrodynamics I () Prereq.: 13.012 or 2.006 or 1.05 Units: 4-1-7 The fundamentals of fluid mechanics are developed in the context of naval architecture and ocean science and engineering. Transport theorem and conservation principles. Navier-Stokes' equation. Dimensional analysis. Ideal and potential flows. Vorticity and Kelvin's theorem. Hydrodynamic forces in potential flow, D'Alembert's paradox, added-mass, slender-body theory. Viscous-fluid flow, laminar and turbulent boundary layers. Model testing, scaling laws. Application of potential theory to surface waves, energy transport, wave/body forces. Linearized theory of lifting surfaces. Experimental project in the towing tank or propeller tunnel. D. K.-P. Yue

13.022 Surface Waves and Their Interaction with Floating Bodies () Prereq.: 13.021, 18.075 Units: 4-0-8 Introduces the physics and mathematical modeling of linear and nonlinear surface wave interactions with floating bodies, e.g., ships and offshore platforms. Surface wave theory, including linear and nonlinear effects in a deterministic and random environment. Ship Kelvin wave pattern and wave resistance. Theory of linear surface wave interactions with floating bodies. Drift forces. Forward speed effects. Ship motions and wave-induced structural loads. P. Sclavounos

13.024 Numerical Marine Hydrodynamics () Prereq.: 13.021, 18.075 Units: 3-0-9 Introduction to numerical methods: interpolation, differentiation, integration, systems of linear equations. Solution of differential equations by numerical integration, partial differential equations of inviscid hydrodynamics: finite difference methods, panel methods. Fast Fourier Transforms. Numerical representation of sea waves. Computation of the motions of ships in waves. Integral boundary layer equations and numerical solutions. J. H. Milgram

3.08 Transport, Fate, and Effects of Ocean Pollutants () Prereq.: 18.03 or equivalent Units: 3-0-9 Lecture: TR1-2:30 (5-134) Provides the background for quantitatively predicting and estimating the distribution of pollution, its by-products, and some of its effects on marine systems, starting with information about the pollution source. Topics include: introduction to physical oceanography, equations of motion for ocean flows, ocean currents, molecular and turbulent diffusion, fluid mechanical transport models, seawater properties and chemistry, important chemicals in the ocean, chemical exchange between sediments and seawater. J. H. Milgram

18.01 Calculus (, ) Prereq.: -- Units: 5-0-7 Credit cannot also be received for 18.013, 18.014 or 18.01A Lecture: MWF1 (2-142) Recitation: TR12 (BEGINS FEB 4) (8-119) +final Differentiation and integration of functions of one variable, with applications. Concepts of function, limits, and continuity. Differentiation rules, application to graphing, rates, approximations, and extremum problems. Definite and indefinite integration. Fundamental theorem of calculus. Applications of integration to geometry and science. Elementary functions. Techniques of integration. Approximation of definite integrals, improper integrals, and l'Hôpital's rule. Information: M. Artin.

18.02 Calculus (, , ) Prereq.: 18.01 or 18.01A or 18.013 or 18.014 Units: 5-0-7 Credit cannot also be received for 18.023, 18.024, 18.02A or 18.02C URL: http://web.mit.edu/18.02-esg/www/18.02IS/main.html RECITATION SCHEDULED REG DAY Lecture: TR1,F2 (54-100) +final Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, approximation techniques. Multiple integrals with applications. Vector fields, line and surface integrals, exact differentials, Green's theorem, Divergence Theorem, Stokes's Theorem. Two versions offered Fall Term: 18.02 and 18.02C. 18.02 includes additional topics in linear algebra. Fall Term: H. Rogers, 18.02C: A. P. Mattuck Spring Term: R. B. Melrose

18.03 Differential Equations (, , ) Prereq.: 18.02 or 18.02A or 18.023 or 18.014 Units: 5-0-7 Credit cannot also be received for 18.034 URL: http://web.mit.edu/18.03-esg/www/home.html RECITATION SCHEDULED REG DAY Lecture: MWF1 (54-100) or MWF2 (10-250) +final Study of ordinary differential equations. Standard solution methods for one first-order equation, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers; Laplace transform. Matrix methods for first-order linear systems with constant coefficients. Non-linear systems; phase-plane analysis. Series solutions to second-order equations. Fourier series solutions. Modeling of physical problems and interpretation of the analytic or graphical solutions. Fall Term: A. Toomre, Staff Spring Term: H. R. Miller

18.04 Complex Variables with Applications (, ) Prereq.: 18.03 or 18.034 Units: 4-0-8 Lecture: MWF12 (4-370) Recitation: M2 (BEGINS FEB 8) (8-205) or T11 (BEGINS FEB 9) (4-153) or T2 (BEGINS FEB 9) (2-142) +final Complex algebra and functions; analyticity; contour integration, Cauchy's theorem; singularities, Taylor and Laurent series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions; Fourier analysis and Laplace transforms. Fall Term: R. P. Stanley Spring Term: Staff