Engineering Sciences

Faculty of the Division of Engineering and Applied Sciences Offering Instruction in Engineering Sciences

Frederick H. Abernathy, Gordon McKay Professor of Mechanical Engineering and Abbott and James Lawrence Professor of Engineering
Ron Noah Alkalay, Lecturer on Engineering Sciences
Donald G. M. Anderson, Gordon McKay Professor of Applied Mathematics
Michael J. Aziz, Gordon McKay Professor of Materials Science
Ana P. Barros, Associate Professor of Environmental Engineering on the Gordon McKay Endowment
Michael S. Brandstein, Associate Professor of Electrical Engineering on the Gordon McKay Endowment
Roger W. Brockett, An Wang Professor of Electrical Engineering and Computer Science
Brian F. Farrell, Robert P. Burden Professor of Meteorology
Joseph J. Harrington, Gordon McKay Professor of Environmental Engineering (FAS), Professor of Environmental Health Engineering (Public Health)
Yu-Chi Ho, T. Jefferson Coolidge Research Professor of Applied Mathematics and Gordon McKay Research Professor of Engineering (on leave fall term)
Robert D. Howe, Gordon McKay Professor of Engineering
John W. Hutchinson, Gordon McKay Professor of Applied Mechanics (Co-Director of Undergraduate Studies, Associate Dean of Academic Programs in the Division of Engineering and Applied Sciences) (on leave fall term)
Daniel J. Jacob, Gordon McKay Professor of Atmospheric Chemistry and Environmental Engineering
R. Victor Jones, Robert L. Wallace Professor of Applied Physics
Aleksandar Kavcic, Assistant Professor of Electrical Engineering on the Gordon McKay Endowment (Co-Director of Undergraduate Studies, spring term only)
H. T. Kung, William H. Gates Professor of Computer Science and Electrical Engineering
S. Daniel Kwak, Lecturer on Engineering Sciences
Jose F. Magalhaes, Visiting Assistant Professor of Engineering Sciences
Scot T. Martin, Associate Professor of Environmental Chemistry on the Gordon McKay Endowment
Igor Mezic, Associate Professor of Mechanical Engineering on the Gordon McKay Endowment
Ralph Mitchell, Gordon McKay Professor of Applied Biology
Venkatesh Narayanamurti, John A. and Elizabeth S. Armstrong Professor of Engineering and Applied Sciences and Professor of Physics (Dean of the Division of Engineering and Applied Sciences)
Alfred A. Pandiscio, Senior Lecturer on Electronics on the Gordon McKay Endowment
James R. Rice, Mallinckrodt Professor of Engineering Sciences and Geophysics
Peter P. Rogers, Gordon McKay Professor of Environmental Engineering
Irvin C. Schick, Lecturer on Engineering Sciences
Garrett B. Stanley, Assistant Professor of Biomedical Engineering on the Gordon McKay Endowment (Co-Director of Undergraduate Studies, fall term only)
Howard A. Stone, Harvard College Professor and Gordon McKay Professor of Chemical Engineering and Applied Mechanics (on leave spring term)
Joost J. Vlassak, Assistant Professor of Materials Engineering on the Gordon McKay Endowment
Steven C. Wofsy, Abbott Lawrence Rotch Professor of Atmospheric and Environmental Science, Associate of the Harvard Forest
Woodward Yang, Gordon McKay Professor of Electrical Engineering and Computer Science (Co-Director of Undergraduate Studies, fall term only) ( )

The Division of Engineering and Applied Sciences offers undergraduate and graduate courses in Applied Mathematics, Applied Physics, Computer Science, Earth and Planetary Sciences, and Engineering Sciences. Recommended curricula may be obtained from the Academic Office, Pierce Hall 110a. Division faculty also offer several courses in the section entitled General Education Electives.

For information concerning concentration in Engineering Sciences, please consult the Co-Directors of Undergraduate Studies or the Academic Office, Division of Engineering and Applied Sciences, Pierce Hall 110a.

Primarily for Undergraduates

Engineering Sciences 50. Introduction to Electrical Engineering
Catalog Number: 4499
Woodward Yang and Alfred A. Pandiscio
Half course (fall term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
Intended for freshmen and sophomore level students. Introduces basic electrical engineering concepts including voltage, current, charge, resistance, capacitance, inductance, Kirchoff’s Current Law, and Kirchoff’s Voltage Law. In addition, a survey of practical digital and analog electronics (such as computers, television, telephones, CDROMs, video games, modems and satellite communications) will be presented to illustrate more advanced topics in electrical engineering and computer science including signal processing, semiconductor circuits, communications and computer architecture. The course assumes only a basic knowledge of high school physics, linear algebra and elementary calculus.
Note: Ordinarily cannot be taken for credit after Engineering Sciences 154 or Computer Science 141 or Physics 123.

[Engineering Sciences 51. A Computer-Aided Design Approach to Engineering ]
Catalog Number: 0322
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Half course (spring term). Hours to be arranged.
A first course in the design and construction of mechanical and electromechanical devices. Computational structures and algorithms for the representation and manipulation of geometrical data. Introduction to materials selections as applied to structural designs, including stress-strain analysis, thermal stresses, analysis, etc. Design of two-dimensional mechanisms; related rates, mechanical advantage. Computer controlled machine tools and their control languages; the speed and precision of machine tool operations. Designing to minimize vibration, wear, and noise; designing for reliability and longevity. Emphasis on laboratory work and individual design projects carried out using numerically controlled machine tools.
Note: Expected to be given in 2001–02. An introductory engineering design course open to freshmen, sophomores, and juniors. May not be taken concurrently with other engineering design courses.
Prerequisite: Mathematics 1b (may be taken concurrently); high school physics; experience with some programming language.

*Engineering Sciences 91r. Supervised Reading and Research
Catalog Number: 1113
John W. Hutchinson and Aleksandar Kavcic
Half course (fall term; repeated spring term). Hours to be arranged.
Guided reading and research.
Note: Normally open to candidates accepted for work on a specific topic by a member of the teaching staff of the Division of Engineering and Applied Sciences. Normally may not be taken for more than two terms; may be counted for concentration in Engineering Sciences if taken for graded credit. Applicants should file a project sheet before study cards are filed. Project sheets may be obtained from the Academic Office, Pierce Hall 110a.

*Engineering Sciences 96. Engineering Design Projects
Catalog Number: 8461 Enrollment: Limited to 25.
Frederick H. Abernathy and R. Victor Jones
Half course (spring term). M., 2–4, W., 8:30–10 p.m. EXAM GROUP: 7, 8
Group project selected to provide experience in the processes and practice of engineering design. It is the central activity of a design seminar which, ordinarily, is taken in the spring term of the junior year.
Note: Preference given to S.B. candidates.

For Undergraduates and Graduates

*Engineering Sciences 100. Engineering Design Projects
Catalog Number: 4268
Robert D. Howe
Half course (fall term; repeated spring term). Th., 4–6. EXAM GROUP: 18
Individual design projects selected to provide experience in the processes and practice of engineering design. Requires proficiency in electronic circuit construction as well as mechanical materials fabrication techniques.
Note: Ordinarily taken in the senior year. This one semester version of *Engineering Sciences 100hf open only to students in special circumstances. Enrolled students are required to file a proposed project form with the Academic Office early in the term. Project forms are available in Pierce Hall 110a. Project approval rests with the faculty Engineering Design Review Board.
Prerequisite: *Engineering Sciences 96.

*Engineering Sciences 100hf. Engineering Design Projects
Catalog Number: 7535
Robert D. Howe
Half course (throughout the year). Th., 4–6. EXAM GROUP: 18
Individual design projects selected to provide experience in the processes and practice of engineering design. Requires proficiency in electronic circuit construction as well as mechanical fabrication techniques.
Note: Ordinarily taken in the senior year. Enrolled students are required to file a proposed project form with the Academic Office early in the term. Project forms are available in Pierce Hall 110a. Project approval rests with the faculty Engineering Design Review Board.
Prerequisite: *Engineering Sciences 96.

Engineering Sciences 101. Applied Statistics
Catalog Number: 3350
Joseph J. Harrington
Half course (fall term). M., W., 2–3:30. EXAM GROUP: 7
Survey course for students in the applied sciences. Probability, statistical inference, estimation and stochastic processes introduced through the solution of several problems in applied science (e.g., environmental sciences, decision analysis, chemical kinetics, fluid and solid mechanics, and oceanography). Generation, manipulation and display of data bases, parameter estimation, choice among models, multivariate analyses, and robustness. Computer exercises will be required.
Note: No previous knowledge of statistics or probability is presumed.
Prerequisite: Applied Mathematics 21b or Mathematics 21b or equivalent.

Engineering Sciences 102. Introduction to Operations Research
Catalog Number: 2844
Irvin C. Schick
Half course (spring term). M., W., 4:30–6. EXAM GROUP: 9
Introduction to analytical and numerical methods for optimization of deterministic and stochastic systems; survey of linear and nonlinear programming, game theory, decision analysis, Markov chains, queuing theory and simulation. Examples taken from a variety of fields. A conceptual introduction to materials covered in depth in Engineering Sciences 201, 202, 205, and 210. Segments of the weekly problem sets can be done on PCs, if desired.
Note: Students who have no background in probability should be prepared to do some extra work. Some PC experience useful but not necessary.
Prerequisite: Applied Mathematics 21b or Mathematics 21b and some knowledge of probability and statistics at the level of Statistics 110 or Engineering Sciences 101.

Engineering Sciences 120. Introduction to the Mechanics of Solids
Catalog Number: 1493
James R. Rice
Half course (spring term). M., W., F., at 10. EXAM GROUP: 3
A first course in the mechanical sciences which explains how materials and structures stretch, bend, twist, shake, buckle, and break. Forces in machines and statically determinate structures. Stress-strain behavior of materials. Statically indeterminate structures. Beam theory with applications to beam deflections, vibrations, and buckling. Energy and virtual work methods for structures. Multiaxial stress and strain. Elements of continuum mechanics. Stress concentration; introduction to fatigue and fracture of solids. Four or five laboratory sessions required.
Prerequisite: Physics 11a or 15a, and Applied Mathematics 21a or Mathematics 21a (previously) and Applied Mathematics 21b or Mathematics 21b (previously or concurrently).

Engineering Sciences 123. Introduction to Fluid Mechanics
Catalog Number: 8323
Igor Mezic
Half course (spring term). Tu., Th., 1–2:30, and laboratory. EXAM GROUP: 15, 16
Statics and dynamics of fluids. Buoyancy, stability, and hydrostatics. Laminar viscous flows, simple boundary layers. Dimensional analysis. Potential flows, origin of lift. Gravity waves, open channel flow. Navier-Stokes equation, Reynolds’ stress, turbulent flows in boundary layers and pipes. Applications in mechanical and chemical engineering, aerodynamics, etc.
Prerequisite: Applied Mathematics 21a,b or Mathematics 21a,b; Engineering Sciences 120 and Applied Mathematics 105a or 105b recommended.

Engineering Sciences 125. Mechanical Systems
Catalog Number: 7274
Frederick H. Abernathy
Half course (fall term). M., W., F., at 1. EXAM GROUP: 6
Modeling and analysis of mechanical and electromechanical systems. Topics include resonance, damping, frequency response, Laplace transform methods, Lagrange’s equations, multiple degree-of-freedom systems, and rigid body rotations. Computer exercises on simulation of linear and nonlinear dynamic systems. Laboratory: experiments on vibration, stabilization, and complex dynamical system using modern electronic instrumentation and data reduction systems. Computer simulations of a few systems will become laboratory exercises.
Note: May not be taken for credit in addition to Physics 151.
Prerequisite: Applied Mathematics 21a,b or Mathematics 21a,b or Mathematics 22a,b; Physics 11a or 15a.

Engineering Sciences 128. Computational Solid and Structural Mechanics
Catalog Number: 0359
Jose F. Magalhaes
Half course (fall term). Tu., Th., 1–2:30. EXAM GROUP: 15, 16
Continuation of Engineering Sciences 120 in which continuum mechanics principles are developed at an intermediate level and implemented by computer, using the finite-element method, to solve problems of stressing, deformation, and motion of solid materials and structures. New concepts include plane stress and strain fields and introductions to wave propagation, vibrations, plate and shell structures, fracture mechanics, and creep and plasticity under general stress states. In computational work students develop simple finite-element analyses for beam structures and two-dimensional stress systems, using the general-purpose program ABAQUS, and do a project addressing a significant problem arising in mechanical, structural or materials engineering, biomechanics, or earth science.
Prerequisite: Engineering Sciences 120.

[Engineering Sciences 143. Introduction to Biotransport Processes]
Catalog Number: 4194
David Edwards
Half course (spring term). Hours to be arranged.
This course aims to apply fundamental engineering science toward solving important biomedical problems. Blood flow, respiration, cellular and extracellular tissue transport will be discussed. Basic principles from fluid mechanics will be used to explore applications to drug delivery systems.
Note: Expected to be given in 2001–02.
Prerequisite: Undergraduate or graduate (preferred) fluid mechanics; mathematics at the level of ordinary and partial differentail equations (e.g. Applied Mathematics 105B).

*Engineering Sciences 144. Introduction to Technology Development in the Biomedical Engineering Industry
Catalog Number: 3580
David A. Edwards
Half course (spring term). M., W., F., at 11. EXAM GROUP: 4
Introduces students to discovery and pre-clinical and clinical development in the genomics, drug delivery, and medical device industries. Overviews biological systems including the immune and circulatory systems, and the lungs, heart and brain. Describes classes of drugs including small molecules and proteins, and the chemistry and engineering involved in drug delivery systems such as polymeric microspheres, gene vectors, pulmonary inhalers, and transdermal patches. Lectures or additional meetings will include speakers from the biotech community (senior officers of biotech companies and leading scientists). Students participate in the class through group projects in which they will research industries, technologies, preclinical and clinical developments, and markets.
Note: Expected to be omitted in 2001–02.
Prerequisite: An understanding of organic chemistry is strongly recommended. Exceptions will be made with approval of the instructor.

Engineering Sciences 145. Introduction to Systems Analysis with Physiological Applications
Catalog Number: 8197
Garrett B. Stanley and guest lecturers
Half course (fall term). Tu., Th., 1–2:30. EXAM GROUP: 15, 16
A survey of systems theory with applications from bioengineering and physiology. Analysis: differential equations; linear and nonlinear systems; stability; the complementary nature of time and frequency domain methods; feedback; and biological oscillations. Applications: nerve function, muscle dynamics, and cardiovascular regulation. Laboratory: neural models; feedback control systems; properties of frog muscle; and cardiovascular function.
Prerequisite: Applied Mathematics 21b or Mathematics 21b or equivalent.

Engineering Sciences 148. Neural Signal Processing
Catalog Number: 0495
Garrett B. Stanley and guest lecturers
Half course (spring term). Tu., Th., 10–11:30, and an additional hour to be arranged. EXAM GROUP: 12, 13
Examines the generation, transmission, and processing of signals in single nerve cells and in neural ensembles, with emphasis on physical principles and contemporary mathematical models. Develops relevant analytical techniques, including: systems theory; filtering; Fourier analysis; stochastic processes; estimation; and network theory. Special attention is given to the physiology of the mammalian visual system.
Prerequisite: Applied Mathematics 21a or Mathematics 21a and physics at the level of Physics 15b. Engineering Sciences 145 is ideal preparation; Biological Sciences 25 may compensate for lesser preparation in mathematics or physics.

Engineering Sciences 149. Muscles, Reflexes, and Locomotion
Catalog Number: 4152
Robert D. Howe and Jack T. Dennerlein (Public Heatlh)
Half course (spring term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
The neuromuscular system and its workings seen through the use of mathematical models. The muscle proteins. Muscle heat. A. F. Huxley’s mathematical model of crossbridge distribution with steady shortening. Models featuring several attached states. Theoretical models of reflex actions and their effects on walking and running. Consequences of body size. Comparison with robotic walking and running.
Prerequisite: Engineering Sciences 145 and a knowledge of basic animal physiology.

Engineering Sciences 151. Electromagnetic Communication with Wireless Applications
Catalog Number: 5742
Aleksandar Kavcic
Half course (spring term). M., W., 2:30–4, and additional laboratory sections to be arranged. EXAM GROUP: 7, 8
A study of basic physics and signal processing that make wireless electromagnetic communications possible. Topics include: electromagnetic properties of matter, Maxwell’s equations, electromagnetic wave propagation through free space and along waveguides, transmission line analysis, characteristics of receiving and transmitting antennas, antenna arrays, stochastic characterization of wireless channels, temporal and spatial filtering, wireless cellular systems, multiaccess methods (TDMA, FDMA, CDMA).
Prerequisite: Familiarity with basic electromagnetics (Physics 15b), circuit analysis (Engineering Sciences 154 or 50), and Fourier analysis (Engineering Sciences 156, 125, or Applied Mathematics 105a).

Engineering Sciences 154. Introduction to Electronic Circuits
Catalog Number: 6319
R. Victor Jones
Half course (fall term). Tu., Th., 10–11:30, plus labs to be arranged. EXAM GROUP: 12, 13
Presentation of basic circuit theory and electronic design. Topics include circuit analysis techniques; transient and frequency response; diode and transistor circuits; operational amplifier circuits; computer simulation of electronic circuits with SPICE. Additional laboratories illustrate techniques for measurement and design of real electronic circuits.
Prerequisite: An introduction to differential equations as in Applied Mathematics 21b or Mathematics 21b, and an introduction to electricity and magnetism as in Physics 11b or 15b.

Engineering Sciences 156. Signals and Systems
Catalog Number: 6284
Michael S. Brandstein
Half course (spring term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
Time and frequency domain representations and analysis of signals and systems. Convolution and linear input-output systems in continuous and discrete time. Fourier transforms and Fourier series for continuous- and discrete-time signals. Laplace and Z transforms. Analog and digital filtering. Modulation. Sampling. FFT. Applications in circuit analysis, communication, control, and computing.
Prerequisite: Applied Mathematics 21b or Mathematics 21b.

Engineering Sciences 157. Computer Speech Generation and Recognition
Catalog Number: 1724
Michael S. Brandstein
Half course (fall term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
Introduction to computer speech processing and human-machine communication by speech. Acoustic theory and models for speech production. Time- and frequency-domain analysis of speech signals. Speech coding: linear prediction, vector quantization. Vocoders and text-to-speech synthesis. Theory and methodologies for computer speech recognition: dynamic pattern matching, hidden Markov models, neural networks.
Prerequisite: Engineering Sciences 156 or permission of instructor.

Engineering Sciences 158. Digital Communications
Catalog Number: 7721
Aleksandar Kavcic
Half course (fall term). M., W., 1–2:30. EXAM GROUP: 6, 7
Examines the fundamental theories behind modern digital communication systems. Topics include: fundamental limits on communications, channel coding theorem, channel capacity theorem; baseband communications, orthogonal signal bases, matched filter receiver; digital representations of analog signals, sampling; waveform coding; baseband waveform coding; baseband waveform shaping, pulse amplitude modulation and intersymbol interference channels; digital modulation techniques; elements of error-control coding/decoding, viterbi decoding/detection; elements of spread-spectrum communications.
Prerequisite: Engineering Sciences 156 and a course in probability theory and/or statistics.

Engineering Sciences 159. Introduction to Robotics
Catalog Number: 3126
Robert D. Howe
Half course (fall term). M., W., F., at 10 and laboratory hours to be arranged. EXAM GROUP: 3
Introduction to computer-controlled robotic manipulators. Topics include coordinate frames and transformations, kinematic structure and solutions, statics and dynamics of serial chain manipulators, control and programming, robot design, and actuation and sensing devices. Laboratory exercises provide experience with industrial robot programming and robot simulation and control.
Prerequisite: Computer Science 50, and either Engineering Sciences 125 or 156.

Engineering Sciences 162. Hydrology
Catalog Number: 4163
Ana P. Barros
Half course (spring term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
Introduces hydrological principles focusing on precipitation, evapotranspiration, infiltration, groundwater, and runoff production mechanisms. Emphasis is placed on water budgets, and the linkages between land-use, land-form, soils, and vegetation and hydrological processes on regional and local scales. Hydrological data collection and standard analysis are presented. Hydrologic planning, restoration, and engineering design methods and technologies are treated in detail.
Note: Students who desire to take the course for graduate credit should enroll in Engineering Sciences 262.
Prerequisite: Applied Mathematics 21b, or equivalent. Knowledge of statistics and probability is desirable.

[Engineering Sciences 165. Introduction to Environmental Engineering]
Catalog Number: 4274
Peter P. Rogers
Half course (fall term). Hours to be arranged.
Introduces engineering technologies for control of the environment and relates them to underlying scientific principles. Efficient design of environmental management facilities and systems. Cases from aquatic, terrestrial, and atmospheric environments discussed.
Note: Expected to be given in 2001–02. For undergraduates or graduates without background in environmental engineering.
Prerequisite: Exposure to the material in Engineering Sciences 162 and 168 is recommended; Applied Mathematics 21a or 21b, or equivalent mathematical background is required.

[Engineering Sciences 166. Principles of Environmental Data Analysis, Measurements, and Modeling]
Catalog Number: 3598
Steven C. Wofsy
Half course (spring term). Hours to be arranged.
An introduction to the experimental, statistical, and computational methods used in environmental research, with an emphasis on atmospheric chemistry and global biogeochemistry. Students will develop and implement computer models of natural systems and will analyze data from laboratory and field measurements using statistical and simulation methods. Applications will be taken from current research in air pollution and global change. The course will be taught partly in seminar format and will include two design projects.
Note: Expected to be given in 2001–02.
Prerequisite: An atmospheric or environmental chemistry course, such as Earth and Planetary Sciences 133 or 200, or permission of the instructor.

Engineering Sciences 167. Environmental Assessment
Catalog Number: 6885
Peter P. Rogers
Half course (spring term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
Examines the methods and approaches to environmental impact assessment currently being used and new approaches which rely on improved scaling and index development. Geographical Information Systems (GIS) will be used extensively. Models of impact and indices for air, water, and land impacts will be examined using data from Asia and North America. Cost-of-remediation and environmental elasticity indicators will be examined and their use in engineering design and regulation of the environment will be assessed.
Prerequisite: Familiarity with the material of Science B-34 and Social Analysis 10.

Engineering Sciences 168. Aquatic Chemistry
Catalog Number: 5874
Scot T. Martin
Half course (fall term). Tu., Th., 1–2:30. EXAM GROUP: 15, 16
Applications of organic, inorganic, and physical chemistry to describe and quantify processes occurring in natural waters. Thermodynamics and kinetics of aqueous solutions, acid-base chemical transformations, role of dissolved carbon dioxide, gas-water exchange, complexation of aqueous metal ions, precipitation and dissolution, oxidation and reduction, electrical aspects of solid-solution interfaces, particle aggregation, trace metal cycling, and photochemistry.
Prerequisite: Chemistry 5 and 7 or equivalent.

Engineering Sciences 181. Thermodynamics
Catalog Number: 3889
Michael J. Aziz
Half course (fall term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
Introduction to engineering thermodynamics with emphasis on elements of classical thermodynamics. Kinetic theory and statistical mechanics briefly discussed to provide a molecular interpretation of thermodynamic properties such as entropy. Topics: zeroth law and temperature. Properties of single-component gases, liquids, and solids; steam tables. Equations of state for ideal and simple nonideal substances. First law, heat and heat transfer, work, internal energy, enthalpy. Second law, entropy, free energy. Third law. Heat engines and important engineering applications such as refrigerators, power cycles, air conditioning. Properties and simple models of solutions. Phase and chemical equilibrium in multicomponent systems; chemical potential. Laboratory included.
Prerequisite: Physics 11 or 15 and Mathematics 21; chemistry at the level of a good secondary school course, or Chemistry 5.

Engineering Sciences 190. Introduction to Materials Science
Catalog Number: 6973
Joost J. Vlassak
Half course (spring term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
Introduction to the structure and properties of materials. Bonding between atoms. Crystal structure and diffraction. Phase transformations: phase diagrams, diffusion, nucleation and growth. Mechanisms of deformation and fracture. Effect of microstructure on properties.
Prerequisite: Engineering Sciences 181 or equivalent, Physics 11 or 15, and Applied Mathematics 21a,b or Mathematics 21a,b.

Cross-listed Courses

Earth and Planetary Sciences 30. Environmental Microbiology

Primarily for Graduates

Additional courses of interest to graduate students in Decision, Control, and Communication include: Economics 2010a, 2010b, 2010c, 2110b, 2140a; Statistics 110, 171.
Engineering Sciences 201. Decision Theory
Catalog Number: 2362
Roger W. Brockett
Half course (spring term). M., W., F., at 10. EXAM GROUP: 3
Mathematical analysis of decision making under uncertainty. Axiomatic derivation of subjective probability and utility. Decision trees, normal and extensive form, value of information. Bayesian inference. Comparison with classical forms of inference. Optimal sample size. Estimation and sequential decision problems. Normal and regression models. Applications to business decisions, engineering problems, sampling, etc.
Prerequisite: Applied Mathematics 21a,b or Mathematics 21a,b, and Statistics 110 or equivalents.

Engineering Sciences 202. Estimation and Control of Dynamic Systems
Catalog Number: 5080
Roger W. Brockett
Half course (fall term). M., W., 4–5:30. EXAM GROUP: 9
Study of dynamic systems under deterministic and stochastic inputs. Calculus of variations. Maximum principle, mathematical and dynamic programming approaches to the optimization of dynamic systems. Controllability and observability, linear quadratic control synthesis, numerical methods for the solution of optimal control problems, Kalman filtering and estimation. Applications from mechanics, aerospace sciences, environmental systems, operations research, and economics.
Prerequisite: Good background in linear differential equations, matrix algebra, and introductory probability. Applied Mathematics 21a,b or Mathematics 21a,b, and Statistics 110 or equivalent.

[Engineering Sciences 203. Stochastic Control]
Catalog Number: 6982
Roger W. Brockett
Half course (spring term). M., W., F., at 10. EXAM GROUP: 3
Introduction to the theory of stochastic differential equations based on Wiener processes and Poisson counters, and an introduction to random fields. The formulation and solution of problems in nonlinear estimation theory. The Kalman-Bucy filter and nonlinear analogues. Identification theory. Adaptive systems. Applications.
Note: Expected to be given in 2001–02.
Prerequisite: Applied Mathematics 105a,b or equivalent. Some prior exposure to probability; Engineering Sciences 202 desirable but not essential.

Engineering Sciences 205. Performance Optimization of Complex Systems
Catalog Number: 1569
Yu-Chi Ho
Half course (spring term). W., 2:30–5:30. EXAM GROUP: 7, 8, 9
Complex human made systems abound in modern civilization ranging from the Internet to the electric power grid of the US. The design and analysis of such systems all require modeling, analysis, optimization, and computerized learning. This course will tackle the study of such systems from a unified viewpoint. It is an expanded version of Engineering Sciences 205 of past years and incorporates parts of Engineering Sciences 102, 201, and 202, and Economics 2052.
Prerequisite: Applied Mathematics 21a,b, or Mathematics 21a,b, and Statistics 110 (or equivalents).

[Engineering Sciences 209. Nonlinear Control Systems]
Catalog Number: 1194
Roger W. Brockett
Half course (fall term). Hours to be arranged.
The study of nonlinear input-output systems and the qualitative behavior of dynamical systems. Topics include controllability, observability, uniqueness of models, decomposition theory, asymptotic stability, periodic solutions, and strange attractors. Local and global methods of differential geometry and Lie theory developed and used as needed.
Note: Expected to be given in 2001–02.

[Engineering Sciences 210. Mathematical Programming]
Catalog Number: 5499
Donald G. M. Anderson
Half course (spring term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
Introduction to basic optimization techniques. Linear programming: the simplex method and related algorithms, duality theory, Karmarkar’s method. Unconstrained optimization, Kuhn-Tucker theory, nonlinear programming.
Note: Expected to be given in 2001–02. Offered in alternate years.
Prerequisite: Applied Mathematics 21a and 21b, or Mathematics 21a and 21b; Applied Mathematics 120, or equivalent, would be helpful, but is not required.

*Engineering Sciences 214. Advanced Introduction to Technology Development in the Biomedical Engineering Industry
Catalog Number: 2663
David A. Edwards
Half course (spring term). M., W., F., at 11. EXAM GROUP: 4
Students are expected to meet all of the requirements of Engineering Sciences 144 and in addition are required to write a term paper with significant analytical and engineering emphasis in the area of technology development in biomedical engineering.
Note: Expected to be omitted in 2001–02.
Prerequisite: An understanding of organic chemistry is strongly recommended. Exceptions will be made with approval of the instructor.

Engineering Sciences 215. Advanced Introduction to Systems Analysis with Physiological Applications
Catalog Number: 5493
Garrett B. Stanley and guest lecturers.
Half course (fall term). Tu., Th., 1–2:30. EXAM GROUP: 15, 16
Students are expected to meet all of the requirements of Engineering Sciences 145 and in addition are required to write a term paper with significant analytic emphasis. Informal discussion groups will be formed to extend material beyond the lectures.
Prerequisite: Applied Mathematics 21b or Mathematics 21b or equivalent.

Engineering Sciences 218. Advanced Neural Signal Processing
Catalog Number: 7709
Garrett B. Stanley and guest lecturers
Half course (spring term). Tu., Th., 10–11:30, and an additional hour to be arranged. EXAM GROUP: 12, 13
Students are expected to meet all of the requirements of Engineering Sciences 148 and in addition are required to write a term paper with significant analytic emphasis.
Prerequisite: Applied Mathematics 21a or Mathematics 21a and physics at the level of Physics 15b. Engineering Sciences 145 is ideal preparation; Biological Sciences 25 may compensate for lesser preparation in mathematics or physics.

*Engineering Sciences 219r. Special Topics in Biomedical Engineering: Orthopedic Biomechanics
Catalog Number: 0696
Ron Noah Alkalay and S. Daniel Kwak
Half course (fall term). Tu., Th., 4–5:30. EXAM GROUP: 18
Introductory course in biomechanics as applied to orthopedic science. Review of anatomy, kinematics, and solid mechanics for the musculoskeletal system. Emphasis on the mechanics of joints (movement, force transmission), bone, and soft tissues (e.g., cartilage, ligament, muscle). Examples from emerging technologies including imaging, cellular mechanics, and tissue engineering.
Note: Expected to be omitted in 2001–02.
Prerequisite: Mathematics 21a,b or Applied Mathematics 21a,b; Physics 11a or 15a; Engineering Sciences 120 or equivalent introductory solid mechanics course.

Engineering Sciences 220. Fluid Dynamics
Catalog Number: 2759
Howard A. Stone
Half course (fall term). M., W., F., at 11. EXAM GROUP: 4
Vector and tensor calculus. Conservation laws; kinematics and constitutive equations. Exact solutions of the Navier-Stokes equations. Lubrication theory and flows at low Reynolds numbers. Potential flows and boundary layer theory. Introduction to turbulent flows and free-surface flows.
Prerequisite: Familiarity with classical mechanics, partial differential equations, and vector and tensor calculus. An undergraduate course in fluid dynamics is strongly recommended.

Engineering Sciences 225r. Special Topics in Fluid Dynamics: Dynamical Systems Methods
Catalog Number: 3982
Igor Mezic
Half course (spring term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
Current topics will center around applications of dynamical systems methods to problems of current interest in fluid mechanics. Topics to be covered include fundamentals of dynamical systems theory and ergodic theory, Lagrangian dynamics in two-dimensional and three-dimensional flows, consequences for advection-diffusion processes and applications to control of mixing.
Prerequisite: A previous graduate course in fluid dynamics is strongly recommended, e.g., Engineering Sciences 220.

[Engineering Sciences 240. Solid Mechanics]
Catalog Number: 2984
John W. Hutchinson
Half course (fall term). Tu., Th., 8:30–10. EXAM GROUP: 10, 11
Foundations of continuum mechanics and development of elasticity theory: conservation laws; concepts of stress and strain; theory of constitutive response; mechanical behavior of materials. Vectorial, dyadic, and tensorial form of equations. Elementary elasticity solutions for waves and vibrations; stresses due to rotation, temperature change, dislocations, and surface loading; bending and torsion; buckling instabilities. Plate theory.
Note: Expected to be given in 2001–02.
Prerequisite: Applied Mathematics 105a,b or equivalent; introduction to solid mechanics at the level of Engineering Sciences 120, or Earth and Planetary Sciences 166, or Applied Physics 293.

Engineering Sciences 241. Advanced Elasticity
Catalog Number: 6711
John W. Hutchinson and James R. Rice
Half course (spring term). Tu., Th., 1–2:30. EXAM GROUP: 15, 16
Plane elasticity and complex variable methods. Elastic crack solutions. Basic three-dimensional problems. Inclusions and inhomogeneities. Thermodynamics of deformation. Dynamic elasticity, waves, radiation from faults and cracks. Elastic theory of composite materials and cracked bodies.
Note: Continuation of Engineering Sciences 240.
Prerequisite: Engineering Sciences 240 and Applied Mathematics 201 or equivalent.

[Engineering Sciences 242r. Solid Mechanics: Advanced Seminar]
Catalog Number: 5379
John W. Hutchinson and Joost Vlassak
Half course (spring term). Hours to be arranged.
Topic in 1999–00: The mechanics of thin films and multilayers. Residual stresses in films and their origin. The mechanics of cracking and decohesion. Yield strength and interface toughness.
Note: Expected to be given in 2001–02.
Prerequisite: Engineering Sciences 240.

Engineering Sciences 246. Plasticity and Finite Deformation
Catalog Number: 4271
Joost J. Vlassak
Half course (fall term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
Phenomenological theories for strain hardening materials; flow and deformation theories. Variational principles and other general theorems. Mechanisms of plastic deformation, physical theories for strain hardening materials, polycrystals. Ideal plasticity. Boundary value problems, plastic collapse, buckling of structures. Finite strain measures of stress and strain, localization instabilities.
Prerequisite: Engineering Sciences 240, or equivalent.

[Engineering Sciences 247. Fracture Mechanics]
Catalog Number: 7152
John W. Hutchinson
Half course (spring term). Tu., Th., 1–2:30. EXAM GROUP: 15, 16
Fundamentals of fracture with applications in materials and structural mechanics. Micromechanics of fracture and fatigue in ceramics, metals, and polymers. Fracture of composite materials. Interfacial fracture mechanics. Plasticity and creep effects.
Note: Expected to be given in 2001–02.
Prerequisite: Engineering Sciences 240 or equivalent.

[Engineering Sciences 248. Fluid Flow in the Human Body]
Catalog Number: 3278
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Half course (spring term). Hours to be arranged.
Principles of fluid mechanics, hydroelasticity, and wave theory important to medical physiology. Analytic descriptions of blood rheology, flow in the microcirculation, pulsatile blood flow, sounds in the cardiovascular and respiratory systems, lung mechanics, deposition of particles, peristalsis.
Note: Expected to be given in 2001–02.
Prerequisite: An introduction to partial differential equations as in Applied Mathematics 105b.

Engineering Sciences 257. Advanced Computer Speech Generation and Recognition
Catalog Number: 5006
Michael S. Brandstein
Half course (fall term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
The contents and course requirements are similar to Engineering Sciences 157, with the exception that students enrolled in Engineering Sciences 257 are required to prepare a more substantial project analyzing a specific problem or methodology of speech processing.
Prerequisite: Engineering Sciences 156 or permission of instructor.

Engineering Sciences 258. Advanced Digital Communications
Catalog Number: 8645
Aleksandar Kavcic
Half course (fall term). M., W., 1–2:30. EXAM GROUP: 6, 7
The contents and the course requirements are similar to those of Engineering Sciences 158, with the exception that students enrolled in Engineering Sciences 258 are required to prepare a term project analyzing current research in a specific area of digital communications.
Prerequisite: Engineering Sciences 156 and a course in probability theory and/or statistics.

Engineering Sciences 259. Advanced Introduction to Robotics
Catalog Number: 3671
Robert D. Howe
Half course (fall term). M., W., F., at 10, and a laboratory section to be arranged. EXAM GROUP: 3
The contents and course requirements are similar to those of Engineering Sciences 159, with the exception that students enrolled in Engineering Sciences 259 are required to prepare a term project analyzing current research in a specific problem area within Robotics.
Prerequisite: Computer Science 50 and either Engineering Sciences 125 or 156.

[Engineering Sciences 260. Engineering Systems for Environmental Control]
Catalog Number: 1180
Joseph J. Harrington
Half course (spring term). Hours to be arranged.
Provision of urban water; engineering aspects of collection and disposal of spent water and solid wastes; significant interchanges between gaseous, liquid, and solid phases of the environment; geographic interchanges; time-dependent developments. Data collection and processing for monitoring and control; maintenance and operation of pollution control systems.
Note: Expected to be given in 2001–02.
Prerequisite: Engineering Sciences 123 or permission of instructor.

Engineering Sciences 261. Design of Water Resource Systems
Catalog Number: 3919
Peter P. Rogers
Half course (fall term). Tu., Th., 11:30–1. EXAM GROUP: 13, 14
Functional design of management systems for collection, storage, conveyance, treatment, and distribution of water. Uses techniques of operations research to develop methods for planning integrated systems of dams, reservoirs, canals, pipe networks, pumps, and treatment plants. Applications in water supply, irrigation hydropower, environmental protection, and conservation of wildlife.
Note: Given in alternate years.
Prerequisite: Applied Mathematics 21b or Mathematics 21b or equivalent.

Engineering Sciences 262 (formerly Engineering Sciences 262r). Advanced Hydrology
Catalog Number: 5658
Ana P. Barros
Half course (spring term). Tu., Th., 2:30–4. EXAM GROUP: 16, 17
The contents and course requirements are similar to those in Engineering Sciences 162, with the exception that students are required to conduct extra reading and complete extra assignments.
Prerequisite: Applied Mathematics 21b, or equivalent. Knowledge of statistics and probability is desirable.

[Engineering Sciences 264. Chemistry of Natural and Polluted Waters]
Catalog Number: 1838
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Half course (spring term). Hours to be arranged.
Chemical aspects of aqueous environmental systems, including thermodynamic, kinetic, biological, and hydrodynamic processes. Applications to water quality management, pollution control, geochemistry, oceanography.
Note: Expected to be given in 2001–02.
Prerequisite: Physical chemistry of electrolyte solutions (e.g., Chemistry 10 or Earth and Planetary Sciences 136), differential equations (e.g., Applied Mathematics 21b or Mathematics 21b), and some experience with biology and geology.

[*Engineering Sciences 266r. Special Topics in Hydrometeorology]
Catalog Number: 4367
Ana P. Barros
Half course (spring term). Hours to be arranged.
The overall focus of the course is on observing, modeling and forecasting of precipitation. Global and local observation networks and instruments. Statistical and physically-based models and parameterizations. Emphasis also placed on understanding the space-time scaling behavior of precipitation processes, use of remote-sensing data, and data-fusion and data-assimilation techniques.
Note: Expected to be given in 2001–02.

*Engineering Sciences 267r. Special Topics in Environmental Hydrology
Catalog Number: 9896
Ana P. Barros
Half course (fall term). M., 3:30–5. EXAM GROUP: 8, 9
Examines a number of topics fundamental to the understanding of water pathways in the environment including land-atmosphere-biosphere interactions, surface-groundwater interactions, transport phenomena, sediment mobility and landscape evolution, and flood and drought hazards. Special attention given to connecting spatial and temporal scales, and to establishing a scientific basis for the development, restoration and sustainability of landscapes and water resource systems.

Engineering Sciences 268. Environmental Chemical Kinetics
Catalog Number: 8711
Scot T. Martin
Half course (spring term). Tu., Th., 10–11:30. EXAM GROUP: 12, 13
Quantifying the time rate of change of chemical species in environmental systems. Common laboratory techniques to measure rate constants. Linear free energy relationships and structural contributions to estimate unknown rate constants. Formulating a coupled chemical system and application of the six principal approximations to obtain analytical solutions. Numerical analysis of complex systems. Concepts are taught by reference to topical problems of current interest in environmental systems. Literature assignments and discussion are part of the course.
Note: Offered in alternate years.
Prerequisite: Physical Chemistry (e.g. Chemistry 60 or Engineering Sciences 168) and Applied Mathematics 21a,b or Mathematics 21a,b or equivalent. Facility in a computational package (e.g., Mathematica).

Engineering Sciences 299r. Special Topics in Engineering Sciences
Catalog Number: 6710
Venkatesh Narayanamurti
Half course (fall term; repeated spring term). Hours to be arranged.
Supervision of experimental or theoretical research on acceptable applied science problems and supervision of reading on topics not covered by regular courses of instruction.
Note: Open to graduate students and A.B./S.M. candidates only. Students must arrange such work with a member of the Division. This course is ordinarily taken with the approval of the Committee on Higher Degrees in certain cases when a letter grade is required. Applicants should file a project sheet before study cards are filed. Project sheets may be obtained from the Academic Office, Pierce Hall 110a.

Cross-listed Courses

Earth and Planetary Sciences 202. Introduction to the Dynamics of Atmospheres and Oceans

Additional courses of interest to graduate students in Environmental Science and Engineering might include courses offered at the Harvard School of Public Health.

Graduate Courses of Reading and Research

Reading courses are odd-numbered; research courses are even-numbered.
*Engineering Sciences 303,304. Topics in Electronic Materials and Semiconductor Heterostructure Physics
Catalog Number: 8668,2824
Venkatesh Narayanamurti 5445

*Engineering Sciences 305,306. Manufacturing
Catalog Number: 6157,6159
Frederick H. Abernathy 1047

*Engineering Sciences 307,308. Control Theory, Robotics, Computer Vision, and Intelligent Machines
Catalog Number: 7566,2719
Roger W. Brockett 3001

*Engineering Sciences 309,310. Design, Sensing, and Control
Catalog Number: 5043,7419
Robert D. Howe 2789

*Engineering Sciences 315,316. Computer Networks
Catalog Number: 2848,2849
H. T. Kung 3155

*Engineering Sciences 317,318. Systems and Control
Catalog Number: 5089,1030
Yu-Chi Ho 1057 (on leave fall term)

*Engineering Sciences 319,320. VLSI Signal Processing
Catalog Number: 3557,2722
Woodward Yang 2790 ( )

*Engineering Sciences 321,322. Shannon Theory, Digital Communications, and Reliable Transmission of Information
Catalog Number: 9317,2330
Aleksandar Kavcic 1261

*Engineering Sciences 335,336. Mechanics of Engineering Materials and Small Devices
Catalog Number: 8173,2399
Joost J. Vlassak 3184

*Engineering Sciences 337,338. Solid Mechanics, Theory of Fracture and Faulting
Catalog Number: 4316,3948
James R. Rice 7270

*Engineering Sciences 339,340. Fluid Mechanics
Catalog Number: 1744,7810
Frederick H. Abernathy 1047

*Engineering Sciences 341,342. Special Topics in Fluid Dynamics
Catalog Number: 2231,2237
Howard A. Stone 2073 (on leave spring term)

*Engineering Sciences 343,344. Deformation and Fracture of Materials
Catalog Number: 3907,2803
John W. Hutchinson 1573 (on leave fall term)

*Engineering Sciences 347,348. Biological Systems Analysis and Control
Catalog Number: 6761,3310
Garrett B. Stanley 2797

*Engineering Sciences 349,350. Special Topics in Dynamical Systems and Applications
Catalog Number: 6691,2087
Igor Mezic 3139

*Engineering Sciences 355,356. Speech and Audio Processing
Catalog Number: 4605,7048
Michael S. Brandstein 2794

*Engineering Sciences 357,358. Atmosphere-Biosphere Interactions
Catalog Number: 7661,8060
Steven C. Wofsy 4396

*Engineering Sciences 359,360. Stratospheric Chemistry and Transport
Catalog Number: 8410,6856
Steven C. Wofsy 4396

*Engineering Sciences 361,362. Atmospheric Chemistry
Catalog Number: 7238,7514
Daniel J. Jacob 1781

*Engineering Sciences 363,364. Dynamic Meterology
Catalog Number: 3756,3757
Brian F. Farrell 7628

*Engineering Sciences 369,370. Urban and Regional Systems Analysis
Catalog Number: 8775,8768
Peter P. Rogers 2804

*Engineering Sciences 375,376. Environmental Biology
Catalog Number: 3985,2863
Ralph Mitchell 1587

*Engineering Sciences 381,382. Physical Hydrology and Hydrometeorology
Catalog Number: 2968,4821
Ana P. Barros 2515

*Engineering Sciences 389. Environmental Chemistry
Catalog Number: 6660
Scot T. Martin 3365

*Engineering Sciences 390. Environmental Chemistry
Catalog Number: 1639
Scot T. Martin 3365

*Engineering Sciences 391,392. Environmental Engineering
Catalog Number: 3979,2860
Joseph J. Harrington 2427