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Course Criteria
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3.00 Credits
Not offered in the period from 08F through 10S While the art of building sailing vessels has been developed over thousands of years, only since the turn of the century has the design of sailboats undergone a major revolution, because of a better knowledge of fluid mechanics and the development of such new strong lightweight materials as fiberglass and Kevlar. The fundamentals of fluid mechanics will be studied in order to understand why and how a sailboat moves. Design criteria will be developed, and modern designs, materials, and sails used for today's sailboats will be discussed. A design project will be assigned to each student. There will be a laboratory and the students will have the opportunity to sail with the College sailing team on Lake Mascoma. Prerequisite: Mathematics 3 or permission. Enrollment is limited to 40 students. Dist: TLA. Richter.
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3.00 Credits
08F: 9S 09S: 12 09F: Arrange 10S: 12 This course introduces concepts and techniques for creating computational solutions to problems in engineering and science. The essentials of computer programming are developed using the C and Matlab languages, with the goal of enabling the student to use the computer effectively in subsequent courses. Programming topics include problem decomposition, control structures, recursion, arrays and other data structures, file I/O, graphics, and code libraries. Applications will be drawn from numerical solution of ordinary differential equations, root finding, matrix operations, searching and sorting, simulation, and data analysis. Good programming style and computational efficiency are emphasized. Although no previous programming experience is assumed, a significant time commitment is required. Students planning to pursue the engineering sciences major are advised to take Engineering Sciences 20. Students considering the computer science major or majors modified with computer science should take Computer Science 5. Prerequisite: Mathematics 3 and prior or concurrent enrollment in Mathematics 8. Dist: TAS. Shepherd.
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3.00 Credits
09S: 12 Continuation of Engineering Sciences 100 with emphasis on variational calculus, integral equations, and asymptotic and perturbation methods for integrals and differential equations. Selected topics include functional differentiation, Hamilton's principle, Rayleigh-Ritz method, Fredholm and Volterra equations, integral transforms, Schmidt-Hilbert theory, asymptotic series, methods of steepest descent and stationary phase, boundary layer theory, WKB methods, and multiple-scale theory. Prerequisite: Engineering Sciences 100, or equivalent. The staff.
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3.00 Credits
09W, 10W: Arrange Analysis of systems with a finite number of degrees of freedom. Qualitative features of the phase plane, critical points, structural stability, limit cycles, domains of attraction, bifurcations. Poincare section. Linear and nonlinear stability. Floquet theory. Asymptotic analysis using multiple time-scale and averaging methods. Examples are derived from problems in nonlinear oscillations, Hamiltonian systems, nonlinear waves, fluid dynamics, and/or control theory. Prerequisite: Engineering Sciences 145 or equivalent. Olfati-Saber.
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3.00 Credits
09S: 11 Offered in alternate years Boundary Element and spectral methods are examined within the numerical analysis framework established in Engineering Sciences 105. The boundary element method is introduced in the context of linear elliptic problems arising in heat and mass transfer, solid mechanics, and electricity and magnetism. Coupling with domain integral methods (e.g. finite elements) is achieved through the natural boundary conditions. Extensions to nonlinear and time-dependent problems are explored. Spectral methods are introduced and their distinctive properties explored in the context of orthogonal bases for linear, time-invariant problems. Extension to nonlinear problems is discussed in the context of fluid mechanics applications. Harmonic decomposition of the time-domain is examined for nonlinear Helmhotz-type problems associated with E&M and physical oceanography. Prerequisite: Engineering Sciences 105. Paulsen.
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3.00 Credits
08F: 10; Laboratory 09S: 11; Laboratory 09F: 10; Laboratory 10S: 11; Laboratory The student is introduced to engineering through participation, as a member of a team, in a complete design project. The synthesis of many fields involving the laws of nature, mathematics, economics, management, and communication is required in the project. Engineering principles of analysis, experimentation, and design are applied to a real problem, from initial concept to final recommendations. The project results are evaluated in terms of technical and economic feasibility plus social significance. Lectures are directed toward the problem, and experiments are designed by students as the need develops. Enrollment is limited to 64 students. Prerequisite: Mathematics 3 or equivalent. Dist: TAS. Collier (fall), Lotko (spring).
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3.00 Credits
09W: 9; Laboratory Tu,Th 09X: 10; Laboratory 10W: 9; Laboratory Tu,Th 10X: 10; Laboratory The student is introduced to the techniques of modeling and analyzing lumped, linear systems. The course will be concerned primarily with an elementary treatment of electrical, mechanical, fluid, and thermal systems. System input will be related to output through ordinary differential equations, which will be solved by analytical and numerical techniques. System concepts, such as time constant, natural frequency, and damping factor, are introduced. The course includes computer and laboratory exercises to enhance the students' understanding of the principles of lumped systems. Prerequisite: Mathematics 13 Physics 14, and Engineering Sciences 20. Dist: TLA. Lynd, Ray (winter), Trembly (summer).
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3.00 Credits
Not offered in the period from 08F through 10S Continuation of Engineering Sciences 120, with emphasis on fundamentals of propagation and radiation of electromagnetic waves and their interaction with material boundaries. Propagation in homogeneous and inhomogeneous media, including anisotropic media; reflection, transmission, guidance and resonance, radiation fields and antennas; diffraction theory; scattering. Prerequisite: Engineering Sciences 100 and 120 or permission of the instructor.
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3.00 Credits
08F: 2 09S: 9 09F: 2 10S: 9 A study of the fundamental properties of distributed systems and their description in terms of scalar and vector fields. After a summary of vector-field theory, the formulation of conservation laws, source laws, and constitutive equations is discussed. Energy and force relations are developed and the nature of potential fields, wave fields, and diffusion fields examined. A survey of elementary transport processes is given. Particular attention is given to the relation between the description of systems in terms of discrete and distributed parameters. Applications are chosen primarily from fluid mechanics, electromagnetic theory, and heat transfer. Prerequisite: Engineering Sciences 22, or equivalent. Dist: TAS. Hansen (fall), Osterberg (spring).
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3.00 Credits
09W, 09S, 10W, 10S: 10; Laboratory An introduction to the structure/property relationships that govern the mechanical, the thermal, and the electrical behavior of solids (ceramics, metals, and polymers). Topics include atomic, crystalline, and amorphous structures; x-ray diffraction; imperfections in crystals; phase diagrams; phase transformations; elastic and plastic deformation; free electron theory and band theory of solids; and electrical conduction in metals and semiconductors. The laboratory consists of an experimental project selected by the student and approved by the instructor. Prerequisite: Physics 14 and Chemistry 5. Dist: TLA. Frost (winter), Gibson (spring).
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