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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.Technical RequirementsMATLAB® software is required to run the .m and .mat files found on this course site.MATLAB® is a trademark of The MathWorks, Inc. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.Technical RequirementsMATLAB® software is required to run the .m and .mat files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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6.253 Convex Analysis and Optimization (MIT) 6.253 Convex Analysis and Optimization (MIT)

Description

6.253 develops the core analytical issues of continuous optimization, duality, and saddle point theory, using a handful of unifying principles that can be easily visualized and readily understood. The mathematical theory of convex sets and functions is discussed in detail, and is the basis for an intuitive, highly visual, geometrical approach to the subject. 6.253 develops the core analytical issues of continuous optimization, duality, and saddle point theory, using a handful of unifying principles that can be easily visualized and readily understood. The mathematical theory of convex sets and functions is discussed in detail, and is the basis for an intuitive, highly visual, geometrical approach to the subject.

Subjects

affine hulls | affine hulls | recession cones | recession cones | global minima | global minima | local minima | local minima | optimal solutions | optimal solutions | hyper planes | hyper planes | minimax theory | minimax theory | polyhedral convexity | polyhedral convexity | polyhedral cones | polyhedral cones | polyhedral sets | polyhedral sets | convex analysis | convex analysis | optimization | optimization | convexity | convexity | Lagrange multipliers | Lagrange multipliers | duality | duality | continuous optimization | continuous optimization | saddle point theory | saddle point theory | linear algebra | linear algebra | real analysis | real analysis | convex sets | convex sets | convex functions | convex functions | extreme points | extreme points | subgradients | subgradients | constrained optimization | constrained optimization | directional derivatives | directional derivatives | subdifferentials | subdifferentials | conical approximations | conical approximations | Fritz John optimality | Fritz John optimality | Exact penalty functions | Exact penalty functions | conjugate duality | conjugate duality | conjugate functions | conjugate functions | Fenchel duality | Fenchel duality | exact penalty functions | exact penalty functions | dual computational methods | dual computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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1.964 Design for Sustainability (MIT) 1.964 Design for Sustainability (MIT)

Description

This course on sustainability will cover the implications of this topic on engineering, design, and architecture. The course will begin with a general survey and discussion of current trends, followed by the introduction of the life cycle assessment (LCA) method as a rigorous, quantitative alternative to current popular sustainability measures for the built environment. This course on sustainability will cover the implications of this topic on engineering, design, and architecture. The course will begin with a general survey and discussion of current trends, followed by the introduction of the life cycle assessment (LCA) method as a rigorous, quantitative alternative to current popular sustainability measures for the built environment.

Subjects

sustainability | sustainability | engineering | engineering | built environment | built environment | life-cycle assessment | life-cycle assessment | LCA | LCA | product impact | product impact | product life cycle | product life cycle | infrastructure | infrastructure | computational methods | computational methods | water | water | wastewater | wastewater | energy | energy | materials | materials | construction | construction

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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1.00 Introduction to Computers and Engineering Problem Solving (MIT) 1.00 Introduction to Computers and Engineering Problem Solving (MIT)

Description

Fundamental software development and computational methods for engineering and scientific applications. Object-oriented software design and development. Weekly programming problems cover programming concepts, graphical user interfaces, numerical methods, data structures, sorting and searching, computer graphics and selected advanced topics. Emphasis is on developing techniques for solving problems in engineering, science, management, and planning. The Java® programming language is used. 3 Engineering Design Points. Java® is a trademark or registered trademark of Sun Microsystems, Inc. in the United States and other countries. Fundamental software development and computational methods for engineering and scientific applications. Object-oriented software design and development. Weekly programming problems cover programming concepts, graphical user interfaces, numerical methods, data structures, sorting and searching, computer graphics and selected advanced topics. Emphasis is on developing techniques for solving problems in engineering, science, management, and planning. The Java® programming language is used. 3 Engineering Design Points. Java® is a trademark or registered trademark of Sun Microsystems, Inc. in the United States and other countries.

Subjects

Java | Java | Java (Computer program language) | Java (Computer program language) | computational methods | computational methods | software development | software development

License

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16.810 Engineering Design and Rapid Prototyping (MIT) 16.810 Engineering Design and Rapid Prototyping (MIT)

Description

This course provides students with an opportunity to conceive, design and implement a product, using rapid protyping methods and computer-aid tools. The first of two phases challenges each student team to meet a set of design requirements and constraints for a structural component. A course of iteration, fabrication, and validation completes this manual design cycle. During the second phase, each team conducts design optimization using structural analysis software, with their phase one prototype as a baseline.AcknowledgmentsThis course is made possible thanks to a grant by the alumni sponsored Teaching and Education Enhancement Program (Class of '51 Fund for Excellence in Education, Class of '55 Fund for Excellence in Teaching, Class of '72 Fund for Educationa This course provides students with an opportunity to conceive, design and implement a product, using rapid protyping methods and computer-aid tools. The first of two phases challenges each student team to meet a set of design requirements and constraints for a structural component. A course of iteration, fabrication, and validation completes this manual design cycle. During the second phase, each team conducts design optimization using structural analysis software, with their phase one prototype as a baseline.AcknowledgmentsThis course is made possible thanks to a grant by the alumni sponsored Teaching and Education Enhancement Program (Class of '51 Fund for Excellence in Education, Class of '55 Fund for Excellence in Teaching, Class of '72 Fund for Educationa

Subjects

engineering design | engineering design | rapid prototyping | rapid prototyping | manufacturing | manufacturing | testing | testing | system components | system components | complex structural parts | complex structural parts | hand sketching | hand sketching | CAD | CAD | CAD modeling | CAD modeling | CAE | CAE | CAE analysis | CAE analysis | CAM programming | CAM programming | CNC | CNC | CNC machining | CNC machining | computer aided design | computer aided design | computer aided | computer aided | structual testing | structual testing | multiobjective design | multiobjective design | optimization | optimization | computational methods | computational methods | tools | tools | design process | design process | design competition | design competition | active learning | active learning | hands-on | hands-on | human creativity | human creativity | holistic | holistic | solidworks | solidworks | finite element | finite element | FEM | FEM | FEM analysis | FEM analysis | COSMOS | COSMOS | omax | omax | presentation | presentation | CDIO | CDIO

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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4.191 Introduction to Integrated Design (MIT) 4.191 Introduction to Integrated Design (MIT)

Description

During this course, we will be exploring basic questions of architecture through several short design exercises. Working with many different media, students will discover the interrelationship of architecture and its related disciplines, such as structures, sustainability, architectural history and the visual arts. Each problem will focus on one of these disciplines and one exploration and presentation technique. During this course, we will be exploring basic questions of architecture through several short design exercises. Working with many different media, students will discover the interrelationship of architecture and its related disciplines, such as structures, sustainability, architectural history and the visual arts. Each problem will focus on one of these disciplines and one exploration and presentation technique.

Subjects

Sustainability | Sustainability | engineering | engineering | built environment | built environment | life-cycle assessment | life-cycle assessment | LCA | LCA | product impact | product impact | product life cycle | product life cycle | infrastructure | infrastructure | computational methods | computational methods | water | water | wastewater | wastewater | energy | energy | materials | materials | construction | construction | introductory design | introductory design | studio | studio | drawing | drawing | modeling | modeling | 3D models | 3D models | architecture | architecture | architectural design | architectural design

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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16.810 Engineering Design and Rapid Prototyping (MIT) 16.810 Engineering Design and Rapid Prototyping (MIT)

Description

Includes audio/video content: AV special element video. This course provides students with an opportunity to conceive, design and implement a product, using rapid prototyping methods and computer-aid tools. The first of two phases challenges each student team to meet a set of design requirements and constraints for a structural component. A course of iteration, fabrication, and validation completes this manual design cycle. During the second phase, each team conducts design optimization using structural analysis software, with their phase one prototype as a baseline. Acknowledgements This course is made possible thanks to a grant by the alumni sponsored Teaching and Education Enhancement Program (Class of '51 Fund for Excellence in Education, Class of '55 Fund for Excellence in Teaching, Includes audio/video content: AV special element video. This course provides students with an opportunity to conceive, design and implement a product, using rapid prototyping methods and computer-aid tools. The first of two phases challenges each student team to meet a set of design requirements and constraints for a structural component. A course of iteration, fabrication, and validation completes this manual design cycle. During the second phase, each team conducts design optimization using structural analysis software, with their phase one prototype as a baseline. Acknowledgements This course is made possible thanks to a grant by the alumni sponsored Teaching and Education Enhancement Program (Class of '51 Fund for Excellence in Education, Class of '55 Fund for Excellence in Teaching,

Subjects

engineering design | engineering design | rapid prototyping | rapid prototyping | manufacturing | manufacturing | testing | testing | system components | system components | complex structural parts | complex structural parts | hand sketching | hand sketching | CAD | CAD | CAD modeling | CAD modeling | CAE | CAE | CAE analysis | CAE analysis | CAM programming | CAM programming | CNC | CNC | CNC machining | CNC machining | computer aided design | computer aided design | computer aided | computer aided | structual testing | structual testing | multiobjective design | multiobjective design | optimization | optimization | computational methods | computational methods | tools | tools | design process | design process | design competition | design competition | active learning | active learning | hands-on | hands-on | human creativity | human creativity | holistic | holistic | solidworks | solidworks | finite element | finite element | FEM | FEM | FEM analysis | FEM analysis | COSMOS | COSMOS | omax | omax | presentation | presentation | CDIO | CDIO

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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16.810 Engineering Design and Rapid Prototyping (MIT) 16.810 Engineering Design and Rapid Prototyping (MIT)

Description

Includes audio/video content: AV special element video. This course provides students with an opportunity to conceive, design and implement a product, using rapid prototyping methods and computer-aid tools. The first of two phases challenges each student team to meet a set of design requirements and constraints for a structural component. A course of iteration, fabrication, and validation completes this manual design cycle. During the second phase, each team conducts design optimization using structural analysis software, with their phase one prototype as a baseline. Acknowledgements This course is made possible thanks to a grant by the alumni sponsored Teaching and Education Enhancement Program (Class of '51 Fund for Excellence in Education, Class of '55 Fund for Excellence in Teachin Includes audio/video content: AV special element video. This course provides students with an opportunity to conceive, design and implement a product, using rapid prototyping methods and computer-aid tools. The first of two phases challenges each student team to meet a set of design requirements and constraints for a structural component. A course of iteration, fabrication, and validation completes this manual design cycle. During the second phase, each team conducts design optimization using structural analysis software, with their phase one prototype as a baseline. Acknowledgements This course is made possible thanks to a grant by the alumni sponsored Teaching and Education Enhancement Program (Class of '51 Fund for Excellence in Education, Class of '55 Fund for Excellence in Teachin

Subjects

engineering design | engineering design | rapid prototyping | rapid prototyping | manufacturing | manufacturing | testing | testing | system components | system components | complex structural parts | complex structural parts | hand sketching | hand sketching | CAD | CAD | CAD modeling | CAD modeling | CAE | CAE | CAE analysis | CAE analysis | CAM programming | CAM programming | CNC | CNC | CNC machining | CNC machining | computer aided design | computer aided design | computer aided | computer aided | structual testing | structual testing | multiobjective design | multiobjective design | optimization | optimization | computational methods | computational methods | tools | tools | design process | design process | design competition | design competition | active learning | active learning | hands-on | hands-on | human creativity | human creativity | holistic | holistic | solidworks | solidworks | finite element | finite element | FEM | FEM | FEM analysis | FEM analysis | COSMOS | COSMOS | omax | omax | presentation | presentation | CDIO | CDIO | structural testing | structural testing

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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1.964 Design for Sustainability (MIT) 1.964 Design for Sustainability (MIT)

Description

The course considers the growing popularity of sustainability and its implications for the practice of engineering, particularly for the built environment. Two particular methodologies are featured: life cycle assessment (LCA) and Leadership in Energy and Environmental Design (LEED). The fundamentals of each approach will be presented. Specific topics covered include water and wastewater management, energy use, material selection, and construction. The course considers the growing popularity of sustainability and its implications for the practice of engineering, particularly for the built environment. Two particular methodologies are featured: life cycle assessment (LCA) and Leadership in Energy and Environmental Design (LEED). The fundamentals of each approach will be presented. Specific topics covered include water and wastewater management, energy use, material selection, and construction.

Subjects

Sustainability | Sustainability | engineering | engineering | built environment | built environment | life-cycle assessment | life-cycle assessment | LCA | LCA | product impact | product impact | product life cycle | product life cycle | infrastructure | infrastructure | computational methods | computational methods | water | water | wastewater | wastewater | energy | energy | materials | materials | construction | construction

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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6.863J Natural Language and the Computer Representation of Knowledge (MIT) 6.863J Natural Language and the Computer Representation of Knowledge (MIT)

Description

6.863 is a laboratory-oriented course on the theory and practice of building computer systems for human language processing, with an emphasis on the linguistic, cognitive, and engineering foundations for understanding their design. 6.863 is a laboratory-oriented course on the theory and practice of building computer systems for human language processing, with an emphasis on the linguistic, cognitive, and engineering foundations for understanding their design.

Subjects

natural language processing | natural language processing | computational methods | computational methods | computer science | computer science | artificial intelligence | artificial intelligence | linguistic theory | linguistic theory | psycholinguistics | psycholinguistics | applications | applications | thematic structure | thematic structure | lexical-conceptual structure | lexical-conceptual structure | semantic structure | semantic structure | pragmatic structure | pragmatic structure | discourse structure | discourse structure | phonology | phonology | morphology | morphology | 2-level morphology | 2-level morphology | kimmo | kimmo | hmm tagging | hmm tagging | tagging | tagging | rule-based tagging | rule-based tagging | part of speech tagging | part of speech tagging | brill tagger | brill tagger | parsing | parsing | syntax | syntax | automata | automata | word modeling | word modeling | grammars | grammars | parsing algorithms | parsing algorithms | shift-reduce parsers | shift-reduce parsers | Earley's algorithm | Earley's algorithm | chart parsing | chart parsing | context-free parsing | context-free parsing | feature-based parsing | feature-based parsing | natural language system design | natural language system design | integrated lexicon | integrated lexicon | syntactic features | syntactic features | semantic interpretation | semantic interpretation | compositionality | compositionality | quantifiers | quantifiers | lexical semantic | lexical semantic | semantics | semantics | machine translation | machine translation | language learning | language learning | computational models of language | computational models of language | origins of language | origins of language | 6.863 | 6.863 | 9.611 | 9.611

License

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16.682 Prototyping Avionics (MIT) 16.682 Prototyping Avionics (MIT)

Description

In the past building prototypes of electronic components for new projects/products was limited to using protoboards and wirewrap. Manufacturing a printed-circuit-board was limited to final production, where mistakes in the implementation meant physically cutting traces on the board and adding wire jumpers - the final products would have these fixes on them! Today that is no longer the case, while you will still cut traces and use jumpers when debugging a board, manufacturing a new final version without the errors is a simple and relatively inexpensive task. For that matter, manufacturing a prototype printed circuit board which you know is likely to have errors but which will get the design substantially closer to the final product than a protoboard setup is not only possible, but desirable In the past building prototypes of electronic components for new projects/products was limited to using protoboards and wirewrap. Manufacturing a printed-circuit-board was limited to final production, where mistakes in the implementation meant physically cutting traces on the board and adding wire jumpers - the final products would have these fixes on them! Today that is no longer the case, while you will still cut traces and use jumpers when debugging a board, manufacturing a new final version without the errors is a simple and relatively inexpensive task. For that matter, manufacturing a prototype printed circuit board which you know is likely to have errors but which will get the design substantially closer to the final product than a protoboard setup is not only possible, but desirable

Subjects

engineering design | engineering design | rapid prototyping | rapid prototyping | manufacturing | manufacturing | testing | testing | system components | system components | complex structural parts | complex structural parts | hand sketching | hand sketching | CAD | CAD | CAD modeling | CAD modeling | CAE | CAE | CAE analysis | CAE analysis | CAM programming | CAM programming | CNC | CNC | CNC machining | CNC machining | computer aided design | computer aided design | computer aided | computer aided | structual testing | structual testing | multiobjective design | multiobjective design | optimization | optimization | computational methods | computational methods | tools | tools | design process | design process | design competition | design competition | active learning | active learning | hands-on | hands-on | human creativity | human creativity | holistic | holistic | solidworks | solidworks | finite element | finite element | FEM | FEM | FEM analysis | FEM analysis | COSMOS | COSMOS | omax | omax | presentation | presentation | CDIO | CDIO

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.417 Introduction to Computational Molecular Biology (MIT) 18.417 Introduction to Computational Molecular Biology (MIT)

Description

This course introduces the basic computational methods used to understand the cell on a molecular level. It covers subjects such as the sequence alignment algorithms: dynamic programming, hashing, suffix trees, and Gibbs sampling. Furthermore, it focuses on computational approaches to: genetic and physical mapping; genome sequencing, assembly, and annotation; RNA expression and secondary structure; protein structure and folding; and molecular interactions and dynamics. This course introduces the basic computational methods used to understand the cell on a molecular level. It covers subjects such as the sequence alignment algorithms: dynamic programming, hashing, suffix trees, and Gibbs sampling. Furthermore, it focuses on computational approaches to: genetic and physical mapping; genome sequencing, assembly, and annotation; RNA expression and secondary structure; protein structure and folding; and molecular interactions and dynamics.

Subjects

basic computational methods cell on a molecular level | basic computational methods cell on a molecular level | sequence alignment algorithms | sequence alignment algorithms | dynamic programming | dynamic programming | hashing | hashing | suffix trees | suffix trees | Gibbs sampling | Gibbs sampling | genetic and physical mapping | genetic and physical mapping | genome sequencing | genome sequencing | assembly | assembly | and annotation | and annotation | RNA expression and secondary structure | RNA expression and secondary structure | protein structure and folding | protein structure and folding | and molecular interactions and dynamics | and molecular interactions and dynamics | annotation | annotation | molecular interactions and dynamics | molecular interactions and dynamics

License

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21M.269 Studies in Western Music History: Quantitative and Computational Approaches to Music History (MIT) 21M.269 Studies in Western Music History: Quantitative and Computational Approaches to Music History (MIT)

Description

The disciplines of music history and music theory have been slow to embrace the digital revolutions that have transformed other fields' text-based scholarship (history and literature in particular). Computational musicology opens the door to the possibility of understanding—even if at a broad level—trends and norms of behavior of large repertories of music. This class presents the major approaches, results, and challenges of computational musicology through readings in the field, gaining familiarity with datasets, and hands on workshops and assignments on data analysis and "corpus" (i.e., repertory) studies. Class sessions alternate between discussion/lecture and labs on digital tools for studying music. A background in music theory and/or history is required, and ex The disciplines of music history and music theory have been slow to embrace the digital revolutions that have transformed other fields' text-based scholarship (history and literature in particular). Computational musicology opens the door to the possibility of understanding—even if at a broad level—trends and norms of behavior of large repertories of music. This class presents the major approaches, results, and challenges of computational musicology through readings in the field, gaining familiarity with datasets, and hands on workshops and assignments on data analysis and "corpus" (i.e., repertory) studies. Class sessions alternate between discussion/lecture and labs on digital tools for studying music. A background in music theory and/or history is required, and ex

Subjects

music informatics | music informatics | computational methods | computational methods | statistical analysis | statistical analysis | musicology | musicology | music theory | music theory | open source software | open source software

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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22.15 Essential Numerical Methods (MIT) 22.15 Essential Numerical Methods (MIT)

Description

Includes audio/video content: AV special element video. This half-semester course introduces computational methods for solving physical problems, especially in nuclear applications. The course covers ordinary and partial differential equations for particle orbit, and fluid, field, and particle conservation problems; their representation and solution by finite difference numerical approximations; iterative matrix inversion methods; stability, convergence, accuracy and statistics; and particle representations of Boltzmann's equation and methods of solution such as Monte-Carlo and particle-in-cell techniques. Includes audio/video content: AV special element video. This half-semester course introduces computational methods for solving physical problems, especially in nuclear applications. The course covers ordinary and partial differential equations for particle orbit, and fluid, field, and particle conservation problems; their representation and solution by finite difference numerical approximations; iterative matrix inversion methods; stability, convergence, accuracy and statistics; and particle representations of Boltzmann's equation and methods of solution such as Monte-Carlo and particle-in-cell techniques.

Subjects

MATLAB | MATLAB | Octave | Octave | numerical methods | numerical methods | numerical analysis | numerical analysis | computational methods | computational methods | differential equations | differential equations | approximation | approximation | finite difference | finite difference | iteration | iteration

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.Technical RequirementsMATLAB® software is required to run the .m and .mat files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.

Subjects

numerical integration | ODEs | ordinary differential equations | finite difference | finite volume | finite element | discretization | PDEs | partial differential equations | numerical linear algebra | probabilistic methods | optimization | omputational methods | aerospace engineering | computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

Subjects

numerical integration | ODEs | ordinary differential equations | finite difference | finite volume | finite element | discretization | PDEs | partial differential equations | numerical linear algebra | probabilistic methods | optimization | omputational methods | aerospace engineering | computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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1.964 Design for Sustainability (MIT)

Description

The course considers the growing popularity of sustainability and its implications for the practice of engineering, particularly for the built environment. Two particular methodologies are featured: life cycle assessment (LCA) and Leadership in Energy and Environmental Design (LEED). The fundamentals of each approach will be presented. Specific topics covered include water and wastewater management, energy use, material selection, and construction.

Subjects

Sustainability | engineering | built environment | life-cycle assessment | LCA | product impact | product life cycle | infrastructure | computational methods | water | wastewater | energy | materials | construction

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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6.253 Convex Analysis and Optimization (MIT)

Description

6.253 develops the core analytical issues of continuous optimization, duality, and saddle point theory, using a handful of unifying principles that can be easily visualized and readily understood. The mathematical theory of convex sets and functions is discussed in detail, and is the basis for an intuitive, highly visual, geometrical approach to the subject.

Subjects

affine hulls | recession cones | global minima | local minima | optimal solutions | hyper planes | minimax theory | polyhedral convexity | polyhedral cones | polyhedral sets | convex analysis | optimization | convexity | Lagrange multipliers | duality | continuous optimization | saddle point theory | linear algebra | real analysis | convex sets | convex functions | extreme points | subgradients | constrained optimization | directional derivatives | subdifferentials | conical approximations | Fritz John optimality | Exact penalty functions | conjugate duality | conjugate functions | Fenchel duality | exact penalty functions | dual computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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1.964 Design for Sustainability (MIT)

Description

This course on sustainability will cover the implications of this topic on engineering, design, and architecture. The course will begin with a general survey and discussion of current trends, followed by the introduction of the life cycle assessment (LCA) method as a rigorous, quantitative alternative to current popular sustainability measures for the built environment.

Subjects

sustainability | engineering | built environment | life-cycle assessment | LCA | product impact | product life cycle | infrastructure | computational methods | water | wastewater | energy | materials | construction

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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1.00 Introduction to Computers and Engineering Problem Solving (MIT)

Description

Fundamental software development and computational methods for engineering and scientific applications. Object-oriented software design and development. Weekly programming problems cover programming concepts, graphical user interfaces, numerical methods, data structures, sorting and searching, computer graphics and selected advanced topics. Emphasis is on developing techniques for solving problems in engineering, science, management, and planning. The Java® programming language is used. 3 Engineering Design Points. Java® is a trademark or registered trademark of Sun Microsystems, Inc. in the United States and other countries.

Subjects

Java | Java (Computer program language) | computational methods | software development

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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16.810 Engineering Design and Rapid Prototyping (MIT)

Description

This course provides students with an opportunity to conceive, design and implement a product, using rapid protyping methods and computer-aid tools. The first of two phases challenges each student team to meet a set of design requirements and constraints for a structural component. A course of iteration, fabrication, and validation completes this manual design cycle. During the second phase, each team conducts design optimization using structural analysis software, with their phase one prototype as a baseline.AcknowledgmentsThis course is made possible thanks to a grant by the alumni sponsored Teaching and Education Enhancement Program (Class of '51 Fund for Excellence in Education, Class of '55 Fund for Excellence in Teaching, Class of '72 Fund for Educationa

Subjects

engineering design | rapid prototyping | manufacturing | testing | system components | complex structural parts | hand sketching | CAD | CAD modeling | CAE | CAE analysis | CAM programming | CNC | CNC machining | computer aided design | computer aided | structual testing | multiobjective design | optimization | computational methods | tools | design process | design competition | active learning | hands-on | human creativity | holistic | solidworks | finite element | FEM | FEM analysis | COSMOS | omax | presentation | CDIO

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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4.191 Introduction to Integrated Design (MIT)

Description

During this course, we will be exploring basic questions of architecture through several short design exercises. Working with many different media, students will discover the interrelationship of architecture and its related disciplines, such as structures, sustainability, architectural history and the visual arts. Each problem will focus on one of these disciplines and one exploration and presentation technique.

Subjects

Sustainability | engineering | built environment | life-cycle assessment | LCA | product impact | product life cycle | infrastructure | computational methods | water | wastewater | energy | materials | construction | introductory design | studio | drawing | modeling | 3D models | architecture | architectural design

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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