Searching for mathematical techniques : 8 results found | RSS Feed for this search

3.016 Mathematics for Materials Scientists and Engineers (MIT) 3.016 Mathematics for Materials Scientists and Engineers (MIT)

Description

The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site. The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site.

Subjects

energetics | energetics | materials structure and symmetry: applied fields | materials structure and symmetry: applied fields | mechanics and physics of solids and soft materials | mechanics and physics of solids and soft materials | linear algebra | linear algebra | orthonormal basis | orthonormal basis | eigenvalues | eigenvalues | eigenvectors | eigenvectors | quadratic forms | quadratic forms | tensor operations | tensor operations | symmetry operations | symmetry operations | calculus | calculus | complex analysis | complex analysis | differential equations | differential equations | theory of distributions | theory of distributions | fourier analysis | fourier analysis | random walks | random walks | mathematical technicques | mathematical technicques | materials science | materials science | materials engineering | materials engineering | materials structure | materials structure | symmetry | symmetry | applied fields | applied fields | materials response | materials response | solids mechanics | solids mechanics | solids physics | solids physics | soft materials | soft materials | multi-variable calculus | multi-variable calculus | ordinary differential equations | ordinary differential equations | partial differential equations | partial differential equations | applied mathematics | applied mathematics | mathematical techniques | mathematical techniques

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

Site sourced from

http://ocw.mit.edu/rss/all/mit-allarchivedcourses.xml

Attribution

Click to get HTML | Click to get attribution | Click to get URL

All metadata

See all metadata

10.34 Numerical Methods Applied to Chemical Engineering (MIT) 10.34 Numerical Methods Applied to Chemical Engineering (MIT)

Description

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. The examples will use MATLAB®. Acknowledgements The instructor would like to thank Robert Ashcraft, Sandeep Sharma, David Weingeist, and Nikolay Zaborenko for their work in preparing materials for this course site. Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. The examples will use MATLAB®. Acknowledgements The instructor would like to thank Robert Ashcraft, Sandeep Sharma, David Weingeist, and Nikolay Zaborenko for their work in preparing materials for this course site.

Subjects

Matlab | Matlab | modern computational techniques in chemical engineering | modern computational techniques in chemical engineering | mathematical techniques in chemical engineering | mathematical techniques in chemical engineering | linear systems | linear systems | scientific computing | scientific computing | solving sets of nonlinear algebraic equations | solving sets of nonlinear algebraic equations | solving ordinary differential equations | solving ordinary differential equations | solving differential-algebraic (DAE) systems | solving differential-algebraic (DAE) systems | probability theory | probability theory | use of probability theory in physical modeling | use of probability theory in physical modeling | statistical analysis of data estimation | statistical analysis of data estimation | statistical analysis of parameter estimation | statistical analysis of parameter estimation | finite difference techniques | finite difference techniques | finite element techniques | finite element techniques | converting partial differential equations | converting partial differential equations | Navier-Stokes equations | Navier-Stokes equations

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

Site sourced from

http://ocw.mit.edu/rss/all/mit-allcourses-10.xml

Attribution

Click to get HTML | Click to get attribution | Click to get URL

All metadata

See all metadata

10.34 Numerical Methods Applied to Chemical Engineering (MIT) 10.34 Numerical Methods Applied to Chemical Engineering (MIT)

Description

This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLAB® computing environment. This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLAB® computing environment.

Subjects

Matlab | Matlab | modern computational techniques in chemical engineering | modern computational techniques in chemical engineering | mathematical techniques in chemical engineering | mathematical techniques in chemical engineering | linear systems | linear systems | scientific computing | scientific computing | solving sets of nonlinear algebraic equations | solving sets of nonlinear algebraic equations | solving ordinary differential equations | solving ordinary differential equations | solving differential-algebraic (DAE) systems | solving differential-algebraic (DAE) systems | probability theory | probability theory | use of probability theory in physical modeling | use of probability theory in physical modeling | statistical analysis of data estimation | statistical analysis of data estimation | statistical analysis of parameter estimation | statistical analysis of parameter estimation | finite difference techniques | finite difference techniques | finite element techniques | finite element techniques | converting partial differential equations | converting partial differential equations

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

Site sourced from

http://ocw.mit.edu/rss/all/mit-allcourses-10.xml

Attribution

Click to get HTML | Click to get attribution | Click to get URL

All metadata

See all metadata

10.34 Numerical Methods Applied to Chemical Engineering (MIT)

Description

This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLAB® computing environment.

Subjects

Matlab | modern computational techniques in chemical engineering | mathematical techniques in chemical engineering | linear systems | scientific computing | solving sets of nonlinear algebraic equations | solving ordinary differential equations | solving differential-algebraic (DAE) systems | probability theory | use of probability theory in physical modeling | statistical analysis of data estimation | statistical analysis of parameter estimation | finite difference techniques | finite element techniques | converting partial differential equations

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

Site sourced from

https://ocw.mit.edu/rss/all/mit-allsimplifiedchinesecourses.xml

Attribution

Click to get HTML | Click to get attribution | Click to get URL

All metadata

See all metadata

3.016 Mathematics for Materials Scientists and Engineers (MIT)

Description

The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site.

Subjects

energetics | materials structure and symmetry: applied fields | mechanics and physics of solids and soft materials | linear algebra | orthonormal basis | eigenvalues | eigenvectors | quadratic forms | tensor operations | symmetry operations | calculus | complex analysis | differential equations | theory of distributions | fourier analysis | random walks | mathematical technicques | materials science | materials engineering | materials structure | symmetry | applied fields | materials response | solids mechanics | solids physics | soft materials | multi-variable calculus | ordinary differential equations | partial differential equations | applied mathematics | mathematical techniques

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

Site sourced from

https://ocw.mit.edu/rss/all/mit-allarchivedcourses.xml

Attribution

Click to get HTML | Click to get attribution | Click to get URL

All metadata

See all metadata

10.34 Numerical Methods Applied to Chemical Engineering (MIT)

Description

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. The examples will use MATLAB®. Acknowledgements The instructor would like to thank Robert Ashcraft, Sandeep Sharma, David Weingeist, and Nikolay Zaborenko for their work in preparing materials for this course site.

Subjects

Matlab | modern computational techniques in chemical engineering | mathematical techniques in chemical engineering | linear systems | scientific computing | solving sets of nonlinear algebraic equations | solving ordinary differential equations | solving differential-algebraic (DAE) systems | probability theory | use of probability theory in physical modeling | statistical analysis of data estimation | statistical analysis of parameter estimation | finite difference techniques | finite element techniques | converting partial differential equations | Navier-Stokes equations

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

Site sourced from

https://ocw.mit.edu/rss/all/mit-allcourses.xml

Attribution

Click to get HTML | Click to get attribution | Click to get URL

All metadata

See all metadata

10.34 Numerical Methods Applied to Chemical Engineering (MIT)

Description

This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLAB® computing environment.

Subjects

Matlab | modern computational techniques in chemical engineering | mathematical techniques in chemical engineering | linear systems | scientific computing | solving sets of nonlinear algebraic equations | solving ordinary differential equations | solving differential-algebraic (DAE) systems | probability theory | use of probability theory in physical modeling | statistical analysis of data estimation | statistical analysis of parameter estimation | finite difference techniques | finite element techniques | converting partial differential equations

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

Site sourced from

https://ocw.mit.edu/rss/all/mit-allcourses.xml

Attribution

Click to get HTML | Click to get attribution | Click to get URL

All metadata

See all metadata

10.34 Numerical Methods Applied to Chemical Engineering (MIT)

Description

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. The examples will use MATLAB®. Acknowledgements The instructor would like to thank Robert Ashcraft, Sandeep Sharma, David Weingeist, and Nikolay Zaborenko for their work in preparing materials for this course site.

Subjects

Matlab | modern computational techniques in chemical engineering | mathematical techniques in chemical engineering | linear systems | scientific computing | solving sets of nonlinear algebraic equations | solving ordinary differential equations | solving differential-algebraic (DAE) systems | probability theory | use of probability theory in physical modeling | statistical analysis of data estimation | statistical analysis of parameter estimation | finite difference techniques | finite element techniques | converting partial differential equations | Navier-Stokes equations

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

Site sourced from

https://ocw.mit.edu/rss/all/mit-allarchivedcourses.xml

Attribution

Click to get HTML | Click to get attribution | Click to get URL

All metadata

See all metadata