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18.156 Differential Analysis (MIT) 18.156 Differential Analysis (MIT)

Description

The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear partial differential equations. It is the second semester of a two-semester, graduate-level sequence on Differential Analysis. The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear partial differential equations. It is the second semester of a two-semester, graduate-level sequence on Differential Analysis.

Subjects

Sobolev spaces | Sobolev spaces | Fredholm alternative | Fredholm alternative | Variable coefficient elliptic | parabolic and hyperbolic linear partial differential equations | Variable coefficient elliptic | parabolic and hyperbolic linear partial differential equations | Variational methods | Variational methods | Viscosity solutions of fully nonlinear partial differential equations | Viscosity solutions of fully nonlinear partial differential equations | Schauder theory | Schauder theory | Holder estimates | Holder estimates | linear equations | linear equations | second derivatives | second derivatives | elliptic | elliptic | parabolic | parabolic | nonlinear partial differential equations | nonlinear partial differential equations | linear partial differential equations | linear partial differential equations | harmonic functions | harmonic functions | elliptic equations | elliptic equations | parabolic equations | parabolic equations

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14.662 Labor Economics II (MIT) 14.662 Labor Economics II (MIT)

Description

This is the second of a two-part sequence of courses in labor economics. The course sequence is also open to qualified students in related fields and classes may be taken individually or out of sequence. This part of the sequence is principally concerned with issues relating to the determinants of the wage and salary distribution. The first half is organized around topics in wage determination, which are of particular interest for current research and policy and culminates with a focus on recent debates about the increasing dispersion of wage and salary income. The second half of the course is focused on labor market institutions and technological changes, and relates the debate about the income distribution to other major changes in the structure and texture of advanced industrial societi This is the second of a two-part sequence of courses in labor economics. The course sequence is also open to qualified students in related fields and classes may be taken individually or out of sequence. This part of the sequence is principally concerned with issues relating to the determinants of the wage and salary distribution. The first half is organized around topics in wage determination, which are of particular interest for current research and policy and culminates with a focus on recent debates about the increasing dispersion of wage and salary income. The second half of the course is focused on labor market institutions and technological changes, and relates the debate about the income distribution to other major changes in the structure and texture of advanced industrial societi

Subjects

labor | labor | economics | economics | trade unions | trade unions | wage differentials | wage differentials | international trade | international trade | wage and salary distribution | wage and salary distribution | wage determination | wage determination | increasing dispersion of wage and salary income | increasing dispersion of wage and salary income | labor market institutions | labor market institutions | technological changes | technological changes | income distribution | income distribution | United States and other advanced industrial countries | United States and other advanced industrial countries | moral hazard and agency | moral hazard and agency | Static single agent models | Static single agent models | Intrinsic motivation | Intrinsic motivation | Multiple tasks | Multiple tasks | Multiple agents | Multiple agents | Dynamic agency | Dynamic agency | Efficiency wages | Efficiency wages | Employer Wage Differentials | Employer Wage Differentials | Industry and firm size differentials | Industry and firm size differentials | Compensating differentials | Compensating differentials | Discrimination and Differentials by Race and Gender | Discrimination and Differentials by Race and Gender | Changes in the Wage Structure and Inequality | Changes in the Wage Structure and Inequality | Worker Motivation and Behavior | Worker Motivation and Behavior | Social Dimensions of the Labor Force | Social Dimensions of the Labor Force | Social class | Social class | Social capital | Social capital | Immigration | Immigration | Quasi-unions in the New Labor Market | Quasi-unions in the New Labor Market | Labor market regulations in a global economy | Labor market regulations in a global economy

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2.29 Numerical Marine Hydrodynamics (13.024) (MIT) 2.29 Numerical Marine Hydrodynamics (13.024) (MIT)

Description

Includes audio/video content: AV faculty introductions. This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.024. In 2005, ocean engineering subjects became part of Course 2 (Department Includes audio/video content: AV faculty introductions. This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.024. In 2005, ocean engineering subjects became part of Course 2 (Department

Subjects

numerical methods | numerical methods | interpolation | interpolation | differentiation | differentiation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential | partial differential | boundary integral equation panel methods | boundary integral equation panel methods | deterministic and random sea waves | deterministic and random sea waves | Fast Fourier Transforms | Fast Fourier Transforms | finite difference methods | finite difference methods | Integral boundary layer equations | Integral boundary layer equations | numerical lifting surface computations | numerical lifting surface computations | Numerical representation | Numerical representation | numerical solutions | numerical solutions | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | incompressible fluid mechanics | calculus | calculus | complex numbers | complex numbers | root finding | root finding | curve fitting | curve fitting | numerical differentiation | numerical differentiation | numerical errors | numerical errors | panel methods | panel methods | oscillating rigid objects | oscillating rigid objects

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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

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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

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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

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13.024 Numerical Marine Hydrodynamics (MIT) 13.024 Numerical Marine Hydrodynamics (MIT)

Description

This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.Technical RequirementMATLAB® software is required to run the .m files found on this course site. The .FIN and .OUT are simply data offest tables. They can be viewed with any text reader. RealOne™ This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.Technical RequirementMATLAB® software is required to run the .m files found on this course site. The .FIN and .OUT are simply data offest tables. They can be viewed with any text reader. RealOne™

Subjects

numerical methods | numerical methods | interpolation | interpolation | differentiation | differentiation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential | partial differential | boundary integral equation panel methods | boundary integral equation panel methods | deterministic and random sea waves | deterministic and random sea waves | Fast Fourier Transforms | Fast Fourier Transforms | finite difference methods | finite difference methods | Integral boundary layer equations | Integral boundary layer equations | numerical lifting surface computations | numerical lifting surface computations | Numerical representation | Numerical representation | numerical solutions | numerical solutions | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | incompressible fluid mechanics | calculus | calculus | complex numbers | complex numbers | root finding | root finding | curve fitting | curve fitting | numerical differentiation | numerical differentiation | numerical errors | numerical errors | panel methods | panel methods | oscillating rigid objects | oscillating rigid objects | 2.29 | 2.29

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14.662 Labor Economics II (MIT) 14.662 Labor Economics II (MIT)

Description

This is the second of a two-part sequence of courses in labor economics. The course sequence is also open to qualified students in related fields and classes may be taken individually or out of sequence. This part of the sequence is principally concerned with issues relating to the determinants of the wage and salary distribution. The first half is organized around topics in wage determination, which are of particular interest for current research and policy and culminates with a focus on recent debates about the increasing dispersion of wage and salary income. The second half of the course is focused on labor market institutions and technological changes, and relates the debate about the income distribution to other major changes in the structure and texture of advanced industrial societi This is the second of a two-part sequence of courses in labor economics. The course sequence is also open to qualified students in related fields and classes may be taken individually or out of sequence. This part of the sequence is principally concerned with issues relating to the determinants of the wage and salary distribution. The first half is organized around topics in wage determination, which are of particular interest for current research and policy and culminates with a focus on recent debates about the increasing dispersion of wage and salary income. The second half of the course is focused on labor market institutions and technological changes, and relates the debate about the income distribution to other major changes in the structure and texture of advanced industrial societi

Subjects

labor | labor | economics | economics | trade unions | trade unions | wage differentials | wage differentials | international trade | international trade | wage and salary distribution | wage and salary distribution | wage determination | wage determination | increasing dispersion of wage and salary income | increasing dispersion of wage and salary income | labor market institutions | labor market institutions | technological changes | technological changes | income distribution | income distribution | United States and other advanced industrial countries | United States and other advanced industrial countries | moral hazard and agency | moral hazard and agency | Static single agent models | Static single agent models | Intrinsic motivation | Intrinsic motivation | Multiple tasks | Multiple tasks | Multiple agents | Multiple agents | Dynamic agency | Dynamic agency | Efficiency wages | Efficiency wages | Employer Wage Differentials | Employer Wage Differentials | Industry and firm size differentials | Industry and firm size differentials | Compensating differentials | Compensating differentials | Discrimination and Differentials by Race and Gender | Discrimination and Differentials by Race and Gender | Changes in the Wage Structure and Inequality | Changes in the Wage Structure and Inequality | Worker Motivation and Behavior | Worker Motivation and Behavior | Social Dimensions of the Labor Force | Social Dimensions of the Labor Force | Social class | Social class | Social capital | Social capital | Immigration | Immigration | Quasi-unions in the New Labor Market | Quasi-unions in the New Labor Market | Labor market regulations in a global economy | Labor market regulations in a global economy

License

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16.920J Numerical Methods for Partial Differential Equations (SMA 5212) (MIT) 16.920J Numerical Methods for Partial Differential Equations (SMA 5212) (MIT)

Description

A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations). A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations).

Subjects

numerical methods | numerical methods | differential equations | differential equations | linear | linear | nonlinear | nonlinear | elliptic | elliptic | parabolic | parabolic | hyperbolic | hyperbolic | partial differential equations | partial differential equations | integral equations | integral equations | mathematical formulations | mathematical formulations | mathematics | mathematics | finite difference | finite difference | finite volume | finite volume | discretisation | discretisation | finite element | finite element | boundary element | boundary element | iteration | iteration | 16.920 | 16.920 | 2.097 | 2.097 | 6.339 | 6.339

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18.152 Introduction to Partial Differential Equations (MIT) 18.152 Introduction to Partial Differential Equations (MIT)

Description

This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications. This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

Subjects

diffusion | diffusion | elliptic | elliptic | hyperbolic | hyperbolic | partial differential equation | partial differential equation | Initial and boundary value problems for ordinary differential equations | Initial and boundary value problems for ordinary differential equations | Sturm-Liouville theory and eigenfunction expansions | Sturm-Liouville theory and eigenfunction expansions | initial value problems | initial value problems | wave equation;heat equation | wave equation;heat equation | Dirichlet problem | Dirichlet problem | Laplace operator and potential theory | Laplace operator and potential theory | Black-Scholes equation | Black-Scholes equation | water waves | water waves | scalar conservation laws | scalar conservation laws | first order equations | first order equations

License

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18.06 Linear Algebra (MIT) 18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

Subjects

Generalized spaces | Generalized spaces | Linear algebra | Linear algebra | Algebra | Universal | Algebra | Universal | Mathematical analysis | Mathematical analysis | Calculus of operations | Calculus of operations | Line geometry | Line geometry | Topology | Topology | matrix theory | matrix theory | systems of equations | systems of equations | vector spaces | vector spaces | systems determinants | systems determinants | eigen values | eigen values | positive definite matrices | positive definite matrices | Markov processes | Markov processes | Fourier transforms | Fourier transforms | differential equations | differential equations | linear algebra | linear algebra | determinants | determinants | eigenvalues | eigenvalues | similarity | similarity | least-squares approximations | least-squares approximations | stability of differential equations | stability of differential equations | networks | networks

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18.086 Mathematical Methods for Engineers II (MIT) 18.086 Mathematical Methods for Engineers II (MIT)

Description

Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization. Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.

Subjects

Scientific computing: Fast Fourier Transform | Scientific computing: Fast Fourier Transform | finite differences | finite differences | finite elements | finite elements | spectral method | spectral method | numerical linear algebra | numerical linear algebra | Complex variables and applications | Complex variables and applications | Initial-value problems: stability or chaos in ordinary differential equations | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | wave equation versus heat equation | conservation laws and shocks | conservation laws and shocks | dissipation and dispersion | dissipation and dispersion | Optimization: network flows | Optimization: network flows | linear programming | linear programming | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Optimization: network flows | linear programming | Optimization: network flows | linear programming

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18.075 Advanced Calculus for Engineers (MIT) 18.075 Advanced Calculus for Engineers (MIT)

Description

This course analyzes the functions of a complex variable and the calculus of residues. It also covers subjects such as ordinary differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory. This course analyzes the functions of a complex variable and the calculus of residues. It also covers subjects such as ordinary differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory.

Subjects

Functions of complex variable | Functions of complex variable | calculus of residues | calculus of residues | Ordinary differential equations | Ordinary differential equations | Bessel and Legendre functions | Bessel and Legendre functions | Sturm-Liouville theory | Sturm-Liouville theory | partial differential equations | partial differential equations

License

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18.305 Advanced Analytic Methods in Science and Engineering (MIT) 18.305 Advanced Analytic Methods in Science and Engineering (MIT)

Description

Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own. Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own.

Subjects

elementary methods complex analysis | elementary methods complex analysis | ordinary differential equations | ordinary differential equations | partial differential equations | partial differential equations | expansions around regular irregular singular points | expansions around regular irregular singular points | asymptotic evaluation integrals | asymptotic evaluation integrals | regular perturbations | regular perturbations | WKB method | WKB method | multiple scale method | multiple scale method | boundary-layer techniques. | boundary-layer techniques. | asymptotic evaluation integrals | regular perturbations | asymptotic evaluation integrals | regular perturbations | boundary-layer techniques | boundary-layer techniques

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18.156 Differential Analysis (MIT)

Description

The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear partial differential equations. It is the second semester of a two-semester, graduate-level sequence on Differential Analysis.

Subjects

Sobolev spaces | Fredholm alternative | Variable coefficient elliptic | parabolic and hyperbolic linear partial differential equations | Variational methods | Viscosity solutions of fully nonlinear partial differential equations | Schauder theory | Holder estimates | linear equations | second derivatives | elliptic | parabolic | nonlinear partial differential equations | linear partial differential equations | harmonic functions | elliptic equations | parabolic equations

License

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2.29 Numerical Fluid Mechanics (MIT) 2.29 Numerical Fluid Mechanics (MIT)

Description

This course introduces students to MATLAB®. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods. This course introduces students to MATLAB®. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods.

Subjects

numerical methods | numerical methods | interpolation | interpolation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | finite difference methods | finite difference methods | boundary integral equation panel methods | boundary integral equation panel methods | numerical lifting surface computations | numerical lifting surface computations | Fast Fourier Transforms | Fast Fourier Transforms | Numerical representation | Numerical representation | deterministic and random sea waves | deterministic and random sea waves | Integral boundary layer equations | Integral boundary layer equations | numerical solutions | numerical solutions

License

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2.087 Engineering Math: Differential Equations and Linear Algebra (MIT) 2.087 Engineering Math: Differential Equations and Linear Algebra (MIT)

Description

Includes audio/video content: AV selected lectures. This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations. Includes audio/video content: AV selected lectures. This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations.

Subjects

differential equations | differential equations | linear algebra | linear algebra | linear differential equations | linear differential equations | ordinary | ordinary | partial | partial | vector space | vector space | first order | first order | second order | second order | Heaviside | Heaviside | delta | delta | Dirac | Dirac | exponential | exponential | sinusoid | sinusoid | real | real | complex | complex | forced oscillations | forced oscillations | Laplace transform | Laplace transform | graph | graph | nonlinear | nonlinear | source | source | sink | sink | saddle | saddle | spiral | spiral | Euler | Euler | linearization | linearization | Guassian | Guassian | matrix | matrix | mechanical engineer | mechanical engineer | eigenvector | eigenvector | eigenvalue | eigenvalue | exponentiation | exponentiation | least squares | least squares

License

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2.04A Systems and Controls (MIT) 2.04A Systems and Controls (MIT)

Description

This course provides an introduction to linear systems, transfer functions, and Laplace transforms. It covers stability and feedback, and provides basic design tools for specifications of transient response. It also briefly covers frequency-domain techniques.   This course provides an introduction to linear systems, transfer functions, and Laplace transforms. It covers stability and feedback, and provides basic design tools for specifications of transient response. It also briefly covers frequency-domain techniques.  

Subjects

systems | systems | controls | controls | ordinary differential equations | ordinary differential equations | ODEs | ODEs | differential equations | differential equations | Laplace | Laplace | transfer function | transfer function | flywheel | flywheel | circuits | circuits | impedance | impedance | feedback | feedback | root locus | root locus | linear systems | linear systems | Laplace transforms | Laplace transforms | stability | stability | frequency-domain | frequency-domain | skyscaper | skyscaper

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.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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6.243J Dynamics of Nonlinear Systems (MIT) 6.243J Dynamics of Nonlinear Systems (MIT)

Description

This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems. This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

Subjects

nonlinear systems | nonlinear systems | deterministic dynamical systems | deterministic dynamical systems | ordinary differential equations | ordinary differential equations | planar autonomous systems | planar autonomous systems | Picard iteration | Picard iteration | contraction mapping theorem | contraction mapping theorem | Bellman-Gronwall lemma | Bellman-Gronwall lemma | Lyapunov methods | Lyapunov methods | feedback linearization | feedback linearization | nonlinear circuits | nonlinear circuits | control systems | control systems | local controllability | local controllability | volume evolution | volume evolution | system analysis | system analysis | singular perturbations | singular perturbations | averaging | averaging | local behavior | local behavior | trajectories | trajectories | equilibria | equilibria | storage functions | storage functions | stability analysis | stability analysis | continuity | continuity | differential equations | differential equations | system models | system models | parameters | parameters | input/output | input/output | state-space | state-space | 16.337 | 16.337

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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

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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

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13.024 Numerical Marine Hydrodynamics (MIT)

Description

This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.Technical RequirementMATLAB® software is required to run the .m files found on this course site. The .FIN and .OUT are simply data offest tables. They can be viewed with any text reader. RealOne™

Subjects

numerical methods | interpolation | differentiation | integration | systems of linear equations | differential equations | numerical integration | partial differential | boundary integral equation panel methods | deterministic and random sea waves | Fast Fourier Transforms | finite difference methods | Integral boundary layer equations | numerical lifting surface computations | Numerical representation | numerical solutions | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | calculus | complex numbers | root finding | curve fitting | numerical differentiation | numerical errors | panel methods | oscillating rigid objects | 2.29

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2.29 Numerical Marine Hydrodynamics (13.024) (MIT)

Description

This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.024. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumber

Subjects

numerical methods | interpolation | differentiation | integration | systems of linear equations | differential equations | numerical integration | partial differential | boundary integral equation panel methods | deterministic and random sea waves | Fast Fourier Transforms | finite difference methods | Integral boundary layer equations | numerical lifting surface computations | Numerical representation | numerical solutions | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | calculus | complex numbers | root finding | curve fitting | numerical differentiation | numerical errors | panel methods | oscillating rigid objects

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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