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7.342 Developmental and Molecular Biology of Regeneration (MIT) 7.342 Developmental and Molecular Biology of Regeneration (MIT)

Description

How does a regenerating animal "know" what's missing? How are stem cells or differentiated cells used to create new tissues during regeneration? In this class we will take a comparative approach to explore this fascinating problem by critically examining classic and modern scientific literature about the developmental and molecular biology of regeneration. We will learn about conserved developmental pathways that are necessary for regeneration, and we will discuss the relevance of these findings for regenerative medicine. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highl How does a regenerating animal "know" what's missing? How are stem cells or differentiated cells used to create new tissues during regeneration? In this class we will take a comparative approach to explore this fascinating problem by critically examining classic and modern scientific literature about the developmental and molecular biology of regeneration. We will learn about conserved developmental pathways that are necessary for regeneration, and we will discuss the relevance of these findings for regenerative medicine. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highl

Subjects

Regeneration | Regeneration | blastema | blastema | embryo | embryo | progenitor | progenitor | stem cells | stem cells | differentiation | differentiation | dedifferentiation | dedifferentiation | hydra | hydra | morphallaxis | morphallaxis | limb | limb | organ | organ | zebrafish | zebrafish | homeostasis | homeostasis | self-renewal | self-renewal | regenerative medicine | regenerative medicine | differentitate | differentitate | regulate | regulate | salamander | salamander | catenin | catenin | newt | newt | liver | liver | pluriptent | pluriptent | fibroblast | fibroblast

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18.01 Single Variable Calculus (MIT) 18.01 Single Variable Calculus (MIT)

Description

Includes audio/video content: AV lectures. This introductory calculus course covers differentiation and integration of functions of one variable, with applications. Includes audio/video content: AV lectures. This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

Subjects

differentiation and integration of functions of one variable | differentiation and integration of functions of one variable | limits | limits | continuity | continuity | differentiation rules | differentiation rules | extremum problems | extremum problems | definite and indefinite integration | definite and indefinite integration | fundamental theorem of calculus | fundamental theorem of calculus | elementary | elementary | techniques of integration | techniques of integration | approximation of definite integrals | approximation of definite integrals | improper integrals | improper integrals | l'H?pital's rule | l'H?pital's rule

License

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18.01 Single Variable Calculus (MIT) 18.01 Single Variable Calculus (MIT)

Description

This introductory calculus course covers differentiation and integration of functions of one variable, with applications. This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

Subjects

differentiation and integration of functions of one variable | differentiation and integration of functions of one variable | limits | limits | continuity | continuity | differentiation rules | differentiation rules | extremum problems | extremum problems | definite and indefinite integration | definite and indefinite integration | fundamental theorem of calculus | fundamental theorem of calculus | elementary | elementary | techniques of integration | techniques of integration | approximation of definite integrals | approximation of definite integrals | improper integrals | improper integrals | l'H?pital's rule | l'H?pital's rule

License

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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

License

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18.01 Single Variable Calculus (MIT) 18.01 Single Variable Calculus (MIT)

Description

This introductory Calculus course covers differentiation and integration of functions of one variable, with applications. Topics include:Concepts of function, limits, and continuityDifferentiation rules, application to graphing, rates, approximations, and extremum problemsDefinite and indefinite integrationFundamental theorem of calculusApplications of integration to geometry and scienceElementary functionsTechniques of integrationApproximation of definite integrals, improper integrals, and L'Hôpital's rule MATLAB® is a trademark of The MathWorks, Inc. This introductory Calculus course covers differentiation and integration of functions of one variable, with applications. Topics include:Concepts of function, limits, and continuityDifferentiation rules, application to graphing, rates, approximations, and extremum problemsDefinite and indefinite integrationFundamental theorem of calculusApplications of integration to geometry and scienceElementary functionsTechniques of integrationApproximation of definite integrals, improper integrals, and L'Hôpital's rule MATLAB® is a trademark of The MathWorks, Inc.

Subjects

differentiation and integration of functions of one variable | differentiation and integration of functions of one variable | limits | limits | continuity | continuity | differentiation rules | differentiation rules | extremum problems | extremum problems | definite and indefinite integration | definite and indefinite integration | fundamental theorem of calculus | fundamental theorem of calculus | elementary | elementary | techniques of integration | techniques of integration | approximation of definite integrals | approximation of definite integrals | improper integrals | improper integrals | l'H?pital's rule | l'H?pital's rule | single variable calculus | single variable calculus | mathematical applications | mathematical applications | function | function | graphing | graphing | rates | rates | approximations | approximations | definite integration | definite integration | indefinite integration | indefinite integration | geometry | geometry | science | science | elementary functions | elementary functions | definite integrals | definite integrals

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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18.01SC Single Variable Calculus (MIT) 18.01SC Single Variable Calculus (MIT)

Description

Includes audio/video content: AV lectures. This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics. Includes audio/video content: AV lectures. This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.

Subjects

differentiation of functions | differentiation of functions | integration of functions | integration of functions | limits | limits | continuity | continuity | differentiation rules | differentiation rules | extremum problems | extremum problems | definite integration | definite integration | indefinite integration | indefinite integration | fundamental theorem of calculus | fundamental theorem of calculus | techniques of integration | techniques of integration | approximation of definite integrals | approximation of definite integrals | improper integrals | improper integrals | l'Hôpital's rule | l'Hôpital's rule

License

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7.349 Stem Cells: A Cure or Disease? (MIT) 7.349 Stem Cells: A Cure or Disease? (MIT)

Description

Have you ever considered going to a pharmacy to order some new cardiomyocytes (heart muscle cells) for your ailing heart? It might sound crazy, but recent developments in stem cell science have made this concept not so futuristic. In this course, we will explore the underlying biology behind the idea of using stem cells to treat disease, specifically analyzing the mechanisms that enable a single genome to encode multiple cell states ranging from neurons to fibroblasts to T cells. Overall, we hope to provide a comprehensive overview of this exciting new field of research and its clinical relevance. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literat Have you ever considered going to a pharmacy to order some new cardiomyocytes (heart muscle cells) for your ailing heart? It might sound crazy, but recent developments in stem cell science have made this concept not so futuristic. In this course, we will explore the underlying biology behind the idea of using stem cells to treat disease, specifically analyzing the mechanisms that enable a single genome to encode multiple cell states ranging from neurons to fibroblasts to T cells. Overall, we hope to provide a comprehensive overview of this exciting new field of research and its clinical relevance. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literat

Subjects

stem cells | stem cells | stem cell therapy | stem cell therapy | cellular reprogramming | cellular reprogramming | transdifferentiation | transdifferentiation | pluripotency | pluripotency | epigenetics | epigenetics | genome-wide sequencing | genome-wide sequencing | transcription-mediated reprogramming | transcription-mediated reprogramming | embryonic stem cell technology | embryonic stem cell technology | transcription factors | transcription factors | chromatin structure | chromatin structure | H3K4me3 | H3K4me3 | H3K27me3 | H3K27me3 | histone deacetylase 1 | histone deacetylase 1 | RNAi screens | RNAi screens | Oct4 | Oct4 | cloning | cloning | Dolly | Dolly | in vitro differentiation | in vitro differentiation | regenerative medicine | regenerative medicine

License

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17.042 Citizenship and Pluralism (MIT) 17.042 Citizenship and Pluralism (MIT)

Description

This course will serve as both an introduction to contemporary political philosophy and a way to explore issues of pluralism and multiculturalism. Racial and ethnic groups, national minorities, aboriginals, women, sexual minorities, and other groups have organized to highlight injustice and demand recognition and accommodation on the basis of their differences. In practice, democratic states have granted a variety of group-differentiated rights, such as exemptions from generally applicable laws, special representation rights, language rights, or limited self-government rights, to different types of groups. This course will examine how different theories of citizenship address the challenges raised by different forms of pluralism. We will focus in particular on the following questions: Do This course will serve as both an introduction to contemporary political philosophy and a way to explore issues of pluralism and multiculturalism. Racial and ethnic groups, national minorities, aboriginals, women, sexual minorities, and other groups have organized to highlight injustice and demand recognition and accommodation on the basis of their differences. In practice, democratic states have granted a variety of group-differentiated rights, such as exemptions from generally applicable laws, special representation rights, language rights, or limited self-government rights, to different types of groups. This course will examine how different theories of citizenship address the challenges raised by different forms of pluralism. We will focus in particular on the following questions: Do

Subjects

citizenship | citizenship | ethnicity | ethnicity | identity | identity | democracy | democracy | nations | nations | politics | politics | class differentiation | class differentiation | pluralism | pluralism | national unity | national unity | contemporary | contemporary | political | political | philosophy | philosophy | multiculturalism | multiculturalism | racial | racial | ethnic | ethnic | groups | groups | national | national | minorities | minorities | aboriginals | aboriginals | women | women | sexual | sexual | injustice | injustice | recognition | recognition | accommodation | accommodation | democratic | democratic | states | states | group-differentiated | group-differentiated | rights | rights | exemptions | exemptions | laws | laws | representation | representation | language | language | limited | limited | self-government | self-government | theories | theories | justice | justice | conflict | conflict | liberalequality | liberalequality | citizens | citizens | multi-religious | multi-religious | multicultural | multicultural | society | society | diversity | diversity | communitarian | communitarian | civic | civic | republican | republican | cosmopolitan | cosmopolitan | pluralist | pluralist | radical | radical | postmodern | postmodern | American | American | gender | gender | class | class | differentiation | differentiation | liberal | liberal | equality | equality | unity | unity

License

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18.01 Single Variable Calculus (MIT)

Description

This introductory Calculus course covers differentiation and integration of functions of one variable, with applications. Topics include:Concepts of function, limits, and continuityDifferentiation rules, application to graphing, rates, approximations, and extremum problemsDefinite and indefinite integrationFundamental theorem of calculusApplications of integration to geometry and scienceElementary functionsTechniques of integrationApproximation of definite integrals, improper integrals, and L'Hôpital's rule MATLAB® is a trademark of The MathWorks, Inc.

Subjects

differentiation and integration of functions of one variable | limits | continuity | differentiation rules | extremum problems | definite and indefinite integration | fundamental theorem of calculus | elementary | techniques of integration | approximation of definite integrals | improper integrals | l'H?pital's rule | single variable calculus | mathematical applications | function | graphing | rates | approximations | definite integration | indefinite integration | geometry | science | elementary functions | definite integrals

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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14.27 Economics and E-commerce (MIT) 14.27 Economics and E-commerce (MIT)

Description

This course uses theoretical models and studies of "old economy" industries to help understand the growth and future of electronic commerce. We will begin with a discussion of relevant topics from industrial organization including monopoly pricing, price discrimination, product differentiation, barriers to entry, network externalities, search and first-mover advantages. The largest part of the course will be a discussion of a number of e-industries. In this section we'll discuss extensions and applications of the ideas from the first part of the course, draw analogies to previous technological revolutions and read current case studies. Finally, we'll discuss two additional topics: bubbles in asset markets and the macroeconomic effects of the Internet. This course uses theoretical models and studies of "old economy" industries to help understand the growth and future of electronic commerce. We will begin with a discussion of relevant topics from industrial organization including monopoly pricing, price discrimination, product differentiation, barriers to entry, network externalities, search and first-mover advantages. The largest part of the course will be a discussion of a number of e-industries. In this section we'll discuss extensions and applications of the ideas from the first part of the course, draw analogies to previous technological revolutions and read current case studies. Finally, we'll discuss two additional topics: bubbles in asset markets and the macroeconomic effects of the Internet.

Subjects

industrial organization | industrial organization | monopoly pricing | monopoly pricing | price discrimination | price discrimination | product differentiation | product differentiation | barriers to entry | barriers to entry | network externalities | network externalities | first-mover advantages | first-mover advantages | E-commerce | E-commerce | Cybercommerce | Cybercommerce | E-business | E-business

License

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7.344 The Fountain of Life: From Dolly to Customized Embryonic Stem Cells (MIT) 7.344 The Fountain of Life: From Dolly to Customized Embryonic Stem Cells (MIT)

Description

During development, the genetic content of each cell remains, with a few exceptions, identical to that of the zygote. Most differentiated cells therefore retain all of the genetic information necessary to generate an entire organism. It was through pioneering technology of somatic cell nuclear transfer (SCNT) that this concept was experimentally proven. Only 10 years ago the sheep Dolly was the first mammal to be cloned from an adult organism, demonstrating that the differentiated state of a mammalian cell can be fully reversible to a pluripotent embryonic state. A key conclusion from these experiments was that the difference between pluripotent cells such as embryonic stem (ES) cells and unipotent differentiated cells is solely a consequence of reversible changes. These changes, which hav During development, the genetic content of each cell remains, with a few exceptions, identical to that of the zygote. Most differentiated cells therefore retain all of the genetic information necessary to generate an entire organism. It was through pioneering technology of somatic cell nuclear transfer (SCNT) that this concept was experimentally proven. Only 10 years ago the sheep Dolly was the first mammal to be cloned from an adult organism, demonstrating that the differentiated state of a mammalian cell can be fully reversible to a pluripotent embryonic state. A key conclusion from these experiments was that the difference between pluripotent cells such as embryonic stem (ES) cells and unipotent differentiated cells is solely a consequence of reversible changes. These changes, which hav

Subjects

embryonic stem cells | embryonic stem cells | stem cells | stem cells | cells | cells | genetics | genetics | genome | genome | Dolly | Dolly | clone | clone | regenerative therapy | regenerative therapy | somatic | somatic | SCNT | SCNT | pluripotent | pluripotent | scientific literature | scientific literature | nuclear | nuclear | embryonic | embryonic | adult | adult | epigenetics | epigenetics | methylation | methylation | DNA | DNA | histone | histone | biomedical | biomedical | differentiation | differentiation | epigenome | epigenome | nuclear transfer | nuclear transfer | customized | customized | zygote | zygote | RNA | RNA | cancer | cancer | medicine | medicine

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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7.342 Reading the Blueprint of Life: Transcription, Stem Cells and Differentiation (MIT) 7.342 Reading the Blueprint of Life: Transcription, Stem Cells and Differentiation (MIT)

Description

In this course, we will address how transcriptional regulators both prohibit and drive differentiation during the course of development. How does a stem cell know when to remain a stem cell and when to become a specific cell type? Are there global differences in the way the genome is read in multipotent and terminally differentiated cells? We will explore how stem cell pluripotency is preserved, how master regulators of cell-fate decisions execute developmental programs, and how chromatin regulators control undifferentiated versus differentiated states. Additionally, we will discuss how aberrant regulation of transcriptional regulators produces disorders such as developmental defects and cancer.This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at In this course, we will address how transcriptional regulators both prohibit and drive differentiation during the course of development. How does a stem cell know when to remain a stem cell and when to become a specific cell type? Are there global differences in the way the genome is read in multipotent and terminally differentiated cells? We will explore how stem cell pluripotency is preserved, how master regulators of cell-fate decisions execute developmental programs, and how chromatin regulators control undifferentiated versus differentiated states. Additionally, we will discuss how aberrant regulation of transcriptional regulators produces disorders such as developmental defects and cancer.This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at

Subjects

blueprint of life | blueprint of life | transcription | transcription | stem cells | stem cells | differentiation | differentiation | human tissues | human tissues | tissue regeneration | tissue regeneration | human disease | human disease | RNA and protein expression patterns | RNA and protein expression patterns | transcriptional regulation | transcriptional regulation | specialized gene expression programs | specialized gene expression programs | genome | genome | multipotent | multipotent | terminally differentiated | terminally differentiated | pluripotency | pluripotency | master regulators | master regulators | chromatin regulators | chromatin regulators | developmental defects | developmental defects | cancer | cancer

License

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Describing motion along a line Describing motion along a line

Description

Motion is vital to life, and to science. This free course, Describing motion along a line, will help you to understand why classical motion is probably the most fundamental part of physics. You will examine motion along a line and the ways in which such motion can be represented, through the use of graphs, equations and differential calculus. First published on Wed, 16 Mar 2016 as Describing motion along a line. To find out more visit The Open University's Openlearn website. Creative-Commons 2016 Motion is vital to life, and to science. This free course, Describing motion along a line, will help you to understand why classical motion is probably the most fundamental part of physics. You will examine motion along a line and the ways in which such motion can be represented, through the use of graphs, equations and differential calculus. First published on Wed, 16 Mar 2016 as Describing motion along a line. To find out more visit The Open University's Openlearn website. Creative-Commons 2016

Subjects

Physics and Astronomy | Physics and Astronomy | charts | charts | Monty Don | Monty Don | Airport Live | Airport Live | time | time | velocity | velocity | acceleration | acceleration | laws | laws | displacement | displacement | drones | drones | gravity | gravity | economic crisis | economic crisis | limits | limits | differentiation | differentiation | S207_2 | S207_2

License

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence Licensed under a Creative Commons Attribution - NonCommercial-ShareAlike 2.0 Licence - see http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ - Original copyright The Open University

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18.100A Introduction to Analysis (MIT) 18.100A Introduction to Analysis (MIT)

Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla

Subjects

mathematical analysis | mathematical analysis | estimations | estimations | limit of a sequence | limit of a sequence | limit theorems | limit theorems | subsequences | subsequences | cluster points | cluster points | infinite series | infinite series | power series | power series | local and global properties | local and global properties | continuity | continuity | intermediate-value theorem | intermediate-value theorem | convexity | convexity | integrability | integrability | Riemann integral | Riemann integral | calculus | calculus | convergence | convergence | Gamma function | Gamma function | Stirling | Stirling | quantifiers and negation | quantifiers and negation | Leibniz | Leibniz | Fubini | Fubini | improper integrals | improper integrals | Lebesgue integral | Lebesgue integral | mathematical proofs | mathematical proofs | differentiation | differentiation | integration | integration

License

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18.024 Multivariable Calculus with Theory (MIT) 18.024 Multivariable Calculus with Theory (MIT)

Description

This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus. This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

Subjects

linear algebra | linear algebra | vector integral calculus | vector integral calculus | Calculus of several variables | Calculus of several variables | Vector algebra in 3-space | Vector algebra in 3-space | determinants | determinants | matrices | matrices | Vector-valued functions of one variable | Vector-valued functions of one variable | space motion | space motion | Scalar functions of several variables | Scalar functions of several variables | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | Double integrals and line integrals in the plane | Double integrals and line integrals in the plane | exact differentials and conservative fields | exact differentials and conservative fields | Green's theorem and applications | Green's theorem and applications | triple integrals | triple integrals | line and surface integrals in space | line and surface integrals in space | Divergence theorem | Divergence theorem | Stokes' theorem | Stokes' theorem | applications | applications

License

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7.342 Cancer Biology: From Basic Research to the Clinic (MIT) 7.342 Cancer Biology: From Basic Research to the Clinic (MIT)

Description

This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highly interactive setting. In 1971, President Nixon declared the "War on Cancer," but after three decades the war is still raging. How much progress have we made toward winning the war and what are we doing to improve the fight? Understanding the molecular and cellular events involved in tumor formation, progression, and metastasis is crucial to the development of innovative therapy for cancer patients. Insights into these processes have been gleaned through basic research using biochemical, molecular, and genetic ana This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highly interactive setting. In 1971, President Nixon declared the "War on Cancer," but after three decades the war is still raging. How much progress have we made toward winning the war and what are we doing to improve the fight? Understanding the molecular and cellular events involved in tumor formation, progression, and metastasis is crucial to the development of innovative therapy for cancer patients. Insights into these processes have been gleaned through basic research using biochemical, molecular, and genetic ana

Subjects

cancer | cancer | tumor | tumor | metastasis | metastasis | genetic analysis | genetic analysis | cancer biology | cancer biology | model organisms | model organisms | genetic pathways | genetic pathways | uncontrolled growth | uncontrolled growth | tumor suppressor genes | tumor suppressor genes | oncogenes | oncogenes | tumor initiation | tumor initiation | cell cycle | cell cycle | chromosomal aberration | chromosomal aberration | apoptosis | apoptosis | cell death | cell death | signal transduction pathways | signal transduction pathways | proto-oncogene | proto-oncogene | mutation | mutation | DNA mismatch repair | DNA mismatch repair | telomeres | telomeres | mouse models | mouse models | tissue specificity | tissue specificity | malignancy | malignancy | stem cells | stem cells | therapeutic resistance | therapeutic resistance | differentiation | differentiation | caner research | caner research | cancer therapeutics | cancer therapeutics | chemotherapy | chemotherapy

License

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18.022 Calculus of Several Variables (MIT) 18.022 Calculus of Several Variables (MIT)

Description

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts. This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.

Subjects

vector algebra | vector algebra | determinant | determinant | matrix | matrix | matrices | matrices | vector-valued functions | vector-valued functions | space motion | space motion | scalar functions | scalar functions | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | double integrals | double integrals | line integrals | line integrals | exact differentials | exact differentials | conservative fields | conservative fields | Green's theorem | Green's theorem | triple integrals | triple integrals | surface integrals | surface integrals | divergence theorem | divergence theorem | Stokes' theorem | Stokes' theorem | geometry | geometry | vector fields | vector fields | linear algebra | linear algebra

License

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18.02 Multivariable Calculus (MIT) 18.02 Multivariable Calculus (MIT)

Description

Includes audio/video content: AV lectures. This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates. Includes audio/video content: AV lectures. This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.

Subjects

calculus | calculus | calculus of several variables | calculus of several variables | vector algebra | vector algebra | determinants | determinants | matrix | matrix | matrices | matrices | vector-valued function | vector-valued function | space motion | space motion | scalar function | scalar function | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | double integrals | double integrals | line integrals | line integrals | exact differential | exact differential | conservative fields | conservative fields | Green's theorem | Green's theorem | triple integrals | triple integrals | surface integrals | surface integrals | divergence theorem Stokes' theorem | divergence theorem Stokes' theorem | applications | applications

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

License

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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

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18.01SC Single Variable Calculus (MIT)

Description

This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.

Subjects

differentiation of functions | integration of functions | limits | continuity | differentiation rules | extremum problems | definite integration | indefinite integration | fundamental theorem of calculus | techniques of integration | approximation of definite integrals | improper integrals | pital's rule

License

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18.098 Street-Fighting Mathematics (MIT) 18.098 Street-Fighting Mathematics (MIT)

Description

This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month. This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

Subjects

extreme-cases reasoning | extreme-cases reasoning | dimensional analysis | dimensional analysis | discretization | discretization | drag | drag | fluid mechanics | fluid mechanics | pendulum | pendulum | pictorial proofs | pictorial proofs | analogy | analogy | operators | operators | summation | summation | square roots | square roots | logarithms | logarithms | musical intervals | musical intervals | taking out the big part | taking out the big part | integration | integration | differentiation | differentiation

License

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18.02 Multivariable Calculus (MIT) 18.02 Multivariable Calculus (MIT)

Description

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space. This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space.

Subjects

Calculus | Calculus | calculus of several variables | calculus of several variables | vector algebra | vector algebra | determinants | determinants | matrix | matrix | matrices | matrices | vector-valued function | vector-valued function | space motion | space motion | scalar function | scalar function | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | double integrals | double integrals | line integrals | line integrals | exact differential | exact differential | conservative fields | conservative fields | Green's theorem | Green's theorem | triple integrals | triple integrals | surface integrals | surface integrals | divergence theorem Stokes' theorem | divergence theorem Stokes' theorem | applications | applications

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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14.27 Economics and E-commerce (MIT) 14.27 Economics and E-commerce (MIT)

Description

This course uses theoretical models and studies of "old economy" industries to help understand the growth and future of electronic commerce. We will begin with a discussion of relevant topics from industrial organization including monopoly pricing, price discrimination, product differentiation, barriers to entry, network externalities, search and first-mover advantages. The largest part of the course will be a discussion of a number of e-industries. In this section we'll discuss extensions and applications of the ideas from the first part of the course, draw analogies to previous technological revolutions and read current case studies. Finally, we'll discuss two additional topics: bubbles in asset markets and the macroeconomic effects of the Internet. This course uses theoretical models and studies of "old economy" industries to help understand the growth and future of electronic commerce. We will begin with a discussion of relevant topics from industrial organization including monopoly pricing, price discrimination, product differentiation, barriers to entry, network externalities, search and first-mover advantages. The largest part of the course will be a discussion of a number of e-industries. In this section we'll discuss extensions and applications of the ideas from the first part of the course, draw analogies to previous technological revolutions and read current case studies. Finally, we'll discuss two additional topics: bubbles in asset markets and the macroeconomic effects of the Internet.

Subjects

industrial organization | industrial organization | monopoly pricing | monopoly pricing | price discrimination | price discrimination | product differentiation | product differentiation | barriers to entry | barriers to entry | network externalities | network externalities | first-mover advantages | first-mover advantages | E-commerce | E-commerce | Cybercommerce | Cybercommerce | E-business | E-business

License

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