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8.282J Introduction to Astronomy (MIT) 8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to physics of the solar system, stars, interstellar medium, the galaxy, and universe, as determined from a variety of astronomical observations and models.Topics include: planets, planet formation; stars, the Sun, "normal" stars, star formation; stellar evolution, supernovae, compact objects (white dwarfs, neutron stars, and black holes), plusars, binary X-ray sources; star clusters, globular and open clusters; interstellar medium, gas, dust, magnetic fields, cosmic rays; distance ladder; galaxies, normal and active galaxies, jets; gravitational lensing; large scaling structure; Newtonian cosmology, dynamical expansion and thermal history of the Universe; cosmic microwave background radiation; big-bang nucleosynthesis Introduction to Astronomy provides a quantitative introduction to physics of the solar system, stars, interstellar medium, the galaxy, and universe, as determined from a variety of astronomical observations and models.Topics include: planets, planet formation; stars, the Sun, "normal" stars, star formation; stellar evolution, supernovae, compact objects (white dwarfs, neutron stars, and black holes), plusars, binary X-ray sources; star clusters, globular and open clusters; interstellar medium, gas, dust, magnetic fields, cosmic rays; distance ladder; galaxies, normal and active galaxies, jets; gravitational lensing; large scaling structure; Newtonian cosmology, dynamical expansion and thermal history of the Universe; cosmic microwave background radiation; big-bang nucleosynthesis

Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | solar system | stars | stars | interstellar medium | interstellar medium | the Galaxy | the Galaxy | the Universe | the Universe | planets | planets | planet formation | planet formation | star formation | star formation | stellar evolution | stellar evolution | supernovae | supernovae | compact objects | compact objects | white dwarfs | white dwarfs | neutron stars | neutron stars | black holes | black holes | plusars | binary X-ray sources | plusars | binary X-ray sources | star clusters | star clusters | globular and open clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | distance ladder | galaxies | normal and active galaxies | jets | galaxies | normal and active galaxies | jets | gravitational lensing | gravitational lensing | large scaling structure | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | cosmic microwave background radiation | big-bang nucleosynthesis | big-bang nucleosynthesis | pulsars | pulsars | binary X-ray sources | binary X-ray sources | gas | gas | dust | dust | magnetic fields | magnetic fields | cosmic rays | cosmic rays | galaxy | galaxy | universe | universe | astrophysics | astrophysics | Sun | Sun | supernova | supernova | globular clusters | globular clusters | open clusters | open clusters | jets | jets | Newtonian cosmology | Newtonian cosmology | dynamical expansion | dynamical expansion | thermal history | thermal history | normal galaxies | normal galaxies | active galaxies | active galaxies | Greek astronomy | Greek astronomy | physics | physics | Copernicus | Copernicus | Tycho | Tycho | Kepler | Kepler | Galileo | Galileo | classical mechanics | classical mechanics | circular orbits | circular orbits | full kepler orbit problem | full kepler orbit problem | electromagnetic radiation | electromagnetic radiation | matter | matter | telescopes | telescopes | detectors | detectors | 8.282 | 8.282 | 12.402 | 12.402

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8.282J Introduction to Astronomy (MIT) 8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models. Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models.

Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | solar system | stars | stars | interstellar medium | interstellar medium | the Galaxy | the Galaxy | the Universe | the Universe | planets | planets | planet formation | planet formation | star formation | star formation | stellar evolution | stellar evolution | supernovae | supernovae | compact objects | compact objects | white dwarfs | white dwarfs | neutron stars | neutron stars | black holes | black holes | plusars | binary X-ray sources | plusars | binary X-ray sources | star clusters | star clusters | globular and open clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | distance ladder | galaxies | normal and active galaxies | jets | galaxies | normal and active galaxies | jets | gravitational lensing | gravitational lensing | large scaling structure | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | cosmic microwave background radiation | big-bang nucleosynthesis | big-bang nucleosynthesis | pulsars | pulsars | binary X-ray sources | binary X-ray sources | gas | gas | dust | dust | magnetic fields | magnetic fields | cosmic rays | cosmic rays | galaxy | galaxy | universe | universe | astrophysics | astrophysics | Sun | Sun | supernova | supernova | globular clusters | globular clusters | open clusters | open clusters | jets | jets | Newtonian cosmology | Newtonian cosmology | dynamical expansion | dynamical expansion | thermal history | thermal history | normal galaxies | normal galaxies | active galaxies | active galaxies | Greek astronomy | Greek astronomy | physics | physics | Copernicus | Copernicus | Tycho | Tycho | Kepler | Kepler | Galileo | Galileo | classical mechanics | classical mechanics | circular orbits | circular orbits | full kepler orbit problem | full kepler orbit problem | electromagnetic radiation | electromagnetic radiation | matter | matter | telescopes | telescopes | detectors | detectors | 8.282 | 8.282 | 12.402 | 12.402 | plusars | plusars | galaxies | galaxies | normal and active galaxies | normal and active galaxies | dynamical expansion and thermal history of the Universe | dynamical expansion and thermal history of the Universe

License

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RES.18-007 Calculus Revisited: Multivariable Calculus (MIT) RES.18-007 Calculus Revisited: Multivariable Calculus (MIT)

Description

Includes audio/video content: AV lectures. Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Multivariable Calculus is the second course in the series, consisting of 26 videos, 4 Study Guides, and a set of Supplementary Notes. The series was first released in 1971 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time. Includes audio/video content: AV lectures. Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Multivariable Calculus is the second course in the series, consisting of 26 videos, 4 Study Guides, and a set of Supplementary Notes. The series was first released in 1971 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time.

Subjects

Vector Arithmetic Vector Calculus | Vector Arithmetic Vector Calculus | Partial Derivatives | Partial Derivatives | Matrix Algebra | Matrix Algebra | Multiple Integration | Multiple Integration | Dot Product | Dot Product | Cross Product | Cross Product | Polar Coordinates | Polar Coordinates | Chain Rule | Chain Rule | Maxima and Minima | Maxima and Minima | Green's Theorem | Green's Theorem | Jacobian | Jacobian

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

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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Inclusive education: Knowing what we mean Inclusive education: Knowing what we mean

Description

This free course, Inclusive education: Knowing what we mean, introduces you to the contested area of educational inclusion. You will look at differing perspectives on inclusion, in particular the way that medical and social models have influenced and shaped current thinking. You will also think about barriers to inclusion and the difference between integration and inclusion. In addition, you will consider some of the key documents, such as the Salamanca Statement, that underpin current thinking in this area. First published on Tue, 19 Jul 2011 as Inclusive education: Knowing what we mean. To find out more visit The Open University's Openlearn website. Creative-Commons 2011 This free course, Inclusive education: Knowing what we mean, introduces you to the contested area of educational inclusion. You will look at differing perspectives on inclusion, in particular the way that medical and social models have influenced and shaped current thinking. You will also think about barriers to inclusion and the difference between integration and inclusion. In addition, you will consider some of the key documents, such as the Salamanca Statement, that underpin current thinking in this area. First published on Tue, 19 Jul 2011 as Inclusive education: Knowing what we mean. To find out more visit The Open University's Openlearn website. Creative-Commons 2011

Subjects

Educational Practice | Educational Practice | E848_1 | E848_1

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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18.024 Calculus with Theory II (MIT) 18.024 Calculus with Theory II (MIT)

Description

This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.Topics include: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.Topics include: Calculus of several variables. Vector algebra in 3-space, determinants, matrices. Vector-valued functions of one variable, space motion. Scalar functions of several variables: partial differentiation, gradient, optimization techniques. Double integrals and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor

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: partial differentiation | Scalar functions of several variables: 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

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

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18.014 Calculus with Theory I (MIT) 18.014 Calculus with Theory I (MIT)

Description

18.014, Calculus with Theory, covers the same material as 18.01 (Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus. Topics: Axioms for the real numbers; the Riemann integral; limits, theorems on continuous functions; derivatives of functions of one variable; the fundamental theorems of calculus; Taylor's theorem; infinite series, power series, rigorous treatment of the elementary functions. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor, Natasha Bershadsky, and Alex Retakh for their help with this course web site. 18.014, Calculus with Theory, covers the same material as 18.01 (Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus. Topics: Axioms for the real numbers; the Riemann integral; limits, theorems on continuous functions; derivatives of functions of one variable; the fundamental theorems of calculus; Taylor's theorem; infinite series, power series, rigorous treatment of the elementary functions. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor, Natasha Bershadsky, and Alex Retakh for their help with this course web site.

Subjects

axioms for the real numbers | axioms for the real numbers | the Riemann integral | the Riemann integral | limits | limits | theorems on continuous functions | theorems on continuous functions | derivatives of functions of one variablethe fundamental theorems of calculus | derivatives of functions of one variablethe fundamental theorems of calculus | Taylor's theorem | Taylor's theorem | infinite series | infinite series | power series | power series | rigorous treatment of the elementary functions | rigorous treatment of the elementary functions

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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RES.18.006 Calculus Revisited: Single Variable Calculus (MIT) RES.18.006 Calculus Revisited: Single Variable Calculus (MIT)

Description

Includes audio/video content: AV lectures. Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time. Includes audio/video content: AV lectures. Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time.

Subjects

License

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RES.18-005 Highlights of Calculus (MIT) RES.18-005 Highlights of Calculus (MIT)

Description

Includes audio/video content: AV faculty introductions, AV lectures. Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The series is divided into three sections: Introduction Why Professor Strang created these videos How to use the materials Highlights of Calculus Five videos reviewing the key topics and ideas of calculus Applications to real-life situations and problems Additional summary slides and practice problems Derivatives Twelve videos focused on differential calculus More applications to real-life situations and problems Additional summary sl Includes audio/video content: AV faculty introductions, AV lectures. Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The series is divided into three sections: Introduction Why Professor Strang created these videos How to use the materials Highlights of Calculus Five videos reviewing the key topics and ideas of calculus Applications to real-life situations and problems Additional summary slides and practice problems Derivatives Twelve videos focused on differential calculus More applications to real-life situations and problems Additional summary sl

Subjects

License

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

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18.02 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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18.013A Calculus with Applications (MIT) 18.013A Calculus with Applications (MIT)

Description

This is an undergraduate course on differential calculus in one and several dimensions. It is intended as a one and a half term course in calculus for students who have studied calculus in high school. The format allows it to be entirely self contained, so that it is possible to follow it without any background in calculus. This is an undergraduate course on differential calculus in one and several dimensions. It is intended as a one and a half term course in calculus for students who have studied calculus in high school. The format allows it to be entirely self contained, so that it is possible to follow it without any background in calculus.

Subjects

vector algebra | vector algebra | taylor series | taylor series | numerical methods | numerical methods | differential calculus | differential calculus | 18.013 | 18.013

License

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RES.18-001 Calculus Online Textbook (MIT) RES.18-001 Calculus Online Textbook (MIT)

Description

Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.  In addition to the Textbook, there is also an online Instructor's Manual and a student Study Guide. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.The 2010 second edition of the Calculus textbook includes a new chapter on "Highlights of Calculus" that connects to the video series of the same name.  The new chapter has summaries and practice questions for all of the videos.  It also introduces The Exponential Function (e^x) as presented in Prof. Strang's video on this to Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.  In addition to the Textbook, there is also an online Instructor's Manual and a student Study Guide. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.The 2010 second edition of the Calculus textbook includes a new chapter on "Highlights of Calculus" that connects to the video series of the same name.  The new chapter has summaries and practice questions for all of the videos.  It also introduces The Exponential Function (e^x) as presented in Prof. Strang's video on this to

Subjects

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8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to physics of the solar system, stars, interstellar medium, the galaxy, and universe, as determined from a variety of astronomical observations and models.Topics include: planets, planet formation; stars, the Sun, "normal" stars, star formation; stellar evolution, supernovae, compact objects (white dwarfs, neutron stars, and black holes), plusars, binary X-ray sources; star clusters, globular and open clusters; interstellar medium, gas, dust, magnetic fields, cosmic rays; distance ladder; galaxies, normal and active galaxies, jets; gravitational lensing; large scaling structure; Newtonian cosmology, dynamical expansion and thermal history of the Universe; cosmic microwave background radiation; big-bang nucleosynthesis

Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | stars | interstellar medium | the Galaxy | the Universe | planets | planet formation | star formation | stellar evolution | supernovae | compact objects | white dwarfs | neutron stars | black holes | plusars | binary X-ray sources | star clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | galaxies | normal and active galaxies | jets | gravitational lensing | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | big-bang nucleosynthesis | pulsars | binary X-ray sources | gas | dust | magnetic fields | cosmic rays | galaxy | universe | astrophysics | Sun | supernova | globular clusters | open clusters | jets | Newtonian cosmology | dynamical expansion | thermal history | normal galaxies | active galaxies | Greek astronomy | physics | Copernicus | Tycho | Kepler | Galileo | classical mechanics | circular orbits | full kepler orbit problem | electromagnetic radiation | matter | telescopes | detectors | 8.282 | 12.402

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18.013A Calculus with Applications (MIT) 18.013A Calculus with Applications (MIT)

Description

Differential calculus in one and several dimensions. Java applets and spreadsheet assignments. Vector algebra in 3D, vector- valued functions, gradient, divergence and curl, Taylor series, numerical methods and applications. Given in the first half of the first term. However, those wishing credit for 18.013A only, must attend the entire semester. Prerequisites: a year of high school calculus or the equivalent, with a score of 4 or 5 on the AB, or the AB portion of the BC, Calculus test, or an equivalent score on a standard international exam, or a passing grade on the first half of the 18.01 Advanced Standing exam.Technical RequirementsThe MathML version of the textbook requires the Internet Explorer 6 browser or above with the MathPlayer plug-in  or Netscape 7.x / Mozill Differential calculus in one and several dimensions. Java applets and spreadsheet assignments. Vector algebra in 3D, vector- valued functions, gradient, divergence and curl, Taylor series, numerical methods and applications. Given in the first half of the first term. However, those wishing credit for 18.013A only, must attend the entire semester. Prerequisites: a year of high school calculus or the equivalent, with a score of 4 or 5 on the AB, or the AB portion of the BC, Calculus test, or an equivalent score on a standard international exam, or a passing grade on the first half of the 18.01 Advanced Standing exam.Technical RequirementsThe MathML version of the textbook requires the Internet Explorer 6 browser or above with the MathPlayer plug-in  or Netscape 7.x / Mozill

Subjects

vector algebra | vector algebra | taylor series | taylor series | numerical methods | numerical methods | differential calculus | differential calculus | 18.013 | 18.013

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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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2.035 Special Topics in Mathematics with Applications: Linear Algebra and the Calculus of Variations (MIT) 2.035 Special Topics in Mathematics with Applications: Linear Algebra and the Calculus of Variations (MIT)

Description

This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. App This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. App

Subjects

calculus of variations | calculus of variations | linear algebra | linear algebra | solid mechanics | solid mechanics | fluid mechanics | fluid mechanics | energy methods | energy methods | microstructures of crystalline | microstructures of crystalline

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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

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18.014 Calculus with Theory (MIT) 18.014 Calculus with Theory (MIT)

Description

18.014, Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus. 18.014, Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus.

Subjects

axioms for the real numbers | axioms for the real numbers | the Riemann integral | the Riemann integral | limits | limits | theorems on continuous functions | theorems on continuous functions | derivatives of functions of one variable | derivatives of functions of one variable | the fundamental theorems of calculus | the fundamental theorems of calculus | Taylor's theorem | Taylor's theorem | infinite series | infinite series | power series | power series | rigorous treatment of the elementary functions | rigorous treatment of the elementary functions

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What children's perspectives tell us about inclusion What children's perspectives tell us about inclusion What children's perspectives tell us about inclusion What children's perspectives tell us about inclusion

Description

The underlying premise of this free course, What children's perspectives tell us about inclusion, is that we are all experts in different ways, and that our different experiences and understandings are of value. Inclusive education is presented and discussed as under construction, both in educational settings and as a concept. The materials to be found in this course are largely rooted in the social model of disability and human/disability rights frameworks. First published on Tue, 12 Jul 2011 as What children's perspectives tell us about inclusion. To find out more visit The Open University's Openlearn website. Creative-Commons 2011 The underlying premise of this free course, What children's perspectives tell us about inclusion, is that we are all experts in different ways, and that our different experiences and understandings are of value. Inclusive education is presented and discussed as under construction, both in educational settings and as a concept. The materials to be found in this course are largely rooted in the social model of disability and human/disability rights frameworks. First published on Tue, 12 Jul 2011 as What children's perspectives tell us about inclusion. To find out more visit The Open University's Openlearn website. Creative-Commons 2011

Subjects

Educational Practice | Educational Practice | E243_1 | E243_1

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8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models.

Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | stars | interstellar medium | the Galaxy | the Universe | planets | planet formation | star formation | stellar evolution | supernovae | compact objects | white dwarfs | neutron stars | black holes | plusars | binary X-ray sources | star clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | galaxies | normal and active galaxies | jets | gravitational lensing | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | big-bang nucleosynthesis | pulsars | binary X-ray sources | gas | dust | magnetic fields | cosmic rays | galaxy | universe | astrophysics | Sun | supernova | globular clusters | open clusters | jets | Newtonian cosmology | dynamical expansion | thermal history | normal galaxies | active galaxies | Greek astronomy | physics | Copernicus | Tycho | Kepler | Galileo | classical mechanics | circular orbits | full kepler orbit problem | electromagnetic radiation | matter | telescopes | detectors | 8.282 | 12.402 | plusars | galaxies | normal and active galaxies | dynamical expansion and thermal history of the Universe

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Math 2B. Calculus. Lecture 04. The Fundamental Theorem of Calculus.

Description

UCI Math 2B: Single-Variable Calculus (Fall 2013) Lec 04. Single-Variable Calculus -- The Fundamental Theorem of Calculus -- View the complete course: http://ocw.uci.edu/courses/math_2b_calculus.html Instructor: Natalia L. Komarova Ph.D. License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/info More courses at http://ocw.uci.edu Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: Definite integrals; the fundamental theorem of calculus. Applications of integration including finding areas and volumes. Techniques of integration. Infinite sequences and series. Parametric and polar equations. Recorded on October 5, 2013 Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/math_2b_calculus.html. [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (http://creativecommons.org/licenses/by-sa/3.0/deed.en_US).

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Math 1A/1B. Pre-Calculus: Law of Sines and Cosines - SSA Case

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UCI Math 1A/1B: Pre-Calculus Pre-Calculus: Law of Sines and Cosines - SSA Case View the complete course: http://ocw.uci.edu/courses/math_1a1b_precalculus.html Instructor: Sarah Eichhorn, Ph.D and Rachel Lehman, Ph.D License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/info More courses at http://ocw.uci.edu Description: UCI Math 1A/1B: Pre-Calculus is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus. Required attribution: Eichhorn, Sarah; Lehman, Rachel Pre-Calculus 1A/1B (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/math_1a1b_precalculus.html. [Access date]. License: Creative Commons Attribution-ShareAlike 4.0 United States License. (http://creativecommons.org/licenses/by-sa/4.0/)

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Math 1A/1B. Pre-Calculus: Law of Sines and Cosines - SAS Case

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UCI Math 1A/1B: Pre-Calculus Pre-Calculus: Law of Sines and Cosines - SAS Case View the complete course: http://ocw.uci.edu/courses/math_1a1b_precalculus.html Instructor: Sarah Eichhorn, Ph.D and Rachel Lehman, Ph.D License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/info More courses at http://ocw.uci.edu Description: UCI Math 1A/1B: Pre-Calculus is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus. Required attribution: Eichhorn, Sarah; Lehman, Rachel Pre-Calculus 1A/1B (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/math_1a1b_precalculus.html. [Access date]. License: Creative Commons Attribution-ShareAlike 4.0 United States License. (http://creativecommons.org/licenses/by-sa/4.0/)

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Math 1A/1B. Pre-Calculus: Conjugate Zeros Theorem

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UCI Math 1A/1B: Pre-Calculus Pre-Calculus: Conjugate Zeros Theorem View the complete course: http://ocw.uci.edu/courses/math_1a1b_precalculus.html Instructor: Sarah Eichhorn, Ph.D and Rachel Lehman, Ph.D License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/info More courses at http://ocw.uci.edu Description: UCI Math 1A/1B: Precalculus is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus. Required attribution: Eichhorn, Sarah; Lehman, Rachel Pre-calculus 1A/1B (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/math_1a1b_precalculus.html. [Access date]. License: Creative Commons Attribution-ShareAlike 4.0 United States License. (http://creativecommons.org/licenses/by-sa/4.0/).

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Math 1A/1B. Pre-Calculus: Converting Between Logarithmic and Exponential Equations

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UCI Math 1A/1B: Pre-Calculus Pre-Calculus: Converting Between Logarithmic and Exponential Equations View the complete course: http://ocw.uci.edu/courses/math_1a1b_precalculus.html Instructor: Sarah Eichhorn, Ph.D and Rachel Lehman, Ph.D License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/info More courses at http://ocw.uci.edu Description: UCI Math 1A/1B: Pre-Calculus is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus. Required attribution: Eichhorn, Sarah; Lehman, Rachel Pre-Calculus 1A/1B (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/math_1a1b_precalculus.html. [Access date]. License: Creative Commons Attribution-ShareAlike 4.0 United States License. (http://creativecommons.org/licenses/by-sa/4.0/)

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