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Massachusetts Institute of Technology
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Courseware
This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebras Linear
- Resource Type:
- Courseware
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Courseware
This course aims to give students the tools and training to recognize convex optimization problems that arise in scientific and engineering applications, presenting the basic theory, and concentrating on modeling aspects and results that are useful in applications. Topics include convex sets, convex functions, optimization problems, least-squares, linear and quadratic programs, semidefinite programming, optimality conditions, and duality theory. Applications to signal processing, control, machine learning, finance, digital and analog circuit design, computational geometry, statistics, and mechanical engineering are presented. Students complete hands-on exercises using high-level numerical software.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex functions Mathematical optimization
- Resource Type:
- Courseware
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Courseware
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Differential equations
- Resource Type:
- Courseware
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Courseware
Vibrations and waves are everywhere. If you take any system and disturb it from a stable equilibrium, the resultant motion will be waves and vibrations. Think of a guitar string—pluck the string, and it vibrates. The sound waves generated make their way to our ears, and we hear the string’s sound. Our eyes see what’s happening because they receive the electromagnetic waves of the light reflected from the guitar string, so that we can recognize the beautiful sinusoidal waves on the string.
- Subjects:
- Physics
- Keywords:
- Waves Vibration
- Resource Type:
- Courseware
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Courseware
The course is taught using the textbook by T. Apostol, "Calculus" Vol. I Second Edition (1967) and the additional course notes by James Raymond Munkres, Professor of Mathematics, Emeritus.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Mathematical analysis
- Resource Type:
- Courseware
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Video
This channel contains the complete 8.01x (Physics I: Classical Mechanics), 8.02x (Physics II: Electricity and Magnetism) and 8.03 (Physics III: Vibrations and Waves) lectures as presented by Walter Lewin in the fall of 1999, spring of 2002 and fall of 2004. The 8.01x and 8.02x edX lectures are high resolution (480p) versions of the more commonly seen OCW versions. Some edits were also made by Lewin. 8.03 is the OCW version, also in a 480p resolution. Links to lecture notes, assignments/solutions and exams/solutions are added. Playlists with Help Sessions for 8.01x, 8.02x and 8.03 are also available. They are "mini lectures". The problems discussed in these videos should be apparent after watching the first few minutes. Other playlists show Lewin in various appearances and his Bi-Weekly Physics problems/solutions and several excellent lectures by Feynman and others.
- Subjects:
- Physics and Electrical Engineering
- Keywords:
- Waves Vibration Magnetism Mechanics Electricity Physics
- Resource Type:
- Video
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e-book
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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Video
In this lecture, we consider strategies for adversarial games such as chess. We discuss the minimax algorithm, and how alpha-beta pruning improves its efficiency. We then examine progressive deepening, which ensures that some answer is always available.
- Course related:
- COMP4431 Artificial Intelligence
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Artificial intelligence
- Resource Type:
- Video
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Video
Professor Strang describes independent vectors and the column space of a matrix as a good starting point for learning linear algebra. His outline develops the five shorthand descriptions of key chapters of linear algebra.
- Course related:
- COMP4432 Machine Learning
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebras Linear
- Resource Type:
- Video