(Complete Item Description)
- Abstract:
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This module derives the Discrete-Time Fourier Series (DTFS), which is a fourier series type expansion for discrete-time, periodic functions. The module also takes some time to review complex sinusoids which will be used as our basis.
- Subject:
-
Mathematics and Statistics,
Science and Technology
- Grade Level:
-
Post-secondary
- Collection:
-
Connexions
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No Strings Attached
(Complete Item Description)
- Abstract:
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This 15-minute video lesson sees that orthonormal bases make for good coordinate systems. [Linear Algebra playlist: Lesson 125 of 143]
- Subject:
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Mathematics and Statistics
- Grade Level:
-
Secondary,
Post-secondary
- Collection:
-
Khan Academy
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(Complete Item Description)
- Abstract:
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This 7-minute video lesson gives an example of finding the transformation matrix for the projection onto a subspace with an orthonormal basis. [Linear Algebra playlist: Lesson 127 of 143]
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Secondary,
Post-secondary
- Collection:
-
Khan Academy
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(Complete Item Description)
- Abstract:
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This 13-minute video lesson uses Gram-Schmidt to find an orthonormal basis for a plane in R3. [Linear Algebra playlist: Lesson 131 of 143]
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Secondary,
Post-secondary
- Collection:
-
Khan Academy
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(Complete Item Description)
- Abstract:
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This 12-minute video lesson looks at sets and bases that are orthonormal -- or where all the vectors have length 1 and are orthogonal to each other. [Linear Algebra playlist: Lesson 124 of 143]
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Secondary,
Post-secondary
- Collection:
-
Khan Academy
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Remix and Share
(Complete Item Description)
- Abstract:
-
This 16-minute video lesson looks at projections onto subspaces with orthonormal bases. [Linear Algebra playlist: Lesson 126 of 143]
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Secondary,
Post-secondary
- Collection:
-
Khan Academy
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Remix and Share
(Complete Item Description)
- Abstract:
-
This 19-minute video lesson finds an orthonormal basis for a subspace using the Gram-Schmidt Process. [Linear Algebra playlist: Lesson 130 of 143]
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Secondary,
Post-secondary
- Collection:
-
Khan Academy
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(Complete Item Description)
- Abstract:
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The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.
- Subject:
-
Science and Technology
- Grade Level:
-
Post-secondary
- Collection:
-
MIT OpenCourseWare
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(Complete Item Description)
- Abstract:
-
This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.
- Subject:
-
Mathematics and Statistics,
Science and Technology
- Grade Level:
-
Post-secondary
- Collection:
-
MIT OpenCourseWare
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(Complete Item Description)
- Abstract:
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The module looks at decomposing signals through orthonormal basis expansion to provide an alternative representation. The module presents many examples of solving these problems and looks at them in several spaces and dimensions.
- Subject:
-
Mathematics and Statistics,
Science and Technology
- Grade Level:
-
Post-secondary
- Collection:
-
Connexions
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No Strings Attached
(Complete Item Description)
- Abstract:
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This module discusses the different types of basis that leads up to the definition of an orthonormal basis. Examples are given and the useful of the orthonormal basis is discussed.
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Post-secondary
- Collection:
-
Connexions
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No Strings Attached
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