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• Orthonormal Basis
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This course covers the mathematical techniques necessary for understanding of materials science ...

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:
Calculus
Material Type:
Full Course
Textbook
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Carter, W. Craig
Conditions of Use:
No Strings Attached
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This module derives the Discrete-Time Fourier Series (DTFS), which is a fourier ...

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.

Material Type:
Syllabus
Provider:
Rice University
Provider Set:
Connexions
Author:
Justin Romberg
Michael Haag
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This 15-minute video lesson sees that orthonormal bases make for good coordinate ...

This 15-minute video lesson sees that orthonormal bases make for good coordinate systems.

Subject:
Algebra
Material Type:
Lecture
Provider:
Provider Set:
Author:
Khan, Salman
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This 7-minute video lesson gives an example of finding the transformation matrix ...

This 7-minute video lesson gives an example of finding the transformation matrix for the projection onto a subspace with an orthonormal basis.

Subject:
Algebra
Material Type:
Lecture
Provider:
Provider Set:
Author:
Khan, Salman
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This 13-minute video lesson uses Gram-Schmidt to find an orthonormal basis for ...

This 13-minute video lesson uses Gram-Schmidt to find an orthonormal basis for a plane in R3.

Subject:
Algebra
Material Type:
Lecture
Provider:
Provider Set:
Author:
Khan, Salman
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This 12-minute video lesson looks at sets and bases that are orthonormal ...

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.

Subject:
Algebra
Material Type:
Lecture
Provider:
Provider Set:
Author:
Khan, Salman
Conditions of Use:
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This 16-minute video lesson looks at projections onto subspaces with orthonormal bases.

Subject:
Algebra
Material Type:
Lecture
Provider:
Provider Set:
Author:
Khan, Salman
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This 19-minute video lesson finds an orthonormal basis for a subspace using ...

This 19-minute video lesson finds an orthonormal basis for a subspace using the Gram-Schmidt Process.

Subject:
Algebra
Material Type:
Lecture
Provider:
Provider Set:
Author:
Khan, Salman
Conditions of Use:
No Strings Attached
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The module looks at decomposing signals through orthonormal basis expansion to provide ...

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.

Material Type:
Syllabus
Provider:
Rice University
Provider Set:
Connexions
Author:
Justin Romberg
Michael Haag
Conditions of Use:
No Strings Attached
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This module discusses the different types of basis that leads up to ...

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
Material Type: