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  • Orthonormal Basis
Fourier Analysis in Complex Spaces
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This module derives the Discrete-Time Fourier Series (DTFS), which is a fourier ... More

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. Less

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Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Justin Romberg
Michael Haag
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Mathematics for Materials Scientists and Engineers, Fall 2005
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Remix and Share
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This course covers the mathematical techniques necessary for understanding of materials science ... More

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. Less

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Subject:
Calculus
Material Type:
Activities and Labs
Full Course
Homework and Assignments
Lecture Notes
Syllabi
Provider:
M.I.T.
Provider Set:
MIT OpenCourseWare
Author:
Carter, W. Craig
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Orthonormal Basis Expansions
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The module looks at decomposing signals through orthonormal basis expansion to provide ... More

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. Less

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Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Justin Romberg
Michael Haag
Less
Types of Basis
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This module discusses the different types of basis that leads up to ... More

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. Less

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Subject:
Mathematics
Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Justin Romberg
Michael Haag
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.)310.1( tcejbus ngised enotspac eht dna )150.1 ,140.1 ,130.1( stcejbus ngised aera ... More

.)310.1( tcejbus ngised enotspac eht dna )150.1 ,140.1 ,130.1( stcejbus ngised aera ytlaiceps tneuqesbus eht ni desu si hcihw decudortni si esac ngised egral A .naps efil detcepxe dna ,srotcaf laicos dna cimonoce ,tnemnorivne larutan ,tnemnorivne tliub gnitsixe eht fo noitaredisnoc sa llew sa sehcaorppa lacinhcet snrecnoc ylticilpxe ngised tcejorP .)sdaor dna segdirb ,sgnidliub ,.g.e( seitilicaf tliub no sisahpme na htiw ,sesac ngised lareves sedulcnI .gnireenigne livic ni secitcarp dna seussi ngised sa llew sa ,gnivlos-melborp evitaerc dna ngised gnireenigne fo seuqinhcet dna ,sloot ,yroeht eht ot stneduts secudortnI Less

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