Keywords: Eigenvalues (26)

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Differential Equations, Spring 2004
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Differential Equations, Spring 2004

Study of ordinary differential equations, including modeling of physical problems and interpretation ... (more)

Study of ordinary differential equations, including modeling of physical problems and interpretation of their solutions. Standard solution methods for single first-order equations, including graphical and numerical methods. Higher-order forced linear equations with constant coefficients. Complex numbers and exponentials. Matrix methods for first-order linear systems with constant coefficients. Non-linear autonomous systems; phase plane analysis. Fourier series; Laplace transforms. (less)

Subject:
Mathematics and Statistics
Material Type:
Activities and Labs
Assessments
Full Course
Homework and Assignments
Lecture Notes
Syllabi
Video Lectures
Other
Provider:
M.I.T.
Provider Set:
MIT OpenCourseWare
Author:
Miller, Haynes R.
Eigenvectores y Eigenvalores
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Eigenvectores y Eigenvalores

This module defines eigenvalues and eigenvectors and explains a method of finding ... (more)

This module defines eigenvalues and eigenvectors and explains a method of finding them given a matrix. These ideas are presented, along with many examples, in hopes of leading up to an understanding of the Fourier Series. (less)

Subject:
Science and Technology
Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Justin Romberg
Michael Haag
Eigenvectors and Eigenvalues
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Eigenvectors and Eigenvalues

This module defines eigenvalues and eigenvectors and explains a method of finding ... (more)

This module defines eigenvalues and eigenvectors and explains a method of finding them given a matrix. These ideas are presented, along with many examples, in hopes of leading up to an understanding of the Fourier Series. (less)

Subject:
Mathematics and Statistics
Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Justin Romberg
Michael Haag
A First Course in Linear Algebra
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A First Course in Linear Algebra

A First Course in Linear Algebra is an introductory textbook aimed at ... (more)

A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way. (less)

Subject:
Mathematics
Material Type:
Textbooks
Provider:
University of Minnesota
Provider Set:
University of Minnesota - Open Academics Textbooks
Author:
Robert Beezer
Introductory Quantum Mechanics I, Fall 2005
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Introductory Quantum Mechanics I, Fall 2005

Fundamental concepts of quantum mechanics: wave properties, uncertainty principles, Schrodinger equation, and ... (more)

Fundamental concepts of quantum mechanics: wave properties, uncertainty principles, Schrodinger equation, and operator and matrix methods. Basic applications to: one-dimensional potentials (harmonic oscillator), three-dimensional centrosymetric potentials (hydrogen atom), and angular momentum and spin. Approximation methods: WKB method, variational principle, and perturbation theory. (less)

Subject:
Science and Technology
Material Type:
Assessments
Full Course
Homework and Assignments
Lecture Notes
Syllabi
Provider:
M.I.T.
Provider Set:
MIT OpenCourseWare
Author:
Voorhis, Troy Van
Linear Algebra II
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Linear Algebra II

Linear Algebra is both rich in theory and full of interesting applications; ... (more)

Linear Algebra is both rich in theory and full of interesting applications; in this course the student will try to balance both. This course includes a review of topics learned in Linear Algebra I. Upon successful completion of this course, the student will be able to: Solve systems of linear equations; Define the abstract notions of vector space and inner product space; State examples of vector spaces; Diagonalize a matrix; Formulate what a system of linear equations is in terms of matrices; Give an example of a space that has the Archimedian property; Use the Euclidean algorithm to find the greatest common divisor; Understand polar form and geometric interpretation of the complex numbers; Explain what the fundamental theorem of algebra states; Determine when two matrices are row equivalent; State the Fredholm alternative; Identify matrices that are in row reduced echelon form; Find a LU factorization for a given matrix; Find a PLU factorization for a given matrix; Find a QR factorization for a given matrix; Use the simplex algorithm; Compute eigenvalues and eigenvectors; State Shur's Theorem; Define normal matrices; Explain the composition and the inversion of permutations; Define and compute the determinant; Explain when eigenvalues exist for a given operator; Normal form of a nilpotent operator; Understand the idea of Jordan blocks, Jordan matrices, and the Jordan form of a matrix; Define quadratic forms; State the second derivative test; Define eigenvectors and eigenvalues; Define a vector space and state its properties; State the notions of linear span, linear independence, and the basis of a vector space; Understand the ideas of linear independence, spanning set, basis, and dimension; Define a linear transformation; State the properties of linear transformations; Define the characteristic polynomial of a matrix; Define a Markov matrix; State what it means to have the property of being a stochastic matrix; Define a normed vector space; Apply the Cauchy Schwarz inequality; State the Riesz representation theorem; State what it means for a nxn matrix to be diagonalizable; Define Hermitian operators; Define a Hilbert space; Prove the Cayley Hamilton theorem; Define the adjoint of an operator; Define normal operators; State the spectral theorem; Understand how to find the singular-value decomposition of an operator; Define the notion of length for abstract vectors in abstract vector spaces; Define orthogonal vectors; Define orthogonal and orthonormal subsets of R^n; Use the Gram-Schmidt process; Find the eigenvalues and the eigenvectors of a given matrix numerically; Provide an explicit description of the Power Method. (Mathematics 212) (less)

Subject:
Mathematics and Statistics
Material Type:
Assessments
Full Course
Homework and Assignments
Readings
Syllabi
Textbooks
Provider:
The Saylor Foundation
Provider Set:
Saylor Foundation
Mathematics for Materials Scientists and Engineers, Fall 2003
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Mathematics for Materials Scientists and Engineers, Fall 2003

The class will cover mathematical techniques necessary for understanding of materials science ... (more)

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. (less)

Subject:
Science and Technology
Material Type:
Full Course
Homework and Assignments
Lecture Notes
Syllabi
Other
Provider:
M.I.T.
Provider Set:
MIT OpenCourseWare
Author:
Carter, W. Craig
Matrix Simulation
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Matrix Simulation

This applet simulates the operation of a 2x2 matrix geometrically. The simulation ... (more)

This applet simulates the operation of a 2x2 matrix geometrically. The simulation shows a 2D image of the transformation of unit vectors due to the matrix. It displays the values of the matrix coefficients, the eigenvectors and the determinant. The matrix can be transposed, inverted or rotated. The page also includes an extensive explanation, and the source. (less)

Subject:
Mathematics
Physics
Material Type:
Instructional Material
Interactive
Reference
Provider:
ComPADRE Digital Library
Provider Set:
ComPADRE: Resources for Physics and Astronomy Education
Author:
Paul Falstad
The Old Laplace Transform
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The Old Laplace Transform

This module examines the Laplace Transform, an analytical tool that produces exact ... (more)

This module examines the Laplace Transform, an analytical tool that produces exact solutions for small, closed-form, tractable systems. We use the Laplace transform to move toward a solution for the nerve fiber potentials modeled by the dynamic Strang Quartet in the earlier module of the same name. (less)

Subject:
Mathematics and Statistics
Science and Technology
Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Doug Daniels
Steven Cox
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