(Complete Item Description)
- Abstract:
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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.
- Subject:
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Mathematics and Statistics
- Grade Level:
-
Post-secondary
- Collection:
-
MIT OpenCourseWare
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This module provides a brief overview and review of the importance of eigenvectors and eigenvalues in analyzing and understanding LTI systems.
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Post-secondary
- Collection:
-
Connexions
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No Strings Attached
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- Abstract:
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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.
- Subject:
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Science and Technology
- Grade Level:
-
Post-secondary
- Collection:
-
Connexions
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No Strings Attached
(Complete Item Description)
- Abstract:
-
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.
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Post-secondary
- Collection:
-
Connexions
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No Strings Attached
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- Abstract:
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Este modulo nos da un pequeño repaso de la importancia de los eigenvectores y eigenvalores en el análisis y entedimiento de los sistemas LTI.
- Subject:
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Science and Technology
- Grade Level:
-
Post-secondary
- Collection:
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Connexions
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No Strings Attached
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- Abstract:
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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.
- Subject:
-
Science and Technology
- Grade Level:
-
Post-secondary
- Collection:
-
MIT OpenCourseWare
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This 14-minute video lesson shows how to determine the eigenvalues of a 3x3 matrix. [Linear Algebra playlist: Lesson 137 of 143]
- Subject:
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Mathematics and Statistics
- Grade Level:
-
Secondary,
Post-secondary
- Collection:
-
Khan Academy
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This 6-minute video lesson gives an example of how to solve for the eigenvalues of a 2x2 matrix. [Linear Algebra playlist: Lesson 135 of 143]
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Secondary,
Post-secondary
- Collection:
-
Khan Academy
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This 15-minute video lesson shows how to find the eigenvectors and eigenspaces of a 2x2 matrix. [Linear Algebra playlist: Lesson 136 of 143]
- Subject:
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Mathematics and Statistics
- Grade Level:
-
Secondary,
Post-secondary
- Collection:
-
Khan Academy
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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)
- Subject:
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Mathematics and Statistics
- Grade Level:
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Post-secondary
- Collection:
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Saylor Foundation
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Read the Fine Print
(Complete Item Description)
- Abstract:
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This 8-minute video explains what eigenvectors and eigenvalues are and why they are interesting. [Linear Algebra playlist: Lesson 133 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 9-minute video lesson shows the proof of the formula for determining Eigenvalues. [Linear Algebra playlist: Lesson 134 of 143]
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Secondary,
Post-secondary
- Collection:
-
Khan Academy
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- Abstract:
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Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB. Compared with 18.700, more emphasis on matrix algorithms and many applications.
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Post-secondary
- Collection:
-
MIT OpenCourseWare
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(Complete Item Description)
- Abstract:
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This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
- Subject:
-
Mathematics and Statistics
- Grade Level:
-
Post-secondary
- Collection:
-
MIT OpenCourseWare
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- Abstract:
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These notes, tutorials, and solutions cover the basic tools and applications in order to prepare the student for the study of Macroeconomics, Microeconomics and Econometrics at an intermediate and advanced level.
- Subject:
-
Business
- Grade Level:
-
Post-secondary
- Collection:
-
University of Cape Town
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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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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.
- 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 lays out the structure for the text of the CAAM 335 course in matrix analysis.
- Subject:
-
Mathematics and Statistics,
Science and Technology
- Grade Level:
-
Post-secondary
- Collection:
-
Connexions
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(Complete Item Description)
- Abstract:
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Together 8.05 and 8.06 cover quantum physics with applications drawn from modern physics. General formalism of quantum mechanics: states, operators, Dirac notation, representations, measurement theory. Harmonic oscillator: operator algebra, states. Quantum mechanics in three-dimensions: central potentials and the radial equation, bound and scattering states, qualitative analysis of wavefunctions. Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coefficients, spin systems, and allotropic forms of hydrogen.
- Subject:
-
Science and Technology
- Grade Level:
-
Post-secondary
- Collection:
-
MIT OpenCourseWare
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