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A First Course in Linear Algebra
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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

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

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Subject:
Chemistry
Material Type:
Assessments
Full Course
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Syllabi
Provider:
M.I.T.
Provider Set:
MIT OpenCourseWare
Author:
Voorhis, Troy Van
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Linear Algebra II
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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

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Subject:
Algebra
Functions
Material Type:
Assessments
Full Course
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Provider:
The Saylor Foundation
Provider Set:
Saylor Foundation
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The Old Laplace Transform
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No Strings Attached
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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

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Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Doug Daniels
Steven Cox
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Quantum Physics II, Fall 2013
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Together, this course and 8.06 Quantum Physics III cover quantum physics with ... More

Together, this course and 8.06 Quantum Physics III cover quantum physics with applications drawn from modern physics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in three-dimensions, angular momentum, spin, and addition of angular momentum. Less

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Subject:
Physics
Material Type:
Full Course
Homework and Assignments
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Provider:
M.I.T.
Provider Set:
MIT OpenCourseWare
Author:
Barton Zwiebach
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Quantum Theory I, Fall 2002
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Topics include uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of ... More

Topics include uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, Transformation Theory, equations of motion, and constants of motion. Symmetry in Quantum Mechanics, Representations of Symmetry Groups. Variational and Perturbation Approximations. Systems of Identical Particles and Applications. Time-Dependent Perturbation Theory. Scattering Theory - Phase Shifts, Born Approximation. The Quantum Theory of Radiation. Second Quantization and Many-Body Theory. Relativistic Quantum Mechanics of One Electron. 8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement. Less

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Subject:
Statistics and Probability
Physics
Material Type:
Full Course
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Provider:
M.I.T.
Provider Set:
MIT OpenCourseWare
Author:
Taylor, Washington
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Quantum Theory II, Spring 2003
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A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, ... More

A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation. Less

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Subject:
Statistics and Probability
Physics
Material Type:
Full Course
Homework and Assignments
Lecture Notes
Syllabi
Provider:
M.I.T.
Provider Set:
MIT OpenCourseWare
Author:
Taylor, Washington
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Trajectories of Linear Systems
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Using Maple, Mathmatica, or MatLab, the learner will investigate the trajectories in ... More

Using Maple, Mathmatica, or MatLab, the learner will investigate the trajectories in the phase plane of 2x2 homogeneous linear systems of first-order differential equations of the form X' = AX. Less

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Subject:
Material Type:
Activities and Labs
Instructional Material
Reference
Provider:
iLumina
Provider Set:
iLumina Digital Library
Author:
David Smith
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Trajectories of Linear Systems
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Using Maple, Mathmatica, or MatLab, learner should be able to investigate the ... More

Using Maple, Mathmatica, or MatLab, learner should be able to investigate the trajectories in the phase plane of 2x2 homogeneous linear systems of first-order differential equations of the form X = AX. Less

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Subject:
Material Type:
Activities and Labs
Instructional Material
Provider:
iLumina
Provider Set:
iLumina Digital Library
Author:
David Smith
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.)310.1( tcejbus ngised enotspac eht dna )150.1 ,140.1 ,130.1( stcejbus ngised aera ... More

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