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Topics in Applied Mathematics
The concepts and basic topics in elementary Linear Algebra and Calculus are reviewed and generalized to Linear Analysis in this first unit. In particular, the dot product, the vector space of R 2(that is, the x − y plane in Plane Geometry), and measurement of lengths of vectors in R2 , are extended to the “inner product,” the “inner-product space,” and “norm” measurement, respecti…
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Linear Algebra with Applications. Open Edition
his textbook is an introduction to the ideas and techniques of linear algebra for first- or second-year students with a working knowledge of high school algebra. The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a onesemester course for beginners whereas Chapters 5–9 contain a second semes…
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Linear Algebra, Theory And Applications
his is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. I think that the subject of linear algebra is likely the most significant topic discussed in undergraduate mathematics c…
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Elementary Linear Algebra
This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. However, this is intended to be a first course in linear algebra for students who are sophomores or j…
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APEX Pre Calculus
This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is de-signed to review mathematical concepts that are o[en stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is …
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Quantum description of light, Part 2
In this lecture, the professor discussed fluctuations and noise, and the single photon.
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Quantum description of light, Part 1
In this lecture, the professor discussed single mode light, thermal states, coherent states
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Atomic Physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change. This comprises ions, neutral atoms and, unless otherwise stated, it can be assumed that the term atom includes ions. The term atomic physics can …
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The Meaning of Clinical Death
Clinical death is the medical term for cessation of blood circulation and breathing, the two necessary criteria to sustain human and many other organisms' lives. It occurs when the heart stops beating in a regular rhythm, a condition called cardiac arrest. The term is also sometimes used in resuscitation research. Stopped blood circulation has historically proven irreversible in most cases. …
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Cancer System Biology
Cancer systems biology encompasses the application of systems biology approaches to cancer research, in order to study the disease as a complex adaptive system with emerging properties at multiple biological scales. More explicitly, because cancer spans multiple biological, spatial and temporal scales, communication and feedback mechanisms across the scales create a highly complex dynamic syste…
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