Transforms And Partial Differential Equations

Z Transform of Difference Equations Z Transform of Difference Equations  Notes
  Since z transforming the convolution representation for digital filters was so fruitful, let's apply it now to the general difference equation, Eg.
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The Z-Transformad The Inverse Z-Transform The Z-Transformad The Inverse Z-Transform Notes
  Modulation, Summation, Convolution Initial Value and Final Value Theorems Inverse z-Transform by Long Division Inverse z-Transform by Partial Fractions Difference Equations
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The Fourier Series The Fourier Series  Notes
  Fourier Coefficients For Full Range Series Over Any Range -L TO L,Dirichlet Conditions etc..,
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The Fourier Integral Theorem The Fourier Integral Theorem  Notes
  The mathematically more precise statement of this theorem is as follows,Theorem 23.1 (Fourier's Integral Theorem)
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Steady state solution of two-dimensional equation Steady state solution of two-dimensional equation  Notes
  The mathematical model for multi-dimensional, steady-state heat-conduction is a second-order, elliptic partial-differential equation (a Laplace, Poisson or Helmholtz Equation). Typical heat transfer textbooks describe several methods to solve this equation for two-dimensional regions with various boundary conditions.
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Solution of Difference Equations Solution of Difference Equations  Notes
  The z-transform can be used to convert a difference equation into an algebraic equation in the same manner that the Laplace converts a differential equation in to an algebraic equation. The one-sided transform is particularly well suited for solving initial condition problems
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Sine and Cosine Transforms Sine and Cosine Transforms Notes
  Fourier Cosine Transform (FCT), Fourier Sine Transform (FST), Discrete Cosine Transform (DCT), Discrete Sine Transform (DST), Properties of DCT and DST, FCT and FST Algorithm Based on FFT, Fourier Cosine Transform Pairs, Fourier Sine Transform Pairs, Notations and Definitions, etc..,
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Partial Differential Equations Partial Differential Equations Notes
  The Partial Differential Equation (PDE) corresponding to a physical system can be formed, either by eliminating the arbitrary constants or by eliminating the arbitrary functions from the given relation.
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Solution of Partial Differentiation Equations Solution of Partial Differentiation Equations Notes
  To determine a particular relation between u, x, and y, expressed as u = f (x, y), that satisfies the basic differential equation,some particular conditions specified.
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Linear Partial Differential Equations Linear Partial Differential Equations  Notes
  where the differential operator L is a linear operator, y is the unknown function, and the right hand side ƒ is a given function (called the source term). The linearity condition on L rules out operations such as taking the square of the derivative of y; but permits, for example, taking the second derivative of y.
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Parseval’s Identity Parseval’s Identity Notes
  (A version of Parseval’s Identity)
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Ritz Solution Techniques Ritz Solution Techniques Notes
  Consider a general elastic rod with attached springs, dampers, and masses and with applied axial forces
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Harmonics Harmonics Notes
  Recall the Fourier series (Full Range Fourier Series)
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Reciprocal Space Fourier Transforms Reciprocal Space Fourier Transforms Notes
  Introduction to reciprocal space, Fourier transformation, Some simple functions, Area and zero frequency components, dimensions Separable, Central slice theorem, Spatial frequencies, Filtering, Modulation Transfer Function.
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Fourier Transform Pair Fourier Transform Pair Notes
  You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
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Fourier Transform Properties Fourier Transform Properties  Notes
  Chemistry often involves the measurement of properties which are the aggregate of many fundamental processes. A variety of techniques have been developed for extracting information about these underlying processes. Fourier analysis is one of the most important and is very widely used - eg: in crystallography, X-ray adsorbtion spectroscopy, NMR, vibrational spectroscopy (FTIR) etc..
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Fourier Series & Fourier Transforms Fourier Series & Fourier Transforms Notes
  Chemistry often involves the measurement of properties which are the aggregate of many fundamental processes. A variety of techniques have been developed for extracting information about these underlying processes. Fourier analysis is one of the most important and is very widely used - eg: in crystallography, X-ray adsorbtion spectroscopy, NMR, vibrational spectroscopy (FTIR) etc..
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Fourier Fourier Notes
  When we analyse a function using Fourier methods, the function is decomposed into its frequency components. This analysis is used in signal processing, filtering.
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Even Functions Even Functions Notes
  Recall: A function y = f(t) is said to be even if f(-t) = f(t) for all values of t. The graph of an even function is always symmetrical about the y-axis (i.e. it is a mirror image).
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Fourier Series Fourier Series Notes
  Jean-Baptiste Fourier (France, 1768 - 1830) proved that almost any period function can be represented as the sum of sinusoids with integrally related frequencies.
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Difference Equations Difference Equations Notes
  Many of the sequences we will study in this course can be expressed as difference equations
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Complex Form of Fourier Series Complex Form of Fourier Series  Notes
  Let the function f (x) be defined on the interval Using the well-known Euler's
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Cartesian Coordinates Cartesian Coordinates  Notes
  The method of separation of variables is useful when the problem has a symmetry and there is a corresponding orthogonal coordinate system in which the Laplacian operator
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Applied Computational Fluid Dynamics Applied Computational Fluid Dynamics Notes
  Boundary conditions are a required component of the mathematical model,Boundaries direct motion of flow. Specify fluxes into the computational domain, e.g.
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Applications of Partial Differential Equations Applications of Partial Differential Equations Notes
  In modern times, the idea that sound consists of waves is a generally accepted truth. In ancient times, however, theories about sound ranged from the idea of streams of atoms, proposed by Gassendi, to ray theories, in which sound travels linearly, proposed by Reynolds and Rayleigh.1 However, evidence for the wave theory, such as diffusion of sound around corners and the detection of distinct frequencies of sound by Pythagoras
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