Search Results: 'Partial Differential Equations'


19 results for "Partial Differential Equations"
Introduction to Partial Differential Equations for Children By Ryan Shuell
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In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. Thus a PDE is solved with respect to two... More > or more independent variables. A special case is an ordinary differential equation (ODE), which deals with functions of a single variable and their derivatives.< Less
Computation and Visualization of Geometric Partial Differential Equations By Christopher Tiee
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This is an extended version of my PhD thesis which extends the theory of finite element exterior calculus (FEEC) to parabolic evolution equations. In the extended version, I explore some more precise... More > visualizations of the defined quantities, as well as explain how the modern theory of functional analysis applies. In the main part, I extend the theory of approximating evolution equations in Euclidean space (using FEEC) to hypersurfaces. After these main results, I describe some possible extensions to nonlinear equations. A few appendices detail one of the original motivations for getting into this theory in the first place: canonical geometries given as steady state solutions and extremals of certain functionals.< Less
Essential Differential Equations By Joseph Previte
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This book is designed to be an affordable, yet complete differential equations textbook. The topics include analytic and numerical solutions of first order ODE with applications. Second Order Linear... More > ODE with an emphasis on the spring/mass system, LRC circuits and resonance. Additional topics include higher order ODE, series solutions, and the Laplace transform and applications. Fourier series and partial differential equations.< Less
Introduction to Ordinary Differential Equations for Children By Ryan Shuell
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In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives. The term ordinary, differentiates... More > this kind of problem from a partial differential equation (PDE), which is actually solved with respect to two or more independent variables.< Less
Numerical Methods for Scientific Computing By Kyle Novak
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This book provides the mathematical insight for mathematics, physics, and engineering masters and PhD students to understand the inner workings of scientific computing. The book consists of three... More > independent courses: Numerical Linear Algebra, Numerical Analysis, and Numerical Methods for Partial Differential Equations.< Less
I do like CFD, VOL.1, Second Edition By Katate Masatsuka
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Version 2.6 (Sep. 2018): This is a unique and highly technical book on Computational Fluid Dynamics (CFD). The first half talks about mathematical foundations and governing equations ranging from... More > simple model equations (advection/diffusion, Euler-Tricomi, Cauchy-Riemann, Burgers, etc.) used for algorithm development to the incompressible/compressible Euler and Navier-Stokes equations in various forms with complete Jacobians and eigen-structures in 1, 2, and 3 dimensions. The other half talks about general methods for deriving exact solutions (separation of variables, transformation, superposition, etc.) and numerous exact solutions that can be readily used for accuracy verification of a CFD code (Ringleb's flow, Fraenkel's flow, boundary layer, viscous shock structure, etc.). This book can be a very useful resource for students studying basics of CFD as well as researchers/practitioners in CFD. - PDF version is available at [Note: PDF does not contain some contents of the Printed version.]< Less
A Matlab based introduction to financial mathematics By Kyriakos Chourdakis
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An introduction to financial mathematics using Matlab. The document is incomplete and needs some editing, but the following contents are there: 1. Elements of stochastic calculus 2. The... More > Black-Scholes world 3. Finite difference methods 4. Transform methods 5. Historical estimation and filtering 6. Volatility 7. Fixed income securities [to be completed] 8. Credit risk [to be added] 9. Risk Management [to be added] A. Using Matlab with Microsoft Excel Any feedback, corrections and suggestions are most welcome! K.-< Less
Un metodo per la risoluzione numerica di modelli analitici differenziali ed il programma PEEI che lo computerizza By Giacomo Lorenzoni
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They are exposed a method for the numerical resolution of differential analytical models (i.e. systems of partial differential equations) and the program PEEI that computerizes it.
Transformation Of Coordinates By narayana dash
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Transformation of orthogonal curvilinear coordinates from one system into another is done through partial differentiation. The transformation matrix is also a simple case of partial... More > differentiation. Another aspect of coordinate transformation is Compression of coordinates ( Change of scale in graph) resulting in deformation of graphs. A grand example of this is given by deriving the equations of conic sections from the equation of circle. Finally a grand example of transformation of coordinates would be Lagrange’s equations. The Newton’s Laws of motion have been transformed from Cartesian coordinates into generalized coordinates, . The beauty of Lagrange’s equations lies in the fact that they are invariant in form in any coordinate system. The wonder about it is, that the for divergent problems of quantum mechanics and electromagnetic theory and optics are easily derived from the same Lagrange’s equations using ; the total energy functions in each area.< Less
Applied Mechanics By Anton Berhulov
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The numerical analytic research approach of stress-strain state of anisotropic composite finite element area with different boundary conditions on the surface, is represented below. The problem is... More > solved by using a spatial model of the elasticity theory. Differential equation system in partial derivatives reduces to one-dimensional problem using spline collocation method in two coordinate directions. Boundary problem for the system of ordinary higher-order differential equation is solved by using the stable numerical technique of discrete orthogonalization.< Less

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