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15 results for "partial differential equations"
More Calculus For Biologists: Partial Differential Equation Models By James Peterson
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In this book, we continue to discuss how to blend mathematics, computational tools and science into a cohesive point of view. Hence, this text is a follow up to our book on mathematics for... More > biologists, Calculus for Biologists. We now add new mathematics such as the ideas of partial differentiation and approximation of functions of more than one variable and a more complete study of nonlinear differential equation models using these new tools. We also discuss more fully how to develop code with MatLab/ Octave to solve our problems numerically. We study a model of the excitable neuron which leads to the cable equation which is a standard equation in biological information processing. We use the cable equation to develop an input side model of an excitable neuron -- the dendrite -- and then build a model of the excitable neuron itself. This consists of a dendrite, a cell body or soma and the axon along which generates the action potential.< Less
Partial Differential Equations with Fourier Series and Boundary Value Problems By Nakhlé H. Asmar
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This book provides a smooth transition from a course in elementary ordinary differential equations to more advanced topics in a first course in partial differential equations and Fourier Series. It... More > is intended for students of engineering, mathematics, and physics, with emphasis on applications. The new topics in this edition offer the instructors the option to teach a theory oriented course on partial differential equations or a course with heavier emphasis on Fourier series and boundary value problems. Beyond the core material for a basic course on partial differential equations, the book includes a number of more specialized topics that the instructor can cover or use as research projects at his or her discretion. The book contains hundreds of completely worked out examples to help students assimilate the new topics. The style is easy to follow and speaks directly to the reader. The book comes with a companion student solutions manual that the reader can download for free from the author’s website.< 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
I do like CFD, VOL.1, Second Edition By Katate Masatsuka
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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 simple model equations... More > (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 cfdbooks.com. [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
Quantitative Methods for Data Science: II - Problems By James Godfrey
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This reference contains problems and solutions in introductory applied mathematics for the following areas: vector and matrix algebra, differential and integral calculus, complex variables, series,... More > vector calculus, transforms, and ordinary and partial differential equations. The focus is on understanding material for solving problems related to the following disciplines: statistics, engineering and the natural sciences, advanced software development, economics and finance, climate analysis, and other data-driven areas.< Less
Calculus: Dynamic Mathematics, Volume Two By Chuck Garner
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This is the second volume of a two-volume series of texts designed to help gifted high school students succeed with calculus. This volume includes a complete treatment of two- and three-dimensional... More > vectors, parametric equations, polar functions, an introduction to linear algebra, partial differentiation, multiple integration, line integrals, surface integrals, and infinite series.< Less
Calculus: Dynamic Mathematics, Volume Two By Chuck Garner
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This is the second volume of a two-volume series of texts designed to help gifted high school students succeed with calculus. This volume includes a complete treatment of two- and three-dimensional... More > vectors, parametric equations, polar functions, an introduction to linear algebra, partial differentiation, multiple integration, line integrals, surface integrals, and infinite series. This is the second edition which features changes to the problem sets and corrects typographical errors.< Less