Read Dynamics and Geometry on Metric Spaces: Flows and Foliations

Dynamics and Geometry on Metric Spaces: Flows and Foliations

Craig James Calcaterra

4.9/5 (34212 ratings)

Description:The scaffolding of metric geometry applied to dynamical systems provides the abstract perspective for addressing all the major subjects and core questions in continuous mathematical modeling. Rigorous answers are given to the 7 fundamental mathematical questions for solutions to ODEs, PDEs, DDEs and SDEs: existence, uniqueness,stability, control, analysis, synthesis and extensibility. Starting with elementary principles of point-set topology on metric spaces, this text is written with the goal of introducing advanced undergraduates and graduate students to the metric geometry necessary to generate flows and foliations on metric spaces, unifying and generalizing the results of differential equations in diverse modeling environments. Exercises and appendices introducing all ancillary technical tools make this self-contained book suitable for a course in the application of real analysis to rigorous mathematical modeling. Written as a text for the senior undergraduate capstone course at Metropolitan State University, this book unifies the undergraduate mathematics curriculum and connects it to advanced applications in pure and applied topics. Studying flows on metric spaces gives a novel perspective to rigorously review the undergraduate subjects of advanced analysis, ODEs, PDEs, and numerical analysis. The generality of metric spaces allows a natural extension of flows to introduce delay differential equations and stochastic differential equations and their stability and control. The abstract perspective of flows on metric spaces highlights the importance of proof in answering the pure mathematical problems of existence and uniqueness of solutions, while the constructive approach of Euler curves gives a concrete method for solving all types of differential equations. Euler curves may be summed to give explicit solutions for linear ODEs, PDEs, DDEs, and SDEs. For nonlinear equations or nonlinear metric spaces, the basic Euler method gives constructive algorithms for approximating solutions.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Dynamics and Geometry on Metric Spaces: Flows and Foliations. To get started finding Dynamics and Geometry on Metric Spaces: Flows and Foliations, you are right to find our website which has a comprehensive collection of manuals listed.
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Description: The scaffolding of metric geometry applied to dynamical systems provides the abstract perspective for addressing all the major subjects and core questions in continuous mathematical modeling. Rigorous answers are given to the 7 fundamental mathematical questions for solutions to ODEs, PDEs, DDEs and SDEs: existence, uniqueness,stability, control, analysis, synthesis and extensibility. Starting with elementary principles of point-set topology on metric spaces, this text is written with the goal of introducing advanced undergraduates and graduate students to the metric geometry necessary to generate flows and foliations on metric spaces, unifying and generalizing the results of differential equations in diverse modeling environments. Exercises and appendices introducing all ancillary technical tools make this self-contained book suitable for a course in the application of real analysis to rigorous mathematical modeling. Written as a text for the senior undergraduate capstone course at Metropolitan State University, this book unifies the undergraduate mathematics curriculum and connects it to advanced applications in pure and applied topics. Studying flows on metric spaces gives a novel perspective to rigorously review the undergraduate subjects of advanced analysis, ODEs, PDEs, and numerical analysis. The generality of metric spaces allows a natural extension of flows to introduce delay differential equations and stochastic differential equations and their stability and control. The abstract perspective of flows on metric spaces highlights the importance of proof in answering the pure mathematical problems of existence and uniqueness of solutions, while the constructive approach of Euler curves gives a concrete method for solving all types of differential equations. Euler curves may be summed to give explicit solutions for linear ODEs, PDEs, DDEs, and SDEs. For nonlinear equations or nonlinear metric spaces, the basic Euler method gives constructive algorithms for approximating solutions.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Dynamics and Geometry on Metric Spaces: Flows and Foliations. To get started finding Dynamics and Geometry on Metric Spaces: Flows and Foliations, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Dynamics and Geometry on Metric Spaces: Flows and Foliations

Dynamics and Geometry on Metric Spaces: Flows and Foliations

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