Introduction to Partial Differential Equations by David Borthwick
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions:
- What is the scientific problem we are trying to understand?
- How do we model that with PDE?
- What techniques can we use to analyze the PDE?
- How do those techniques apply to this equation?
- What information or insight did we obtain by developing and analyzing the PDE?
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Linear Functional Analysis
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An Introduction to Manifolds
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Riemannian Geometry
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Galois Theory
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Symbolic Dynamics
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Stochastic Calculus
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Geometry I
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Galois Cohomology and Class Field Theory
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Mathematical Gauge Theory
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Nonlinear Differential Equations and Dynamical Systems
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Mathematical Analysis I
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Differential Forms and Applications
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Geometry
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From Elementary Probability to Stochastic Differential Equations with MAPLE (R)
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Applied Stochastic Control of Jump Diffusions
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Probability Essentials
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Real Algebra
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Stochastic Differential Equations
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Elements of Functional Analysis
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Selected Topics in Partial Differential Equations
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The Essentials of Measure Theory
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On the Theory of Maass Wave Forms
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Potential Theory
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Fluctuations of Levy Processes with Applications
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Discrete Mathematics
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Automorphic Forms
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Matrix Theory
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Frontiers of Numerical Analysis
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Spectra of Graphs
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Polyhedral and Algebraic Methods in Computational Geometry
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Theory and Numerics of Differential Equations
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Dynamical Systems
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A Course on Tug-of-War Games with Random Noise
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Sphere Packings
“The book under review is intended for an introductory course for studentsThe author gives a balanced presentation that includes modern methods, without requiring prerequisites beyond vector calculus and linear algebra. Concepts and definitions from analysis are introduced only as they are needed in the text.” (Dian K. Palagachev, zbMATH 1364.35001, 2017)
David Borthwick is Professor and Director of the Graduate Studies Department of Mathematics and Computer Science at Emory University, Georgia, USA.
| SKU | Unavailable |
| ISBN 13 | 9783319840512 |
| ISBN 10 | 3319840517 |
| Title | Introduction to Partial Differential Equations |
| Author | David Borthwick |
| Series | Universitext |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer International Publishing AG |
| Year published | 2018-07-13 |
| Number of pages | 283 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |