From Ordinary to Partial Differential Equations 1st edition by Giampiero Esposito 9783319575445 3319575449

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Product details:

• ISBN 10:3319575449 

• ISBN 13:9783319575445

• Author:Giampiero Esposito 

 From Ordinary to Partial Differential Equations
This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.

 From Ordinary to Partial Differential Equations 1st Table of contents:

 Frontmatter
1. Ordinary Differential Equations
1. Linear Differential Equations
2. Non-linear Equations
2. Linear Elliptic Equations
3. Harmonic Functions
4. Mathematical Theory of Surfaces
5. Distributions and Sobolev Spaces
6. The Caccioppoli-Leray Theorem
7. Advanced Tools for the Caccioppoli-Leray Inequality
8. Aspects of Spectral Theory
9. Laplace Equation with Mixed Boundary Conditions
10. New Functional Spaces: Morrey and Campanato
11. Pseudo-Holomorphic and Polyharmonic Frameworks
3. Calculus of Variations
12. The Euler Equations
13. Classical Variational Problems
4. Linear and Non-linear Hyperbolic Equations
14. Characteristics and Waves, 1
15. Characteristics and Waves, 2
16. Fundamental Solution and Characteristic Conoid
17. How to Build the Fundamental Solution
18. Examples of Fundamental Solutions
19. Linear Systems of Normal Hyperbolic Form
20. Linear System from a Non-linear Hyperbolic System
21. Cauchy Problem for General Relativity
22. Causal Structure and Global Hyperbolicity
5. Parabolic Equations
23. The Heat Equation
24. The Nash Theorem on Parabolic Equations
6. Fuchsian Functions
25. The Poincaré Work on Fuchsian Functions
26. The Kernel of (Laplacian Plus Exponential)
7. A Window on Modern Theory
27. The Functional Equations of Number Theory
8. A Window on Modern Theory
28. The Symbol of Pseudo-Differential Operators
Backmatter

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