Introduction to Partial Differential Equation – Peter J. Olver – 1st Edition


This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples.

Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject.

No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green’s functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens’ Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research.

Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.

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  • Chapter 1. What are Partial Differential Equations?
    Chapter 2. Linear and Nonlinear Waves
    Chapter 3. Fourier Series
    Chapter 4. Separation of Variables
    Chapter 5. Finite Differences
    Chapter 6. Generalized Functions and Green’s Functions
    Chapter 7. Complex Analysis and Conformal Mapping
    Chapter 8. Fourier Transforms
    Chapter 9. Linear and Nonlinear Evolution Equations
    Chapter 10. A General Framework for Linear Partial Differential Equations
    Chapter 11. Finite Elements and Weak Solutions
    Chapter 12. Dynamics of Planar Media
    Chapter 13. Partial Differential Equations in Space
  • Citation
    • Full Title: Introduction to Partial Differential Equation
    • Author/s:
    • ISBN-10: 3319020986
    • ISBN-13: 9783319020983
    • Edition: 1st Edition
    • Publication date: 2013
    • Topic: Math
    • Subtopic: Differential Equations
    • File Type: eBook
    • Idioma: English

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