Introduction to Partial Differential Equation – David Borthwick – 1st Edition


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:

1. What is the scientific problem we are trying to understand?
2. How do we model that with PDE?
3. What techniques can we use to analyze the PDE?
4. How do those techniques apply to this equation?
5. What information or insight did we obtain by developing and analyzing the PDE?

The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.

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  • Chapter 1. Introduction
    Chapter 2. Preliminaries
    Chapter 3. Conservation Equations and Characteristics
    Chapter 4. TheWave Equation
    Chapter 5. Separation of Variables
    Chapter 6. The Heat Equation
    Chapter 7. Function Spaces
    Chapter 8. Fourier Series
    Chapter 9. Maximum Principles
    Chapter 10. Weak Solutions
    Chapter 11. Variational Methods
    Chapter 12. Distributions
    Chapter 13. The Fourier Transform
    Chapter 14. Introduction to Partial Differential Equations
  • Citation
    • Full Title: Introduction to Partial Differential Equation
    • Author/s:
    • ISBN-10: 3319489348
    • ISBN-13: 9783319489346
    • Edition: 1st Edition
    • Publication date: 2017
    • Topic: Math
    • Subtopic: Differential Equations
    • File Type: eBook
    • Idioma: English

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