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?
Perfect book for a One-semester PDE course
Includes a thorough discussion of modeling process for each equation
Covers indepth three types of linear PDES: elliptic, parabolic, and hyperbolic
3. Conservation Equations and Characteristics
4. The Wave Equation
5. Separation of Variables
6. The Heat Equation
7. Function Spaces
8. Fourier Series
9. Maximum Principles
10. Weak Solutions
11. Variational Methods
13. The Fourier Transform
A. Appendix: Analysis Foundations
“The book under review is intended for an introductory course for students. The 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)
ABOUT THE AUTHOR
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- Neural Networks P.D. Picton
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