Introduction to Partial Differential Equations

• Main Author: Olver, Peter J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Fourier analysis.; Partial differential equations.; System theory.; Partial Differential Equations.; Complex Systems.; Fourier Analysis.

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...

Table of Contents:

• What are Partial Differential Equations?
• Linear and Nonlinear Waves
• Fourier Series
• Separation of Variables
• Finite Differences
• Generalized Functions and Green’s Functions
• Complex Analysis and Conformal Mapping
• Fourier Transforms
• Linear and Nonlinear Evolution Equations
• A General Framework for Linear Partial Differential Equations
• Finite Elements and Weak Solutions
• Dynamics of Planar Media
• Partial Differential Equations in Space .