09-03-2026, 11:44 PM
Introduction to Partial Differential Equations
Author: Peter J. Olver
Publication date: 2014 (eBook first published 8 November 2013)
Publisher: Springer Cham
Peter J. Olver’s Introduction to Partial Differential Equations is a comprehensive introductory textbook intended for advanced undergraduate and beginning graduate students in mathematics, science, and engineering. It balances three major aspects of PDEs: practical methods for solving equations, rigorous mathematical theory, and applications. The book assumes no previous course in PDEs or Fourier analysis; the main prerequisites are multivariable calculus, ordinary differential equations, and elementary linear algebra.
The text begins with the basic nature of partial differential equations and then develops the classical theory through wave equations, Fourier series, separation of variables, boundary-value problems, Fourier transforms, generalized functions, and Green's functions. It also goes substantially beyond the traditional introductory syllabus, treating linear and nonlinear waves, shock phenomena, evolution equations, maximum principles, symmetry and similarity methods, weak solutions, finite elements, dispersion, planar media, and higher-dimensional PDEs. Numerical methods receive serious attention as well, particularly finite-difference and finite-element techniques.
A major strength is the large collection of exercises accompanying almost every section. These range from routine calculations to theoretical proofs, computational projects, and more challenging conceptual problems. This makes the book particularly suitable for a full-year PDE course or for independent study. Overall, it is broader than many first PDE textbooks and gives students a strong bridge between classical techniques and more modern areas of PDE research.
Main topics
BOOK
Author: Peter J. Olver
Publication date: 2014 (eBook first published 8 November 2013)
Publisher: Springer Cham
Peter J. Olver’s Introduction to Partial Differential Equations is a comprehensive introductory textbook intended for advanced undergraduate and beginning graduate students in mathematics, science, and engineering. It balances three major aspects of PDEs: practical methods for solving equations, rigorous mathematical theory, and applications. The book assumes no previous course in PDEs or Fourier analysis; the main prerequisites are multivariable calculus, ordinary differential equations, and elementary linear algebra.
The text begins with the basic nature of partial differential equations and then develops the classical theory through wave equations, Fourier series, separation of variables, boundary-value problems, Fourier transforms, generalized functions, and Green's functions. It also goes substantially beyond the traditional introductory syllabus, treating linear and nonlinear waves, shock phenomena, evolution equations, maximum principles, symmetry and similarity methods, weak solutions, finite elements, dispersion, planar media, and higher-dimensional PDEs. Numerical methods receive serious attention as well, particularly finite-difference and finite-element techniques.
A major strength is the large collection of exercises accompanying almost every section. These range from routine calculations to theoretical proofs, computational projects, and more challenging conceptual problems. This makes the book particularly suitable for a full-year PDE course or for independent study. Overall, it is broader than many first PDE textbooks and gives students a strong bridge between classical techniques and more modern areas of PDE research.
Main topics
- Linear and nonlinear wave equations
- Fourier series and Fourier transforms
- Separation of variables
- Boundary-value problems
- Finite-difference methods
- Generalized functions and Green's functions
- Linear and nonlinear evolution equations
- Weak solutions
- Finite-element methods
- Dynamics of two- and three-dimensional media
- Shock waves, dispersion, symmetry, and similarity methods
BOOK
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