Ebook: Partial Differential Equations: Second Edition

This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton--Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions.

Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct misprints, and improve clarity. The work can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists.

The newly added three last chapters, on first order non-linear PDEs (Chapter 8), quasilinear elliptic equations with measurable coefficients (Chapter 9) and DeGiorgi classes (Chapter 10), point to issues and directions at the forefront of current investigations.

Reviews of the first edition:

The author's intent is to present an elementary introduction to PDEs... In contrast to other elementary textbooks on PDEs . . . much more material is presented on the three basic equations: Laplace's equation, the heat and wave equations. . . . The presentation is clear and well organized. . . . The text is complemented by numerous exercises and hints to proofs.

---Mathematical Reviews

This is a well-written, self-contained, elementary introduction to linear, partial differential equations.

---Zentralblatt MATH

---

This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton--Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions.

Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct misprints, and improve clarity. The work can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists.

The newly added three last chapters, on first order non-linear PDEs (Chapter 8), quasilinear elliptic equations with measurable coefficients (Chapter 9) and DeGiorgi classes (Chapter 10), point to issues and directions at the forefront of current investigations.

Reviews of the first edition:

The author's intent is to present an elementary introduction to PDEs... In contrast to other elementary textbooks on PDEs . . . much more material is presented on the three basic equations: Laplace's equation, the heat and wave equations. . . . The presentation is clear and well organized. . . . The text is complemented by numerous exercises and hints to proofs.

---Mathematical Reviews

This is a well-written, self-contained, elementary introduction to linear, partial differential equations.

---Zentralblatt MATH

---

This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton--Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions.

Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct misprints, and improve clarity. The work can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists.

The newly added three last chapters, on first order non-linear PDEs (Chapter 8), quasilinear elliptic equations with measurable coefficients (Chapter 9) and DeGiorgi classes (Chapter 10), point to issues and directions at the forefront of current investigations.

Reviews of the first edition:

The author's intent is to present an elementary introduction to PDEs... In contrast to other elementary textbooks on PDEs . . . much more material is presented on the three basic equations: Laplace's equation, the heat and wave equations. . . . The presentation is clear and well organized. . . . The text is complemented by numerous exercises and hints to proofs.

---Mathematical Reviews

This is a well-written, self-contained, elementary introduction to linear, partial differential equations.

---Zentralblatt MATH

Content:
Front Matter....Pages 1-20
Preliminaries....Pages 1-16
Quasi-Linear Equations and the Cauchy–Kowalewski Theorem....Pages 17-35
The Laplace Equation....Pages 37-86
Boundary Value Problems by Double-Layer Potentials....Pages 87-107
Integral Equations and Eigenvalue Problems....Pages 109-134
The Heat Equation....Pages 135-181
The Wave Equation....Pages 183-224
Quasi-Linear Equations of First-Order....Pages 225-263
Non-Linear Equations of First-Order....Pages 265-295
Linear Elliptic Equations with Measurable Coefficients....Pages 297-345
DeGiorgi Classes....Pages 347-371
Back Matter....Pages 1-17

---

This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton--Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions.

Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct misprints, and improve clarity. The work can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists.

The newly added three last chapters, on first order non-linear PDEs (Chapter 8), quasilinear elliptic equations with measurable coefficients (Chapter 9) and DeGiorgi classes (Chapter 10), point to issues and directions at the forefront of current investigations.

Reviews of the first edition:

The author's intent is to present an elementary introduction to PDEs... In contrast to other elementary textbooks on PDEs . . . much more material is presented on the three basic equations: Laplace's equation, the heat and wave equations. . . . The presentation is clear and well organized. . . . The text is complemented by numerous exercises and hints to proofs.

---Mathematical Reviews

This is a well-written, self-contained, elementary introduction to linear, partial differential equations.

---Zentralblatt MATH

Content:
Front Matter....Pages 1-20
Preliminaries....Pages 1-16
Quasi-Linear Equations and the Cauchy–Kowalewski Theorem....Pages 17-35
The Laplace Equation....Pages 37-86
Boundary Value Problems by Double-Layer Potentials....Pages 87-107
Integral Equations and Eigenvalue Problems....Pages 109-134
The Heat Equation....Pages 135-181
The Wave Equation....Pages 183-224
Quasi-Linear Equations of First-Order....Pages 225-263
Non-Linear Equations of First-Order....Pages 265-295
Linear Elliptic Equations with Measurable Coefficients....Pages 297-345
DeGiorgi Classes....Pages 347-371
Back Matter....Pages 1-17
....