- Preface
-
1 Origins and History of Partial Differential Equations
- 1.1 Functions of Several Variables and the Notion of a PDE
- 1.2 D’Alembert and the Question of Data
- 1.3 Cauchy, Characteristics, and the Answer
-
2 General First-Order Equations and Their Classification
- 2.1 Partial Differential Equations and Their Classification
- 2.2 Hypersurfaces, Hyperplanes, and the Cauchy Problem
-
3 Linear Equations and the Method of Characteristics
- 3.1 Why the Characteristics Are the Right Object to Study
- 3.2 The Noncharacteristic Condition
- 3.3 Worked Examples in the Linear Setting
-
4 Semilinear Equations and Fixed Characteristic Propagation
- 4.1 How the Semilinear Case Differs from the Linear
- 4.2 Worked Examples of Semilinear Equations
-
5 Quasilinear Equations and Coupled Characteristics
- 5.1 How the Quasilinear Case Differs from the Semilinear
- 5.2 Worked Examples of Quasilinear Equations
-
6 Fully Nonlinear Equations and Extended Characteristics
- 6.1 Why the Characteristics Must Be Extended into a Larger Space
- 6.2 The Extended Characteristic System
- 6.3 Worked Examples of Fully Nonlinear Equations
- 7 Closing Remarks on the Method of Characteristics
First-Order Partial Differential Equations and the Method of Characteristics
A Foundation Course in Classical PDE Theory
This book is 100% completeLast updated on 2026-07-09
How first-order PDEs propagate data along characteristics, from linear to fully nonlinear settings with explicit step-by-step solutions throughout.
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How first-order PDEs propagate data along characteristics, from linear to fully nonlinear settings with explicit step-by-step solutions throughout.
Author
About the Author
Abdurrahman Tukur
A master's student in applied mathematics specializing in disease epidemiology modeling, a zbMATH Open reviewer authoring post-publication reviews, and a writer committed to science communication and personal essay writing, aiming to produce short course books tied mostly to mathematical biology, publish essays, and grow further as a writer.
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