An Introduction to First-Order Partial Differential Equations and the Method of Characteristics

A Foundation Course in Classical PDE Theory

This book is 100% completeLast updated on 2026-05-23

A short course book on the classical theory of the method of characteristics for first-order partial differential equations, taking you from first principles to explicit solutions in twenty pages, and working through every example step by step.

This book is 100% completeLast updated on 2026-05-23

Abdurrahman Tukur

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This is a course book of 20 pages on the method of characteristics as a tool for finding classical solutions to first-order partial differential equations—starting from the historical origins of PDEs in the vibrating string and the heat equation, it develops the Cauchy problem, the noncharacteristic condition, and the full hierarchy of four equation types (linear, semilinear, quasilinear, and fully nonlinear)—with worked examples carried through to explicit solutions at every level, and the only assumed background is calculus of several variables and ordinary differential equations.

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Abdurrahman Tukur

As a writer committed to science communication and creative writing, I am also a master's student in applied mathematics with a particular interest in disease epidemiology modeling, and a zbMATH Open reviewer, where I author post-publication reviews. All my work explores the intersections of scientific inquiry with human experience, with the long-term goal of publishing essays, growing as a writer, and authoring self-guided course books. And my personal website is on own2share.wordpress.com.

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