09-03-2026, 11:54 PM
Ordinary Differential Equations
Authors: William A. Adkins, Mark G. Davidson
Publication date: July 1, 2012
Publisher: Springer New York
Ordinary Differential Equations is an undergraduate textbook covering the standard theory and techniques of ordinary differential equations, aimed primarily at second-year mathematics, science, and engineering students. Its most distinctive feature is that the Laplace transform is introduced unusually early, immediately after first-order differential equations. The authors then use it systematically to motivate and simplify the solution of constant-coefficient linear differential equations and systems. The book assumes roughly one year of college calculus and combines computational techniques with a stronger theoretical component than many introductory ODE texts.
The material progresses from first-order differential equations to the Laplace transform, second-order and general linear equations, discontinuous and impulse-type functions, power-series methods, matrices, and finally systems of linear differential equations. The text also includes proofs that introductory books often omit, including the injectivity of the Laplace transform and existence-and-uniqueness results for constant-coefficient linear equations. Numerous examples and exercises are used throughout, while the final treatment of matrices and systems provides a bridge toward more advanced courses in differential equations, linear algebra, dynamical systems, and applied mathematics.
The book is therefore somewhat more mathematically substantial than a purely computational engineering ODE textbook. Reviews highlighted its clear exposition, its discussion of both the geometric and algebraic meaning of important theorems, and its suitability both for classroom teaching and independent study.
Key takeaways
Springer book page
Authors: William A. Adkins, Mark G. Davidson
Publication date: July 1, 2012
Publisher: Springer New York
Ordinary Differential Equations is an undergraduate textbook covering the standard theory and techniques of ordinary differential equations, aimed primarily at second-year mathematics, science, and engineering students. Its most distinctive feature is that the Laplace transform is introduced unusually early, immediately after first-order differential equations. The authors then use it systematically to motivate and simplify the solution of constant-coefficient linear differential equations and systems. The book assumes roughly one year of college calculus and combines computational techniques with a stronger theoretical component than many introductory ODE texts.
The material progresses from first-order differential equations to the Laplace transform, second-order and general linear equations, discontinuous and impulse-type functions, power-series methods, matrices, and finally systems of linear differential equations. The text also includes proofs that introductory books often omit, including the injectivity of the Laplace transform and existence-and-uniqueness results for constant-coefficient linear equations. Numerous examples and exercises are used throughout, while the final treatment of matrices and systems provides a bridge toward more advanced courses in differential equations, linear algebra, dynamical systems, and applied mathematics.
The book is therefore somewhat more mathematically substantial than a purely computational engineering ODE textbook. Reviews highlighted its clear exposition, its discussion of both the geometric and algebraic meaning of important theorems, and its suitability both for classroom teaching and independent study.
Key takeaways
- Introduces the Laplace transform very early and makes it a central tool throughout the course.
- Covers the complete standard undergraduate ODE syllabus, including $1^{st}$- and $2^{nd}$-order equations, linear systems, power series, and matrices.
- Gives more theoretical justification and proofs than many introductory differential-equations textbooks.
- Particularly suitable for mathematics students or engineering/science students who want to understand why the methods work, rather than only learning computational recipes.
Springer book page
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