Differential Equations as a Language for Engineering Systems
Differential equations occupy a central position in engineering mathematics, yet they are often introduced as a collection of solution techniques rather than as a modeling language. In engineering practice, differential equations are not merely mathematical objects; they are the formal expression of how systems evolve in time.
Differential Equations for Engineering Systems was developed at Maxdi Research to restore this perspective.
Link to obtain a digital copy: Differential Equations for Engineering Systems: Modeling, Analysis, and Transform-Based Solution Methods
The book approaches ordinary differential equations as models of dynamic behavior, emphasizing formulation, interpretation, and system response rather than procedural manipulation. From first-order dynamics to higher-order linear systems, the focus remains on understanding what a solution represents in an engineering context.
A defining feature of the text is the integration of transform methods into the core narrative. Laplace transforms are not treated as an auxiliary topic, but as a natural extension of system modeling, enabling efficient solution of initial-value problems and direct insight into stability and transient behavior.
Throughout the book, mathematical solutions are consistently linked to physical meaning. Step responses, impulse inputs, and exponential excitations are analyzed not only for correctness, but for what they reveal about system structure and performance. This alignment between mathematics and engineering interpretation is essential for both advanced study and professional practice.
The text also reflects a broader research philosophy at Maxdi Research: mathematical clarity is a prerequisite for meaningful engineering innovation. Whether applied to classical systems or emerging computational paradigms, differential equations remain one of the most powerful tools available to engineers.
This book represents an effort to present that tool in a form that is coherent, rigorous, and directly aligned with how engineers think.
Jan 16, 2026
Mahdi Haghzadeh, PhD
Maxdi Research — Cognitave Inc.
