- Develops students’ intuition by building the mathematical theory from the ground up and illustrating the theorems with examples
- Demonstrates the analysis of mathematical models through concrete applications
- Uses MATLAB GUIs that enable students to discover patterns and make conjectures
- Presents heuristic commentary and motivation in each chapter
- Includes numerous hands-on student activities that facilitate exploration of the tools and models
- Provides MATLAB GUIs as well as solutions and hints to exercises on a supplementary web page
A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance.
The first part of the book presents systems of linear ODEs. The text develops mathematical models from ten disparate fields, including pharmacokinetics, chemistry, classical mechanics, neural networks, physiology, and electrical circuits. Focusing on linear PDEs, the second part covers PDEs that arise in the mathematical modeling of phenomena in ten other areas, including heat conduction, wave propagation, fluid flow through fissured rocks, pattern formation, and financial mathematics.
The authors engage students by posing questions of all types throughout, including verifying details, proving conjectures of actual results, analyzing broad strokes that occur within the development of the theory, and applying the theory to specific models. The authors’ accessible style encourages students to actively work through the material and answer these questions. In addition, the extensive use of MATLAB®GUIs allows students to discover patterns and make conjectures.