Differential Equations: Modeling with MATLAB
Utilizing MATLAB's computational and graphical tools right from the start, this analysis of differential equations helps users probe a variety of mathematical models, encouraging them to develop problem-solving skills and independent judgment as they derive mathematical models, select approaches to their analysis, and find answers to the original physical questions. Providing immediate graphic and numeric support, it demonstrates how physical problems motivate the central ideas and techniques of differential equations, showing how they model physical phenomena by examining ideas from four perspectives: geometric, analytic, numeric, and physical.Introduces qualitative analysis and numerical methods for scalar equations and systems early on, without sacrificing coverage of the most important traditional analytical methods. Fully integrates MATLAB into the text and exercises, and uses mathematical models of physical problems throughout to emphasize the interplay between the physical problem and the analytic, graphical, and numeric information available from the differential equation model. Seamlessly integrates over 1,400 exercises, open-ended chapter projects, and motivational 'Thought Questions'.For scientists and engineers.