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Full Description
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.
Contents
ORDINARY DIFFERENTIAL EQUATIONS: Welcome! A Basic Analysis Toolbox. A First Wave of Mathematical Models. Finite-Dimensional Theory—Ground Zero: The Homogenous Case. Finite-Dimensional Theory—Next Step: The Non-Homogenous Case. A Second Wave of Mathematical Models—Now, with Nonlinear Interactions. Finite-Dimensional Theory—Last Step: The Semi-Linear Case. ABSTRACT ORDINARY DIFFERENTIAL EQUATIONS: Getting the Lay of a New Land. Three New Mathematical Models. Formulating a Theory for (A-HCP). The Next Wave of Mathematical Models—With Forcing. Remaining Mathematical Models. Formulating a Theory for (A-NonCP). A Final Wave of Models—Accounting for Semilinear Effects. Appendix. Bibliography. Index.
