A First Course in Differential Equations, Modeling, and Simulation

A First Course in Differential Equations, Modeling, and Simulation shows how differential equations arise from applying basic physical principles and experimental observations to engineering systems. Avoiding overly theoretical explanations, the textbook also discusses classical and Laplace transform methods for obtaining the analytical solution of differential equations. In addition, the authors explain how to solve sets of differential equations where analytical solutions cannot easily be obtained. Incorporating valuable suggestions from mathematicians and mathematics professors, the third edition: - Reworks the chapter "Response of First and Second Order Systems" to include the system response to step changes, impulses, rectangular pulses, and sinusoid forcing functions as well as the response of coupled first- and second-order ordinary differential equations (ODEs); it also introduces Bode plots to analyze the frequency response of second-order ODEs and the principle of oscillation modes in coupled second-order ODEs - Adds a new section on springs and dampers in series or parallel - Includes new content on Simulink® and modeling - Contains new exercises that can be used as projects and answers to many of the end-ofchapter problems - Features new end-of-chapter problems and updates throughout This textbook provides students with a practical understanding of how to apply differential equations in modern engineering and science. A solutions manual and files of all figures in the text are available to adopting professors.

Carlos A. Smith is Professor Emeritus of Chemical Engineering at the University of South Florida. He has been on the faculty for 52 years, serving in different capacities. Professor Smith has lectured in Europe and many countries in Latin America. He is the coauthor of three editions of a textbook on process control and the author of another book on the same subject. These books have been translated into Spanish and Portuguese. Scott W. Campbell served on the faculty of the Department of Chemical, Biological & Materials Engineering at the University of South Florida from 1986 until he retired in 2022. After a year away, he has returned to teach part-time, including the course that uses this textbook. He has authored or co-authored over 60 technical peer-reviewed articles, mostly in the area of thermodynamics, and has received numerous teaching awards at the department, college, university, and state levels. Ryan G. Toomey is a professor of chemical engineering at the University of South Florida. Following receipt of his BS (University of California Berkeley, 1996) and PhD (University of Minnesota, 2002) in chemical engineering, he was a postdoctoral associate with the Institute for Microsystems Technology at the University of Freiburg (Germany). His research activities focus primarily on using responsive, surface-tethered polymer networks to mediate interfacial interactions. His group is concerned with structure-property-function relationships of stimuli-sensitive polymers in confined geometries and how volume-phase transitions in thin films can be harnessed to direct and control adsorption and desorption phenomena at surfaces. He is the recipient of a Camille and Henry Dreyfus New Faculty Award (2005), a National Science Foundation CAREER Award (2007), and the Outstanding American Institute of Chemical Engineers student chapter advisor award (2023).

1 Introduction. 2 Objects in a Gravitational Field. 3 Classical Solutions of Ordinary Linear Differential Equations. 4 Laplace Transforms. 5 Response of First- and Second-Order Systems. 6 Mechanical Systems: Translational. 7 Mechanical Systems: Rotational. 8 Mass Balances. 9 Thermal Systems.10 Electrical Systems..11 Numerical Simulation. Answers to Selected Problems