A First Course in Differential Equations, Modeling, and SimulationEmphasizing a practical approach for engineers and scientists, A First Course in Differential Equations, Modeling, and Simulation avoids overly theoretical explanations and shows readers how differential equations arise from applying basic physical principles and experimental observations to engineering systems. It also covers classical methods for |
Contents
Introduction | 1 |
Objects in a Gravitational Field | 15 |
Classical Solutions of Ordinary Linear Differential Equations | 29 |
Laplace Transforms | 81 |
Mechanical Systems Translational | 137 |
Mechanical Systems Rotational | 175 |
Mass Balances | 201 |
Thermal Systems | 223 |
Electrical Systems | 249 |
Numerical Simulation | 295 |
Back Cover | 327 |
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algebraic analytical solution angular applied force Assuming block diagram capacitor chapter characteristic equation circuit shown coefficient constant convection damping dashpot dependent variable describes the position Develop the model differential equation displacement dt dt dx dt dy dt energy Euler’s method Example exiting exponential expression fA(t first-order flow rate fluid friction forcing function Free body diagrams given by Equation graph heat transfer inductor initial conditions input integrator kg/min Laplace transform linear mass balance mass flow rate mass fraction Mechanical system model that describes NaOH node Note Obtain the analytical particular solution pellet RC circuit rearranging response roots rotational second-order Section shown in Figure shows simulation sole plate spring steady steady-state step change step response Substituting Equations system for Problem system shown tank temperature term theorem tion torque torsion spring transfer function unknowns valve velocity voltage drop voltage source yields zero