Material Detail

This is a complete college textbook, including a detailed Table of Contents, seventeen Chapters (each with a set of relevant homework problems), a list of References, two Appendices, and a detailed Index. The book is intended to enable students to:

• Solve first-, second-, and higher-order, linear, time-invariant (LTI) or­dinary differential equations (ODEs) with initial conditions and excitation, using both time-domain and Laplace-transform methods;
• Solve for the frequency response of an LTI system to periodic sinusoi­dal excitation and plot this response in standard form;
• Explain the role of the time constant in the response of a first-order LTI system, and the roles of natural frequency, damping ratio, and resonance in the response of a second-order LTI system;
• Derive and analyze mathematical models (ODEs) of low-order me­chanical systems, both translational and rotational, that are com­posed of inertial elements, spring elements, and damping devices;
• Derive and analyze mathematical models (ODEs) of low-order electri­cal circuits composed of resistors, capacitors, inductors, and op­erational amplifiers;
• Derive (from ODEs) and manipulate Laplace transfer functions and block diagrams representing output-to-input relationships of discrete ele­ments and of systems;
• Define and evaluate the stability of an LTI system;
• Explain proportional, integral, and derivative types of feedback control for single-input, single-output (SISO), LTI systems;
• Sketch the locus of characteristic values, as a control parameter varies, for a feedback-controlled SISO, LTI system;
• Use MATLAB as a tool to study the time and frequency responses of LTI systems.

The general minimum prerequisite for understanding this book is the intellectual matur­ity of a junior-level (third-year) college student in an accredited four-year engineering curriculum.  A mathematical second-order system is represented in this book primarily by a single second-order ODE, not in the state-space form by a pair of coupled first-order ODEs.  Similarly, a two-degrees-of-freedom (fourth-order) system is represented by two coupled second-order ODEs, not in the state-space form by four coupled first-order ODEs.  The book does not use bond graph modeling, the general and powerful, but complicated, modern tool for analysis of complex, multidisciplinary dynamic systems.  The homework problems at the ends of chapters are very important to the learning objectives, so the author attempted to compose problems of practical interest and to make the problem statements as clear, correct, and unambiguous as possible.  A major focus of the book is computer calculation of system characteristics and responses and graphical display of results, with use of basic (not advanced) MATLAB commands and programs.  

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