introduction to linear time invariant dynamic systems

This is a complete college textbook, or workbook, 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 stability for 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.