2016 by Wiliam Hallauerl, Virginia Tech.
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 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.
Updated 2020 by Jirí Lebl, Oklahoma State University.
A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. Can be used as a companion to a course using another book such as Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling or Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (section correspondence to these two is given). I developed and used these notes to teach Math 286/285 at the University of Illinois at Urbana-Champaign S
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