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ebook
"Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student's place, and have chosen to err on the side of too much detail rather than not enough. An elementary text can't be better than its exercises. This text includes 2041 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and defonitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 299 completely worked out examples. Where appropriate, concepts and results are depicted in 188 figures."BCcampus website.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations Textbooks
 Resource Type:
 ebook

ebook
This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take. This book consists of 10 chapters, and the course is 12 weeks long. Each chapter is covered in a week, and in the remaining two weeks I summarize the entire course, answer lots of questions, and prepare the students for the exam. I do not cover the material in the appendices in the lectures. Some of it is basic material that the students have already seen that I include for completeness and other topics are "tasters" for more advanced material that students will encounter in later courses or in their project work. Students are very curious about the notion of chaos, and I have included some material in an appendix on that concept. The focus in that appendix is only to connect it with ideas that have been developed in this course related to ODEs and to prepare them for more advanced courses in dynamical systems and ergodic theory that are available in their third and fourth years.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations Textbooks Differential equations Partial
 Resource Type:
 ebook

ebook
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 higherorder, linear, timeinvariant (LTI) ordinary differential equations (ODEs) with initial conditions and excitation, using both timedomain and Laplacetransform 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 firstorder LTI system, and the roles of natural frequency, damping ratio, and resonance in the response of a secondorder LTI system; Derive and analyze mathematical models (ODEs) of loworder mechanical systems, both translational and rotational, that are composed of inertial elements, spring elements, and damping devices; Derive and analyze mathematical models (ODEs) of loworder electrical circuits composed of resistors, capacitors, inductors, and operational amplifiers; Derive (from ODEs) and manipulate Laplace transfer functions and block diagrams representing outputtoinput 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 singleinput, singleoutput (SISO), LTI systems; Sketch the locus of characteristic values, as a control parameter varies, for a feedbackcontrolled SISO, LTI system; Use MATLAB as a tool to study the time and frequency responses of LTI systems. The book's general organization is: Chapters 110 deal primarily with the ODEs and behaviors of firstorder and secondorder dynamic systems; Chapters 11 and 12 discuss the ODEs and behaviors of mechanical systems having two degrees of freedom, i.e., fourthorder systems; Chapters 13 and 14 introduce classical feedback control; Chapter 15 presents the basic features of proportional, integral, and derivative types of classical control; Chapters 16 and 17 discuss methods for analyzing the stability of classical control systems. The general minimum prerequisite for understanding this book is the intellectual maturity of a juniorlevel (thirdyear) college student in an accredited fouryear engineering curriculum. A mathematical secondorder system is represented in this book primarily by a single secondorder ODE, not in the statespace form by a pair of coupled firstorder ODEs. Similarly, a twodegreesoffreedom (fourthorder) system is represented by two coupled secondorder ODEs, not in the statespace form by four coupled firstorder 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. The book includes many examples and homework problems relevant to aerospace engineering, among which are rolling dynamics of flight vehicles, spacecraft actuators, aerospace motion sensors, and aeroelasticity. There are also several examples and homework problems illustrating and validating theory by using measured data to identify first and secondorder system dynamic characteristics based on mathematical models (e.g., time constants and natural frequencies), and system basic properties (e.g., mass, stiffness, and damping). Applications of real and simulated experimental data appear in many homework problems. The book contains somewhat more material than can be covered during a single standard college semester, so an instructor who wishes to use this as a onesemester course textbook should not attempt to cover the entire book, but instead should cover only those parts that are most relevant to the course objectives.
 Keywords:
 Differential equations Engineering mathematics Differential equations Partial Textbooks
 Resource Type:
 ebook

ebook
A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. This free online book (ebook in webspeak) should be usable as a standalone textbook or 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 UrbanaChampaign Sample Dirichlet problem solution (one is a 4dayaweek, the other a 3dayaweek semesterlong course). I have also taught Math 20D at University of California, San Diego with these notes (a 3dayaweek quarterlong course). There is enough material to run a 2quarter course, and even perhaps a two semester course depending on lecturer speed.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations Textbooks Boundary value problems
 Resource Type:
 ebook

Courseware
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Differential equations
 Resource Type:
 Courseware