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E-grāmata: Elementary Differential Equations: Applications, Models, and Computing

(Indiana State University, Terre Haute, USA)
  • Formāts: 554 pages
  • Sērija : Textbooks in Mathematics
  • Izdošanas datums: 13-Dec-2018
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-13: 9781498776103
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Elementary Differential Equations: Applications, Models, and ComputingPalielināt
  • Formāts: 554 pages
  • Sērija : Textbooks in Mathematics
  • Izdošanas datums: 13-Dec-2018
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-13: 9781498776103
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Elementary Differential Equations, Second Edition is written with the knowledge that there has been a dramatic change in the past century in how solutions to differential equations are calculated. However, the way the topic has been taught in introductory courses has barely changed to reflect these advances, which leaves students at a disadvantage. This second edition has been created to address these changes and help instructors facilitate new teaching methods and the latest tools, which includes computers.

The text is designed to help instructors who want to use computers in their classrooms. It accomplishes this by emphasizing and integrating computers in teaching elementary or ordinary differential equations. Many examples and exercises included in the text require the use of computer software to solve problems. It should be noted that since instructors use their own preferred software, this book has been written to be independent of any specific software package.

Features:











Focuses on numerical methods and computing to generate solutions





Features extensive coverage of nonlinear differential equations and nonlinear systems





Includes software programs to solve problems in the text which are located on the author's website





Contains a wider variety of non-mathematical models than any competing textbook

This second edition is a valuable, up-to-date tool for instructors teaching courses about differential equations. It serves as an excellent introductory textbook for undergraduate students majoring in applied mathematics, computer science, various engineering disciplines and other sciences. They also will find that the textbook will aide them greatly in their professional careers because of its instructions on how to use computers to solve equations.
Preface xi
1 Introduction
1(32)
1.1 Historical Prologue
1(4)
1.2 Definitions and Terminology
5(12)
1.3 Solutions and Problems
17(10)
1.4 A Nobel Prize Winning Application
27(6)
2 The Initial Value Problem y' = f(x,y); y(c) = d
33(60)
2.1 Direction Fields
34(8)
2.2 Fundamental Theorems
42(12)
2.3 Solution of Simple First-Order Differential Equations
54(19)
2.3.1 Solution of y' = g(x)
54(3)
2.3.2 Solution of the Separable Equation y' = g(x)/h(y)
57(7)
2.3.3 Solution of the Linear Equation y' = a(x)y + b(x)
64(9)
2.4 Numerical Solution
73(20)
2.4.1 Euler's Method
77(5)
2.4.2 Pitfalls of Numerical Methods
82(11)
3 Applications of the Initial Value Problem y' = f(x, y); y(c) = d
93(50)
3.1 Calculus Revisited
93(11)
3.2 Learning Theory Models
104(2)
3.3 Population Models
106(7)
3.4 Simple Epidemic Models
113(5)
3.5 Falling Bodies
118(3)
3.6 Mixture Problems
121(7)
3.7 Curves of Pursuit
128(4)
3.8 Chemical Reactions
132(11)
4 N-th Order Linear Differential Equations
143(56)
4.1 Basic Theory
144(21)
4.2 Roots of Polynomials
165(12)
4.3 Homogeneous Linear Equations with Constant Coefficients
177(11)
4.4 Nonhomogeneous Linear Equations with Constant Coefficients
188(7)
4.5 Initial Value Problems
195(4)
5 The Laplace Transform Method
199(48)
5.1 The Laplace Transform and Its Properties
199(17)
5.2 Using the Laplace Transform and Its Inverse to Solve Initial Value Problems
216(8)
5.3 Convolution and the Laplace Transform
224(6)
5.4 The Unit Function and Time-Delay Function
230(9)
5.5 Impulse Function
239(8)
6 Applications of Linear Differential Equations with Constant Coefficients
247(38)
6.1 Second-Order Differential Equations
247(22)
6.1.1 Free Motion
253(1)
6.1.1.1 Free Undamped Motion
254(1)
6.1.1.2 Free Damped Motion
255(9)
6.1.2 Forced Motion
264(1)
6.1.2.1 Undamped Forced Motion
264(1)
6.1.2.2 Damped Forced Motion
265(4)
6.2 Higher Order Differential Equations
269(16)
7 Systems of First-Order Differential Equations
285(20)
7.1 Properties of Systems of Differential Equations
285(12)
7.2 Writing Systems as Equivalent First-Order Systems
297(8)
8 Linear Systems of First-Order Differential Equations
305(42)
8.1 Matrices and Vectors
305(12)
8.2 Eigenvalues and Eigenvectors
317(13)
8.3 Linear Systems with Constant Coefficients
330(17)
9 Applications of Linear Systems with Constant Coefficients
347(22)
9.1 Coupled Spring-Mass Systems
347(6)
9.2 Pendulum Systems
353(2)
9.3 The Path of an Electron
355(5)
9.4 Mixture Problems
360(9)
10 Applications of Systems of Equations
369(90)
10.1 Richardson's Arms Race Model
369(9)
10.2 Phase-Plane Portraits
378(16)
10.3 Modified Richardson's Arms Race Models
394(11)
10.4 Lanchester's Combat Models
405(7)
10.5 Models for Interacting Species
412(18)
10.6 Epidemics
430(10)
10.7 Pendulums
440(9)
10.8 Duffing's Equation
449(1)
10.9 Van der Pol's Equation
450(1)
10.10 Mixture Problems
451(3)
10.11 The Restricted Three-Body Problem
454(5)
Appendix A Numerical Solution of the Initial Value Problem y' = f(x, y); y(c) =d 459(30)
Answers to Selected Exercises 489(34)
References 523(4)
Index 527
Charles E. Roberts, Jr. is a Professor Emeritus in the Department of Mathematics and Computer Science at Indiana State University. He has written other books and papers about ordinary differential equations.
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