An Introduction to Differential Equations: Order and Chaos

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Editorial Reviews

In this text, Diacu (U. of Victoria) reconciles the split between the traditional approach to teaching calculus (and consequently that of differential equations) and a more intuitive one, commonly known as "reform." He eliminates the nonessential and heavy-going and includes the newer, more qualitative methods that cover all aspects of theory<- ->exact, qualitative, numerical, computer techniques, and some elements of modeling, thus providing a realistic view of the methods used today. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780716732969
  • Publisher: Freeman, W. H. & Company
  • Publication date: 8/28/2000
  • Edition number: 1
  • Pages: 450

Table of Contents

Preface ix
1 Introduction 1
2 First-Order Equations 13
2.1 Equations and Solutions 13
2.2 Separable Equations 21
2.3 Linear Equations 32
2.4 Qualitative Methods 41
2.5 Existence and Uniqueness 50
2.6 Numerical Methods 60
2.7 Computer Applications 68
2.8 Modeling Experiments 80
3 Second-Order Equations 83
3.1 Homogeneous Equations 83
3.2 Integrable Cases 92
3.3 Nonhomogeneous Equations 102
3.4 Harmonic Oscillators 110
3.5 Qualitative Methods 121
3.6 Numerical Methods 134
3.7 Computer Applications 142
3.8 Modeling Experiments 156
4 Linear Systems 159
4.1 Linear Algebra 159
4.2 Fundamental Results 169
4.3 Equations with Constant Coefficients 179
4.4 Qualitative Methods 189
4.5 Numerical Methods 200
4.6 Computer Applications 208
4.7 Modeling Experiments 222
5 Nonlinear Systems 225
5.1 Linearization 225
5.2 Periodic Solutions 235
5.3 Gradient and Hamiltonian Systems 241
5.4 Stability 251
5.5 Chaos 259
5.6 Modeling Experiments 266
6 The Laplace Transform 269
6.1 Fundamental Properties 269
6.2 Step Functions 277
6.3 Initial Value Problems 288
6.4 Computer Applications 297
6.5 Modeling Experiments 306
7 Power Series Solutions 309
7.1 The Power Series Method 309
7.2 Approximations 316
7.3 Regular Singular Points 323
7.4 Computer Applications 331
7.5 Modeling Experiments 343
Solutions to Odd Numbered Problems 345
Bibliography 389
Sources of Photographs 391
Index 393
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