Abell / Braselton Introductory Differential Equations

4. Auflage 2014
ISBN: 978-0-12-417282-1
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 530 Seiten

Introductory Differential Equations, Fourth Edition, offers both narrative explanations and robust sample problems for a first semester course in introductory ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. The book provides the foundations to assist students in learning not only how to read and understand differential equations, but also how to read technical material in more advanced texts as they progress through their studies. This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, and Fourier Series. It follows a traditional approach and includes ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple. Because many students need a lot of pencil-and-paper practice to master the essential concepts, the exercise sets are particularly comprehensive with a wide array of exercises ranging from straightforward to challenging. There are also new applications and extended projects made relevant to everyday life through the use of examples in a broad range of contexts. This book will be of interest to undergraduates in math, biology, chemistry, economics, environmental sciences, physics, computer science and engineering. - Provides the foundations to assist students in learning how to read and understand the subject, but also helps students in learning how to read technical material in more advanced texts as they progress through their studies - Exercise sets are particularly comprehensive with a wide range of exercises ranging from straightforward to challenging - Includes new applications and extended projects made relevant to 'everyday life' through the use of examples in a broad range of contexts - Accessible approach with applied examples and will be good for non-math students, as well as for undergrad classes

Martha L. Abell and James P. Braselton are graduates of the Georgia Institute of Technology and the Ohio State University, respectively, and teach at Georgia Southern University, Statesboro where they have extensive experience instructing students at both the undergraduate and graduate levels. Other books by the authors include Differential Equations with Mathematica and Mathematica by Example.

Autoren/Hrsg.

Abell, Martha L.

Braselton, James P.

Inhaltsverzeichnis

1;Front Cover ;1
2;Introductory Differential Equations;4
3;Copyright;5
4;Contents;6
5;Preface;8
5.1; Technology;9
5.2; Applications;9
5.3; Style;9
5.4; Features;10
5.5; Pedagogical Features;10
5.6; Content;12
6;Chapter 1: Introduction to Differential Equations;14
6.1;1.1 Introduction to Differential Equations: Vocabulary;16
6.2;Exercises 1.1;23
6.3;1.2 A Graphical Approach to Solutions: Slope Fields and Direction Fields;28
6.4;Exercises 1.2;32
6.5;Chapter 1 Summary: Essential Concepts and Formulas;35
6.6; Chapter 1 Review Exercises;36
7;Chapter 2: First-Order Equations;40
7.1;2.1 Introduction to First-Order Equations;40
7.2;Exercises 2.1;45
7.3;2.2 Separable Equations;46
7.4;Exercises 2.2;52
7.5;2.3 First-Order Linear Equations;57
7.6;Exercises 2.3;62
7.7;2.4 Exact Differential Equations;66
7.8;Exercises 2.4;70
7.9;2.5 Substitution Methodsand Special Equations;73
7.10;Exercises 2.5;77
7.11;2.6 Numerical Methods for First-Order Equations;82
7.12;Exercises 2.6;91
7.13;Chapter 2 Summary: Essential Concepts and Formulas;93
7.14;Chapter 2 Review Exercises;93
7.15;Differential Equations at Work;96
7.15.1;A. Modeling the Spread of a Disease;96
7.15.2;B. Linear Population Model with Harvesting;97
7.15.3;C. Logistic Model with Harvesting;98
7.15.4;D. Logistic Model with Predation;99
7.16;References;100
8;Chapter 3: Applications of First-Order Differential Equations;102
8.1;3.1 Population Growth and Decay;102
8.2;Exercises 3.1;110
8.3;3.2 Newton's Law of Cooling and Related Problems;115
8.4;Exercises 3.2;120
8.5;3.3 Free-Falling Bodies;122
8.6;Exercises 3.3;128
8.7;Chapter 3 Summary: Essential Concepts and Formulas;131
8.8;Chapter 3 Review Exercises;132
8.9;Differential Equations at Work;137
8.9.1;A. Mathematics of Finance;137
8.9.2;B. Algae Growth;139
8.9.3;C. Dialysis;140
8.9.4;D. Antibiotic Production;142
9;Chapter 4: Higher Order Equations;144
9.1;4.1 Second-Order Equations: An Introduction;145
9.2;Exercises 4.1;154
9.3;4.2 Solutions of Second-Order Linear Homogeneous Equations with Constant Coefficients;156
9.4;Exercises 4.2;160
9.5;4.3 Solving Second-Order Linear Equations: Undetermined Coefficients;162
9.6;Exercises 4.3;168
9.7;4.4 Solving Second-Order Linear Equations: Variation of Parameters;171
9.8;Exercises 4.4;176
9.9;4.5 Solving Higher Order Linear Homogeneous Equations;179
9.10;Exercises 4.5;188
9.11;4.6 Solving Higher Order Linear Equations: Undetermined Coefficients and Variation of Parameters;192
9.12;Exercises 4.6;200
9.13;4.7 Cauchy-Euler Equations;202
9.14;Exercises 4.7;208
9.15;4.8 Power Series Solutions of Ordinary Differential Equations;210
9.16;Exercises 4.8;216
9.17;4.9 Series Solutions of Ordinary Differential Equations;219
9.18;Exercises 4.9;228
9.19;Chapter 4 Summary: Essential Concepts and Formulas;231
9.20;Chapter 4 Review Exercises;232
9.21;Differential Equations at Work;234
9.21.1;A. Testing for Diabetes;234
9.21.2;B. Modeling the Motion of a Skier;235
9.21.3;C. The Schrödinger Equation;237
10;Chapter 5: Applications of Higher Order Differential Equations;240
10.1;5.1 Simple Harmonic Motion;240
10.2;Exercises 5.1;245
10.3;5.2 Damped Motion;247
10.4;Exercises 5.2;254
10.5;5.3 Forced Motion;256
10.6;Exercises 5.3;262
10.7;5.4 Other Applications;265
10.8;Exercises 5.4;270
10.9;5.5 The Pendulum Problem;272
10.10;Exercises 5.5;275
10.11;Chapter 5 Summary: Essential Concepts and Formulas;278
10.12;Chapter 5 Review Exercises;278
10.13;Differential Equations at Work;282
10.13.1;A. Rack-and-Gear Systems;282
10.13.2;B. Soft, Hard, and Aging Springs;283
10.13.3;C. Bodé Plots;284
10.13.4;D. The Catenary;285
10.13.5;E. The Wave Equation on a Circular Plate;285
10.13.6;F. Duffing’s Equation;286
10.13.7;G. Suspending an Object from a Cable;286
10.13.8;H. Can Resonance Impact Machinery?;287
10.13.9;I. Inventory Management;287
10.13.10;J. Heat Transfer;287
11;Chapter 6: Systems of Differential Equations;290
11.1;6.1 Introduction;290
11.2;Exercises 6.1;295
11.3;6.2 Review of Matrix Algebra and Calculus;298
11.4;Exercises 6.2;306
11.5;6.3 An Introduction to Linear Systems;308
11.6;Exercises 6.3;314
11.7;6.4 First-Order Linear Homogeneous Systems with Constant Coefficients;317
11.8;Exercises 6.4;329
11.9;6.5 First-Order Linear Nonhomogeneous Systems: Undetermined Coefficients and Variation of Parameters;332
11.10;Exercises 6.5;338
11.11;6.6 Phase Portraits;342
11.12;Exercises 6.6;352
11.13;6.7 Nonlinear Systems;354
11.14;Exercises 6.7;358
11.15;6.8 Numerical Methods;363
11.16;Exercises 6.8;368
11.17;Chapter 6 Summary: Essential Concepts and Formulas;370
11.18;Chapter 6 Review Exercises;370
11.19;Differential Equations at Work;372
11.19.1;A. Modeling a Fox Population in Which Rabies Is Present;372
11.19.2;B. Controlling the Spread of a Disease;373
11.19.3;C. FitzHugh-Nagumo Model;375
11.19.4;D. An Agricultural Model;375
11.19.5;E. Modeling the Spread of Dengue in Indonesia;376
12;Chapter 7: Applications of Systems of Ordinary Differential Equations;378
12.1;7.1 Mechanical and Electrical Problems with First-Order Linear Systems;378
12.2;Exercises 7.1;383
12.3;7.2 Diffusion and Population Problems with First-Order Linear Systems;385
12.4;Exercises 7.2;391
12.5;7.3 Nonlinear Systems of Equations;393
12.6;Exercises 7.3;397
12.7;Chapter 7 Summary: Essential Concepts and Formulas;402
12.8;Chapter 7 Review Exercises;402
12.9;Differential Equations at Work;405
12.9.1;A. Competing Species;405
12.9.2;B. Food Chains;405
12.9.3;C. Chemical Reactor;407
12.9.4;D. Food Chains in a Chemostat;408
12.9.5;E. The Rössler System and Attractor;409
12.9.6;F. Cell Dynamics in Colon Cancer;410
13;Chapter 8: Introduction to the Laplace Transform;412
13.1;8.1 The Laplace Transform: Preliminary Definitions and Notation;413
13.2;Exercises 8.1;418
13.3;8.2 The Inverse Laplace Transform;420
13.4;Exercises 8.2;423
13.5;8.3 Solving Initial-Value Problems with the Laplace Transform;424
13.6;Exercises 8.3;427
13.7;8.4 Laplace Transforms of Several Important Functions;428
13.8;Exercises 8.4;437
13.9;8.5 The Convolution Theorem;440
13.10;Exercises 8.5;443
13.11;8.6 Laplace Transform Methods for Solving Systems;444
13.12;Exercises 8.6;447
13.13;8.7 Some Applications Using Laplace Transforms;448
13.14;Exercises 8.7;455
13.15;Chapter 8 Summary: Essential Concepts and Formulas;464
13.16;Chapter 8 Review Exercises;465
13.17;Differential Equations at Work;468
13.17.1;A. The Tautochrone;468
13.17.2;B. Vibration Absorbers;469
13.17.3;C. Airplane Wing;470
13.17.4;D. Free Vibration of a Three-Story Building;471
13.17.5;E. Control Systems;473
14;Answers to Selected Exercises;474
15;Bibliography;520
16;Appendices;522
17;Index;526