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E-raamat: Differential Equations: Theory,Technique and Practice with Boundary Value Problems

(Washington University, St. Louis, Missouri, USA)
  • Formaat: 480 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 07-Oct-2015
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781498735025
  • Formaat - PDF+DRM
  • Hind: 143,00 €*
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  • Formaat: 480 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 07-Oct-2015
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781498735025

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Differential Equations: Theory, Technique, and Practice with Boundary Value Problems presents classical ideas and cutting-edge techniques for a contemporary, undergraduate-level, one- or two-semester course on ordinary differential equations. Authored by a widely respected researcher and teacher, the text covers standard topics such as partial differential equations (PDEs), boundary value problems, numerical methods, and dynamical systems. Lively historical notes and mathematical nuggets of information enrich the reading experience by offering perspective on the lives of significant contributors to the discipline. "Anatomy of an Application" sections highlight applications from engineering, physics, and applied science. Problems for review and discovery provide students with open-ended material for further exploration and learning.

Streamlined for the interests of engineers, this version:





Includes new coverage of Sturm-Liouville theory and problems Discusses PDEs, boundary value problems, and dynamical systems Features an appendix that provides a linear algebra review Augments the substantial and valuable exercise sets Enhances numerous examples to ensure clarity

A solutions manual is available with qualifying course adoption.

Differential Equations: Theory, Technique, and Practice with Boundary Value Problems delivers a stimulating exposition of modeling and computing, preparing students for higher-level mathematical and analytical thinking.

Arvustused

Praise for Differential Equations: Theory, Technique, and Practice, Second Edition

"Krantz is a very prolific writer. He creates excellent examples and problem sets." Albert Boggess, Professor and Director of the School of Mathematics and Statistical Sciences, Arizona State University, Tempe, USA

A first course in differential equations lends itself to the introduction of many interesting applications of mathematics. In this well-written text, Krantz (mathematics, Washington Univ. in St. Louis) emphasizes the differential equations needed to succeed as an engineer. This work is similar to Krantz and Simmonss Differential Equations: Theory, Technique, and Practice (2007), yet the current work adds the necessary exposure to Sturm-Liouville problems and boundary value problems for the intended engineering audience. This enables the reader access to the all-important introduction to the partial differential equations; namely, the heat and wave equations, as well as the Dirichlet problem. This text has two features that differentiate it from all others on the market at this level: the sections entitled, Anatomy of an Application and Problems for Review and Discovery. The former analyzes a particular application, while the latter introduces open-ended material for further student exploration. These features will serve students well in their pursuit of garnishing the applied fruits of the subject. This text sets a new standard for the modern undergraduate course in differential equations. --J. T. Zerger, Catawba College

Preface to the Second Edition xiii
Preface to the First Edition xv
1 What Is a Differential Equation?
1(62)
1.1 Introductory Remarks
1(4)
1.2 A Taste of Ordinary Differential Equations
5(1)
1.3 The Nature of Solutions
6(7)
1.4 Separable Equations
13(3)
1.5 First-Order Linear Equations
16(4)
1.6 Exact Equations
20(5)
1.7 Orthogonal Trajectories and Families of Curves
25(6)
1.8 Homogeneous Equations
31(3)
1.9 Integrating Factors
34(4)
1.10 Reduction of Order
38(5)
1.10.1 Dependent Variable Missing
39(1)
1.10.2 Independent Variable Missing
40(3)
1.11 The Hanging Chain and Pursuit Curves
43(9)
1.11.1 The Hanging Chain
43(5)
1.11.2 Pursuit Curves
48(4)
1.12 Electrical Circuits
52(11)
Anatomy of an Application
56(4)
Problems for Review and Discovery
60(3)
2 Second-Order Linear Equations
63(56)
2.1 Second-Order Linear Equations with Constant Coefficients
63(6)
2.2 The Method of Undetermined Coefficients
69(4)
2.3 The Method of Variation of Parameters
73(5)
2.4 The Use of a Known Solution to Find Another
78(3)
2.5 Vibrations and Oscillations
81(11)
2.5.1 Undamped Simple Harmonic Motion
82(2)
2.5.2 Damped Vibrations
84(3)
2.5.3 Forced Vibrations
87(2)
2.5.4 A Few Remarks about Electricity
89(3)
2.6 Newton's Law of Gravitation and Kepler's Laws
92(12)
2.6.1 Kepler's Second Law
95(2)
2.6.2 Kepler's First Law
97(3)
2.6.3 Kepler's Third Law
100(4)
2.7 Higher-Order Equations
104(15)
Historical Note: Euler
110(2)
Anatomy of an Application
112(4)
Problems for Review and Discovery
116(3)
3 Power Series Solutions and Special Functions
119(52)
3.1 Introduction and Review of Power Series
119(10)
3.1.1 Review of Power Series
120(9)
3.2 Series Solutions of First-Order Equations
129(5)
3.3 Second-Order Linear Equations: Ordinary Points
134(8)
3.4 Regular Singular Points
142(6)
3.5 More on Regular Singular Points
148(8)
3.6 Gauss's Hypergeometric Equation
156(15)
Historical Note: Gauss
161(2)
Historical Note: Abel
163(2)
Anatomy of an Application
165(3)
Problems for Review and Discovery
168(3)
4 Numerical Methods
171(24)
4.1 Introductory Remarks
172(1)
4.2 The Method of Euler
173(4)
4.3 The Error Term
177(3)
4.4 An Improved Euler Method
180(4)
4.5 The Runge--Kutta Method
184(11)
Anatomy of an Application
189(3)
Problems for Review and Discovery
192(3)
5 Fourier Series: Basic Concepts
195(44)
5.1 Fourier Coefficients
195(9)
5.2 Some Remarks about Convergence
204(6)
5.3 Even and Odd Functions: Cosine and Sine Series
210(5)
5.4 Fourier Series on Arbitrary Intervals
215(4)
5.5 Orthogonal Functions
219(20)
Historical Note: Riemann
224(2)
Anatomy of an Application
226(10)
Problems for Review and Discovery
236(3)
6 Sturm--Liouville Problems and Boundary Value Problems
239(30)
6.1 What is a Sturm--Liouville Problem?
239(7)
6.2 Analyzing a Sturm--Liouville Problem
246(4)
6.3 Applications of the Sturm--Liouville Theory
250(6)
6.4 Singular Sturm--Liouville
256(13)
Anatomy of an Application
263(4)
Problems for Review and Discovery
267(2)
7 Partial Differential Equations and Boundary Value Problems
269(36)
7.1 Introduction and Historical Remarks
269(4)
7.2 Eigenvalues, Eigenfunctions, and the Vibrating String
273(9)
7.2.1 Boundary Value Problems
273(1)
7.2.2 Derivation of the Wave Equation
274(3)
7.2.3 Solution of the Wave Equation
277(5)
7.3 The Heat Equation
282(6)
7.4 The Dirichlet Problem for a Disc
288(17)
7.4.1 The Poisson Integral
291(5)
Historical Note: Fourier
296(1)
Historical Note: Dirichlet
297(1)
Problems for Review and Discovery
298(3)
Anatomy of an Application
301(4)
8 Laplace Transforms
305(40)
8.0 Introduction
305(3)
8.1 Applications to Differential Equations
308(5)
8.2 Derivatives and Integrals of Laplace Transforms
313(6)
8.3 Convolutions
319(8)
8.3.1 Abel's Mechanics Problem
322(5)
8.4 The Unit Step and Impulse Functions
327(18)
Historical Note: Laplace
335(1)
Anatomy of an Application
336(3)
Problems for Review and Discovery
339(6)
9 Systems of First-Order Equations
345(34)
9.1 Introductory Remarks
345(3)
9.2 Linear Systems
348(8)
9.3 Homogeneous Linear Systems with Constant Coefficients
356(7)
9.4 Nonlinear Systems: Volterra's Predator-Prey Equations
363(16)
Anatomy of an Application
370(5)
Problems for Review and Discovery
375(4)
10 The Nonlinear Theory
379(64)
10.1 Some Motivating Examples
380(1)
10.2 Specializing Down
380(5)
10.3 Types of Critical Points: Stability
385(9)
10.4 Critical Points and Stability for Linear Systems
394(11)
10.5 Stability by Liapunov's Direct Method
405(6)
10.6 Simple Critical Points of Nonlinear Systems
411(7)
10.7 Nonlinear Mechanics: Conservative Systems
418(6)
10.8 Periodic Solutions: The Poincare--Bendixson Theorem
424(19)
Historical Note: Poincare
434(2)
Anatomy of an Application
436(3)
Problems for Review and Discovery
439(4)
Appendix: Review of Linear Algebra 443(12)
Bibliography 455(4)
Index 459
Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has written more than 175 scholarly papers and more than 65 books, including the following books published by CRC Press: Foundations of Analysis (2014), Convex Analysis (2014), Real Analysis and Foundations, Third Edition (2013), and Elements of Advanced Mathematics, Third Edition (2012). An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D from Princeton University.