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Informationen zum Autor Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has previously taught at UCLA, Princeton University, and Pennsylvania State University. He has written more than 130 books and more than 250 scholarly papers and is the founding editor of the Journal of Geometric Analysis . 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. Klappentext This new edition is re-organized to make it more useful and more accessible. The most frequently taught topics are now up front. And the major applications are isolated in their own chapters. This makes this edition the most useable and flexible of any previous editions. Zusammenfassung This new edition is re-organized to make it more useful and more accessible. The most frequently taught topics are now up front. And the major applications are isolated in their own chapters. This makes this edition the most useable and flexible of any previous editions. Inhaltsverzeichnis Preface 1. What Is a Differential Equation? 1.1 Introductory Remarks 1.2 A Taste of Ordinary Differential Equations 1.3 The Nature of Solutions 2. Solving First-Order Equations 2.1 Separable Equations 2.2 First-Order Linear Equations 2.3 Exact Equations 2.4 Orthogonal Trajectories and Curves 2.5 Homogeneous Equations 2.6 Integrating Factors 2.7 Reduction of Order 2.7.1 Dependent Variable Missing 2.7.2 Independent Variable Missing 3. Some Applications of the First-Order Theory 3.1 The Hanging Chain and Pursuit Curves 3.1.1 The Hanging Chain 3.1.2 Pursuit Curves 3.2 Electrical Circuits Anatomy of an Application Problems for Review and Discovery 4. Second-Order Linear Equations 4.1 Second-Order Linear Equations with Constant Coefficients 4.2 The Method of Undetermined Coefficients 4.3 The Method of Variation of Parameters 4.4 The Use of a Known Solution to Find Another 4.5 Higher-Order Equations 5. Applications of the Second-Order Theory 5.1 Vibrations and Oscillations 5.1.1 Undamped Simple Harmonic Motion 5.1.2 Damped Vibrations 5.1.3 Forced Vibrations 5.1.4 A Few Remarks About Electricity 5.2 Newton’s Law of Gravitation and Kepler’s Laws 5.2.1 Kepler’s Second Law 5.2.2 Kepler’s First Law 5.2.3 Kepler’s Third Law Historical Note Anatomy of an Application Problems for Review and Discovery 6. Power Series Solutions and Special Functions 6.1 Introduction and Review of Power Series 6.1.1 Review of Power Series 6.2 Series Solutions of First-Order Equations 6.3 Ordinary Points 6.4 Regular Singular Points 6.5 More on Regular Singular Points Historical Note Historical Note Anatomy of an Application Problems for Review and Discovery 7. Fourier Series: Basic Concepts 7.1 Fourier Coefficients 7.2 Some Remarks about Convergence 7.3 Even and Odd Functions: Cosine and Sine Series 7.4 Fourier Series on Arbitrary Intervals 7.5 Orthogonal Functions Historical Note Anatomy of an Application Problems for Review and Discovery 8. Laplace Transforms 8.0 Introduction 8.1 Applications to Differential Equations 8.2 Derivatives and Integrals 8.3 Convolutions 8.3.1 Abel’s Mechanics Problem 8.4 The Unit Step and Impulse Functions Historical Note Anatomy of an Application Problems for Review and Discovery 9. The Calculus of Variations 9.1 Introductory Remarks 9.2 Euler’s Equation 9.3 Isoperimetric Problems and the Like 9.3.1 Lagrange Multipliers 9.3.2 Integral Side Conditions 9.3.3 Finite Side Conditions Historical Note Anatomy of an Application Problems for Review and Discovery 10. S...
