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Klappentext Boyce's Elementary Differential Equations and Boundary Value Problems is written from the viewpoint of the applied mathematician, with diverse interest in differential equations, ranging from quite theoretical to intensely practical-and usually a combination of both. The intended audience for the text is undergraduate STEM students taking an introductory course in differential equations. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent, while a basic familiarity with matrices is helpful.This new edition of the book aims to preserve, and to enhance the qualities that have made previous editions so successful. It offers a sound and accurate exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. Zusammenfassung Boyce's Elementary Differential Equations and Boundary Value Problems is written from the viewpoint of the applied mathematician, with diverse interest in differential equations, ranging from quite theoretical to intensely practical-and usually a combination of both. The intended audience for the text is undergraduate STEM students taking an introductory course in differential equations. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent, while a basic familiarity with matrices is helpful.This new edition of the book aims to preserve, and to enhance the qualities that have made previous editions so successful. It offers a sound and accurate exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. Inhaltsverzeichnis TABLE OF CONTENTS 1 Introduction 1.1 Some Basic Mathematical Models 1.2 Solutions of Some Differential Equations 1.3 Classification of Differential Equations 2 First-Order Differential Equations 2.1 Linear Differential Equations; Method of Integrating Factors 2.2 Separable Differential Equations 2.3 Modeling with First-Order Linear Differential Equations 2.4 Differences Between Linear and Nonlinear Differential Equations 2.5 Autonomous Differential Equations and Population Dynamics 2.6 Exact Differential Equations and Integrating Factors 2.7 Numerical Approximations: Euler's Method 2.8 The Existence and Uniqueness Theorem 2.9 First-Order Difference Equations 3 Second-Order Linear Differential Equations 3.1 Homogeneous Differential Equations with Constant Coefficients 3.2 Solutions of Linear Homogeneous Equations; the Wronskian 3.3 Complex Roots of the Characteristic Equation 3.4 Repeated Roots; Reduction of Order 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients 3.6 Variation of Parameters 3.7 Mechanical and Electrical Vibrations 3.8 Forced Periodic Vibrations 3.9 Central Gravitational Forces and Kepler's Laws 4 Higher-Order Linear Differential Equations 4.1 General Theory of n¿¿ Order Linear Differential Equations 4.2 Homogeneous Differential Equations with Constant Coefficients 4.3 The Method of Undetermined Coefficients 4.4 The Method of Variation of Parameters 5 Series Solutions of First-Order and Second-Order Linear Equations 5.1 Review of Power Series 5.2 Series Solution of First Order Equations 5.3 Series Solutions Near an Ordinary Point, Part I 5...
