Description: About this productProduct InformationSuperb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Major focus on stability theory and its applications to oscillation phenomena, self-excited oscillations and regulator problem of Lurie. Bibliography. Exercises.Product IdentifiersPublisherDover Publications, IncorporatedISBN-100486658465ISBN-139780486658469eBay Product ID (ePID)308289Product Key FeaturesAuthorJohn A. Nohel, Fred BrauerPublication NameQualitative Theory of Ordinary Differential Equations : an IntroductionFormatTrade PaperbackLanguageEnglishFeaturesNew EditionPublication Year1989SeriesDover Books ON Mathematics Ser.TypeTextbookNumber of Pages320 PagesDimensionsItem Length8.5in.Item Height0.7in.Item Width5.4in.Item Weight12.2 OzAdditional Product FeaturesLc Classification NumberQa372.B823Edition DescriptionNew EditionTable of ContentPrefaceChapter 1. Systems of Differential Equations 1.1 A Simple Mass-Spring System 1.2 Coupled Mass-Spring Systems 1.3 Systems of First-Order Equations 1.4 Vector-Matrix Notation for Systems 1.5 The Need for a Theory 1.6 Existence, Uniqueness, and Continuity 1.7 The Gronwall InequalityChapter 2. Linear Systems, with an Introduction to Phase Space Analysis 2.1 Introduction 2.2 Existence and Uniqueness for Linear Systems 2.3 Linear Homogeneous Systems 2.4 Linear Nonhomogeneous Systems 2.5 Linear Systems with Constant Coefficients 2.6 Similarity of Matrices and the Jordan Canonical Form 2.7 Asymptotic Behavior of Solutions of Linear Systems with Constant Coefficients 2.8 Autonomous Systems--Phase Space--Two-Dimensional Systems 2.9 Linear Systems with Periodic Coefficients; Miscellaneous ExercisesChapter 3. Existence Theory 3.1 Existence in the Scalar Case 3.2 Existence Theory for Systems of First-Order Equations 3.3 Uniqueness of Solutions 3.4 Continuation of Solutions 3.5 Dependence on Initial Conditions and Parameters; Miscellaneous ExercisesChapter 4. Stability of Linear and Almost Linear Systems 4.1 Introduction 4.2 Definitions of Stability 4.3 Linear Systems 4.4 Almost Linear Systems 4.5 Conditional Stability 4.6 Asymptotic Equivalence 4.7 Stability of Periodic SolutionsChapter 5. Lyapunov's Second Method 5.1 Introductory Remarks 5.2 Lyapunov's Theorems 5.3 Proofs of Lyapunov's Theorems 5.4 Invariant Sets and Stability 5.5 The Extent of Asymptotic Stability--Global Asymptotic Stability 5.6 Nonautonomous SystemsChapter 6. Some Applications 6.1 Introduction 6.2 The Undamped Oscillator 6.3 The Pendulum 6.4 Self-Excited Oscillations--Periodic Solutions of the Liénard Equation 6.5 The Regulator Problem 6.6 Absolute Stability of the Regulator SystemAppendix 1. Generalized Eigenvectors, Invariant Subspaces, and Canonical Forms of MatricesAppendix 2. Canonical Forms of 2 x 2 MatricesAppendix 3. The Logarithm of a MatrixAppendix 4. Some Results from Matrix Theory Bibliography; IndexCopyright Date1989Target AudienceCollege AudienceTopicDifferential Equations / GeneralLccn88-030943Dewey Decimal517/.382IllustratedYesGenreMathematics
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Book Title: N/A
Item Length: 8.5in.
Item Height: 0.7in.
Item Width: 5.4in.
Author: John A. Nohel, Fred Brauer
Publication Name: Qualitative Theory of Ordinary Differential Equations : an Introduction
Format: Trade Paperback
Language: English
Features: New Edition
Publisher: Dover Publications, Incorporated
Publication Year: 1989
Series: Dover Books ON Mathematics Ser.
Type: Textbook
Item Weight: 12.2 Oz
Number of Pages: 320 Pages
