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001469489 001__ 1469489
001469489 003__ OCoLC
001469489 005__ 20230803003332.0
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001469489 019__ $$a1381708445
001469489 020__ $$a9783031251306$$q(electronic bk.)
001469489 020__ $$a303125130X$$q(electronic bk.)
001469489 020__ $$z9783031251290
001469489 020__ $$z3031251296
001469489 0247_ $$a10.1007/978-3-031-25130-6$$2doi
001469489 035__ $$aSP(OCoLC)1381445884
001469489 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCF
001469489 049__ $$aISEA
001469489 050_4 $$aQA371
001469489 08204 $$a515/.352$$223/eng/20230619
001469489 1001_ $$aHenner, Victor,$$eauthor.
001469489 24500 $$aOrdinary differential equations :$$banalytical methods and applications /$$cVictor Henner, Alexander Nepomnyashchy, Tatyana Belozerova, Mikhail Khenner.
001469489 264_1 $$aCham :$$bSpringer,$$c[2023]
001469489 264_4 $$c©2023
001469489 300__ $$a1 online resource (xii, 606 pages) :$$billustrations
001469489 336__ $$atext$$btxt$$2rdacontent
001469489 337__ $$acomputer$$bc$$2rdamedia
001469489 338__ $$aonline resource$$bcr$$2rdacarrier
001469489 504__ $$aIncludes bibliographical references and index.
001469489 5050_ $$aIntro -- Preface -- Contents -- Chapter 1: Introduction -- Chapter 2: First-Order Differential Equations -- 2.1 Existence and Uniqueness of a Solution -- 2.2 Integral Curves and Isoclines -- 2.3 Separable Equations -- 2.4 Linear First-Order Differential Equations -- 2.4.1 Homogeneous Linear Equations -- 2.4.2 Nonhomogeneous Linear Equations: Method of a Parameter Variation -- 2.4.3 Nonhomogeneous Linear Equations: Method of Integrating Factor -- 2.4.4 Nonlinear Equations That Can Be Transformed into Linear Equations -- 2.5 Exact Equations
001469489 5058_ $$a2.6 Equations Unresolved with Respect to a Derivative -- 2.6.1 Regular and Irregular Solutions -- 2.6.2 Lagrangeś Equation -- 2.6.3 Clairautś Equation -- 2.7 Qualitative Approach for Autonomous First-Order Equations: Equilibrium Solutions and Phase Lines -- 2.8 Examples of Problems Leading to First-Order Differential Equations -- Chapter 3: Differential Equations of Order n > 1 -- 3.1 General Considerations -- 3.2 Second-Order Differential Equations -- 3.3 Reduction of Order -- 3.4 Linear Second-Order Differential Equations -- 3.4.1 Homogeneous Equations
001469489 5058_ $$a3.4.2 Reduction of Order for a Linear Homogeneous Equation -- 3.4.3 Nonhomogeneous Equations -- 3.5 Linear Second-Order Equations with Constant Coefficients -- 3.5.1 Homogeneous Equations -- 3.5.2 Nonhomogeneous Equations: Method of Undetermined Coefficients -- 3.6 Linear Second-Order Equations with Periodic Coefficients -- 3.6.1 Hill Equation -- 3.6.2 Mathieu Equation -- 3.7 Linear Equations of Order n > 2 -- 3.8 Linear Equations of Order n > 2 with Constant Coefficients -- 3.9 Euler Equation -- 3.10 Applications -- 3.10.1 Mechanical Oscillations -- 3.10.2 RLC Circuit
001469489 5058_ $$a3.10.3 Floating Body Oscillations -- Chapter 4: Systems of Differential Equations -- 4.1 General Considerations -- 4.2 Systems of First-Order Differential Equations -- 4.3 Systems of First-Order Linear Differential Equations -- 4.4 Systems of Linear Homogeneous Differential Equations with Constant Coefficients -- 4.5 Systems of Linear Nonhomogeneous Differential Equations with Constant Coefficients -- 4.6 Matrix Approach -- 4.6.1 Homogeneous Systems of Equations -- 4.6.1.1 Matrix Equation -- 4.6.1.2 Series Solution for a Constant Matrix A -- 4.6.1.3 The Case of a Diagonalizable Constant Matrix A
001469489 5058_ $$a4.6.1.4 The Case of a Non-diagonalizable Constant Matrix A -- 4.6.2 Nonhomogeneous Systems of Equations -- 4.6.2.1 The General Case -- 4.6.2.2 The Case of a Constant Matrix A -- 4.7 Applications -- 4.7.1 Charged Particle in a Magnetic Field -- 4.7.2 Precession of a Magnetic Moment in a Magnetic Field -- 4.7.3 Spring-Mass System -- 4.7.4 Mutual Inductance -- Chapter 5: Qualitative Methods and Stability of ODE Solutions -- 5.1 Phase Plane Approach -- 5.2 Phase Portraits and Stability of Solutions in the Case of Linear Autonomous Systems -- 5.2.1 Equilibrium Points
001469489 506__ $$aAccess limited to authorized users.
001469489 520__ $$aThe textbook presents a rather unique combination of topics in ODEs, examples and presentation style. The primary intended audience is undergraduate (2nd, 3rd, or 4th year) students in engineering and science (physics, biology, economics). The needed pre-requisite is a mastery of single-variable calculus. A wealth of included topics allows using the textbook in up to three sequential, one-semester ODE courses. Presentation emphasizes the development of practical solution skills by including a very large number of in-text examples and end-of-section exercises. All in-text examples, be they of a mathematical nature or a real-world examples, are fully solved, and the solution logic and flow are explained. Even advanced topics are presented in the same undergraduate-friendly style as the rest of the textbook. Completely optional interactive laboratory-type software is included with the textbook.
001469489 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed June 19, 2023).
001469489 650_0 $$aDifferential equations.
001469489 655_0 $$aElectronic books.
001469489 655_7 $$aTextbooks.$$2fast$$0(OCoLC)fst01423863
001469489 655_7 $$aTextbooks.$$2lcgft
001469489 7001_ $$aNepomni͡ashchiĭ, A. A.$$q(Aleksandr Abovich),$$eauthor.
001469489 7001_ $$aBelozerova, Tatyana,$$eauthor.
001469489 7001_ $$aKhenner, Mikhail,$$eauthor.
001469489 77608 $$iPrint version: $$z3031251296$$z9783031251290$$w(OCoLC)1356572091
001469489 852__ $$bebk
001469489 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-25130-6$$zOnline Access$$91397441.1
001469489 909CO $$ooai:library.usi.edu:1469489$$pGLOBAL_SET
001469489 980__ $$aBIB
001469489 980__ $$aEBOOK
001469489 982__ $$aEbook
001469489 983__ $$aOnline
001469489 994__ $$a92$$bISE