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Differential Equations 4th Revised edition [Kõva köide]

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  • Formaat: Hardback, 864 pages, kõrgus x laius x paksus: 246x189x20 mm
  • Ilmumisaeg: 11-Mar-2011
  • Kirjastus: Brooks/Cole
  • ISBN-10: 0495561983
  • ISBN-13: 9780495561989
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Differential Equations 4th Revised editionSuurem pilt
  • Formaat: Hardback, 864 pages, kõrgus x laius x paksus: 246x189x20 mm
  • Ilmumisaeg: 11-Mar-2011
  • Kirjastus: Brooks/Cole
  • ISBN-10: 0495561983
  • ISBN-13: 9780495561989
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780495561989.html
Märksõnad:
Incorporating an innovative modeling approach, this book for a one-semester differential equations course emphasizes conceptual understanding to help users relate information taught in the classroom to real-world experiences. Certain models reappear throughout the book as running themes to synthesize different concepts from multiple angles, and a dynamical systems focus emphasizes predicting the long-term behavior of these recurring models. Users will discover how to identify and harness the mathematics they will use in their careers, and apply it effectively outside the classroom.
1. FIRST-ORDER DIFFERENTIAL EQUATIONS. Modeling via Differential
Equations. Analytic Technique: Separation of Variables. Qualitative
Technique: Slope Fields. Numerical Technique: Euler's Method. Existence and
Uniqueness of Solutions. Equilibria and the Phase Line. Bifurcations. Linear
Equations. Integrating Factors for Linear Equations.
2. FIRST-ORDER SYSTEMS.
Modeling via Systems. The Geometry of Systems. Analytic Methods for Special
Systems. Euler's Method for Systems. The Lorenz Equations.
3. LINEAR SYSTEMS.
Properties of Linear Systems and the Linearity Principle. Straight-Line
Solutions. Phase Planes for Linear Systems with Real Eigenvalues. Complex
Eigenvalues. Special Cases: Repeated and Zero Eigenvalues. Second-Order
Linear Equations. The Trace-Determinant Plane. Linear Systems in Three
Dimensions.
4. FORCING AND RESONANCE. Forced Harmonic Oscillators. Sinusoidal
Forcing. Undamped Forcing and Resonance. Amplitude and Phase of the Steady
State. The Tacoma Narrows Bridge.
5. NONLINEAR SYSTEMS. Equilibrium Point
Analysis. Qualitative Analysis. Hamiltonian Systems. Dissipative Systems.
Nonlinear Systems in Three Dimensions. Periodic Forcing of Nonlinear Systems
and Chaos.
6. LAPLACE TRANSFORMS. Laplace Transforms. Discontinuous
Functions. Second-Order Equations. Delta Functions and Impulse Forcing.
Convolutions. The Qualitative Theory of Laplace Transforms.
7. NUMERICAL
METHODS. Numerical Error in Euler's Method. Improving Euler's Method. The
Runge-Kutta Method. The Effects of Finite Arithmetic.
8. DISCRETE DYNAMICAL
SYSTEMS. The Discrete Logistic Equation. Fixed Points and Periodic Points.
Bifurcations. Chaos. Chaos in the Lorenz System. APPENDICES. A. Changing
Variables. B. The Ultimate Guess. C. Complex Numbers and Euler's Formula.