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Differential Equations and Boundary Value Problems: Computing and Modeling 2nd edition [Kõva köide]

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  • Formaat: Hardback, 787 pages, kõrgus x laius x paksus: 243x210x33 mm, kaal: 1455 g
  • Ilmumisaeg: 10-Aug-1999
  • Kirjastus: Pearson
  • ISBN-10: 0130797707
  • ISBN-13: 9780130797704
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  • Kõva köide
  • Hind: 105,84 €*
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Differential Equations and Boundary Value Problems: Computing and Modeling 2nd editionSuurem pilt
  • Formaat: Hardback, 787 pages, kõrgus x laius x paksus: 243x210x33 mm, kaal: 1455 g
  • Ilmumisaeg: 10-Aug-1999
  • Kirjastus: Pearson
  • ISBN-10: 0130797707
  • ISBN-13: 9780130797704
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780130797704.html
Märksõnad:
A text for a contemporary differential equations course that augments core skills with conceptual perspectives, with greater emphasis on conceptual ideas and the use of computer laboratory projects to involve students in more intense and sustained problem-solving experiences. Offers an early introduction to mathematical modeling and numerical methods, and provides a flexible treatment of linear systems. Features computer-generated graphics and computing projects, plus exercises and answers. The authors are affiliated with the University of Georgia. Annotation c. Book News, Inc., Portland, OR (booknews.com) This book reflects the new excitement in Elementary Differential Equations as the availability of specialized scientific computing environments and software systems continues to reshape the role and applications of the discipline. The new approach found in the Second Edition employs tools like Maple, Mathematica, and MATLAB to shift in emphasis from traditional manual methods to new computer-based methods that open a wider range of realistic applications. Coverage begins and ends with discussions of mathematical modeling of real-world phenomena, with a fresh new computational flavor evident in figures, examples, problems, and projects throughout the text.

1. First-Order Differential Equations.
Differential Equations and Mathematical Models. Integrals as General and Particular Solutions. Direction Fields and Solutions Curves. Separable Equations and Applications. Linear First-Order Equations. Substitution Methods and Exact Equations.


2. Mathematical Models and Numerical Methods.
Population Models. Equilibrium Solutions and Stability. Acceleration-Velocity Models. Numerical Approximation: Euler's Method. A Closer Look at the Euler Method. The Runge-Kutta Method.


3. Linear Equations of Higher Order.
Introduction: Second-Order Linear Equations. General Solutions of Linear Equations. Homogeneous Equations with Constant Coefficients. Mechanical Vibrations. Nonhomogeneous Equations and the Method of Undetermined Coefficients. Forced Oscillations and Resonance. Electrical Circuits. Endpoint Problems and Eigenvalues.


4. Introduction to Systems of Differential Equations.
First-Order Systems and Applications. The Method of Elimination. Numerical Methods for Systems.


5. Linear Systems of Differential Equations.
Linear Systems and Matrices. The Eigenvalue Method for Homogeneous Systems. Second Order Systems and Mechanical Applications. Multiple Eignvalue Solutions. Matrix Exponentials and Linear Systems. Nonhomogeneous Linear Systems.


6. Nonlinear Systems and Phenomena.
Stability and the Phase Plane. Linear and Almost Linear Systems. Ecological Models: Predators and Competitors. Nonlinear Mechanical Systems. Chaos in Dynamical Systems.


7. Laplace Transform Methods.
Laplace Transforms and Inverse Transforms. Transformation of Initial Value Problems. Translation and Partial Fractions. Derivatives, Integrals, and Products of Transforms. Periodic and Piecewise Continuous Forcing Functions. Impulses and Delta Functions.


8. Power Series Methods.
Introduction and Review of Power Series. Series Solutions Near Ordinary Points. Regular Singular Points. Method of Frobenius: The Exceptional Cases. Bessel's Equation. Applications of Bessel Functions.


9. Fourier Series Methods.
Periodic Functions and Trigonometric Series. General Fourier Series and Convergence. Fourier Sine and Cosine Series. Applications of Fourier Series. Heat Conduction and Separation of Variables. Vibrating Strings and the One-Dimensional Wave Equation. Steady-State Temperature and Laplace's Equation.


10. Eigenvalues and Boundary Value Problems.
Strum-Liouville Problems and Eigenfunction Expansions. Applications of Eigenfunction Series. Steady Periodic Solutions and Natural Frequencies. Cylindrical Coordinate Problems. Higher-Dimensional Phenomena.