Differential Equations

Differential Equations

3.44 (58 ratings by Goodreads)
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Description

This text on differential equations seeks to strike a balance between analytic, numeric and graphical techniques, emphasizes modelling, stresses qualitative theory throughout the course, uses technology, presents linear and nonlinear systems in parallel, and includes an introduction to discrete models of dynamical systems.
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Product details

  • Hardback | 657 pages
  • 208 x 230 x 30mm | 1,301.8g
  • BROOKS/COLE
  • CA, United States
  • New edition
  • New edition
  • 0534345506
  • 9780534345501

Table of contents

Part 1 First-order differential equations: modelling 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 differential equations; changing variables. Part 2 First-order systems: the predator-prey model; systems of differential equations; graphical representation of solutions of systems; second-order equations and the harmonic oscillator; Euler's method for autonomous systems; qualitative analysis; the Lorenz equations. Part 3 Linear systems: properties of linear systems and the linearity principle; straight-line solutions; phase planes for linear systems with real Eigenvalues; complex Eigenvalues; the special cases - repeated and zero Eigenvalues; one-parameter families of linear systems; linear systems in three dimensions. Part 4 Nonlinear systems: equilibrium point analysis; Hamiltonian systems; dissipative systems; nonlinear systems in three dimensions. Part 5 Forcing and resonance: forced harmonic oscillators; sinusoidal forcing and resonance; qualitative analysis of the forced harmonic oscillator; the tacoma narrows bridge; periodic forcing of nonlinear systems and chaos. Part 6 Discrete dynamical systems: the discrete logistic equation; fixed and periodic runs; bifurcations; chaos; chaos in the Lorenz system. Part 7 Numerical methods: numerical error in Euler's method; improving Euler's method; the Runge-Kutta method; the effects of finite arithmetic. Part 8 Laplace transforms: Laplace transforms and second-order equations; impulse-forcing and delta functions; the qualitative theory of Laplace transforms;
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Review quote

"There are many texts that claim to be written in the spirit of the so-called calculus reform movement. In my opinion, the text under review achieves this goal better than any book that I have seen. This book presents at a very elementary level the kinds of material that opens the door for the understanding of many of the great achievements in dynamical systems that have been accomplished over the last 30 years."
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Rating details

58 ratings
3.44 out of 5 stars
5 19% (11)
4 40% (23)
3 19% (11)
2 12% (7)
1 10% (6)
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