Fundamentals of Differential Equations, Volume 1*New applications-driven sections have been added to the chapter on linear second-order equations. *The chapter regarding the introduction to systems and phase plane analysis has been reorganized and modernized to better facilitate student understanding of the material. *More material on dynamical systems has been added. *A new section on the phase line has been added to the beginning of the text. *Group Projects relating to the material covered appear at the end of each chapter. *Revised exercise sets provide fresh material for instructors who have used the text before. *Updated Interactive Differential Equations CD is keyed specifically to the text, and included free with every book. *An updated Instructors MAPLE Manual, tied to development of the text, with suggestions on incorporating MAPLE into the courses, and including sample worksheets for labs, is available. *The texts also allow optional use of Computer Algebra Systems, with many exercises and projects included to let students use software to solve interesting and realistic problems and exercises. *Necessary proofs in a conceptual presentation are always included, but may be skipped, allowing flexibility in the level of c |
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a₁ a²u annihilator method approximate the solution arbitrary constants auxiliary equation C₁ c₁e c₂ Cauchy-Euler equation compute constant coefficients convergence corresponding homogeneous equation critical points d²y damping derivatives determine differential equation direction field dy/dx eigenvalues eigenvectors equilibrium Euler's method EXAMPLE exponential Figure force formula Fourier series frequency function fundamental solution set given graph Hence indicial equation initial conditions initial value problem integral interval k₁ L/min Laplace transform linear differential linear equations linearly independent linearly independent solutions mass mass-spring system matrix nonlinear numerical obtain oscillator particular solution phase plane piecewise continuous Poincaré map Poincaré section polynomial power series r₁ roots Runge-Kutta satisfies Section separation of variables Show solution to equation solve spring ẞx Substituting tank Theorem tion trajectories undetermined coefficients variable vector velocity Wronskian x₁ x²y y₁ y₁(x Yp(x zero ди