An Introduction to Differential Equations and Their ApplicationsIntended for use in a beginning one-semester course in differential equations, this text is designed for students of pure and applied mathematics with a working knowledge of algebra, trigonometry, and elementary calculus. Its mathematical rigor is balanced by complete but simple explanations that appeal to readers' physical and geometric intuition. Starting with an introduction to differential equations, the text proceeds to examinations of first- and second-order differential equations, series solutions, the Laplace transform, systems of differential equations, difference equations, nonlinear differential equations and chaos, and partial differential equations. Numerous figures, problems with solutions, and historical notes clarify the text. |
Contents
INTRODUCTION TO DIFFERENTIAL EQUATIONS | 1 |
FIRSTORDER DIFFERENTIAL EQUATIONS | 29 |
SECONDORDER LINEAR EQUATIONS | 109 |
Copyright | |
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Other editions - View all
An Introduction to Differential Equations and Their Applications Stanley J. Farlow Limited preview - 2006 |
An Introduction to Differential Equations and Their Applications Stanley J. Farlow Limited preview - 2012 |
Common terms and phrases
a₁ algebraic approximate arbitrary constants boundary conditions c₁ and c₂ c₁e called chaotic characteristic equation complex numbers constant coefficients convergence damped defined derivative determine difference equation eigenvalues eigenvectors equilibrium point Euler's Example exponential find the solution first-order equations Fourier series frequency function given Hence homogeneous equation initial conditions initial-value problem integrating factor interval inverse Julia sets Laplace transform Laplace's equation linear equation linear system linearly independent linearly independent solutions mathematical matrix method nonhomogeneous equation nonlinear partial differential equations particular solution phase plane polynomial power series r₁ roots satisfies second-order equation Section separation of variables sequence Show simple harmonic motion sine singular point sketch the graph solution of Eq solve spring Substituting tank temperature theorem trajectories vector verify Wronskian x₁ x²y y₁ y₁(x yp(x zero ηπ λ₁ πχ Уп Уп+1