Differential Equations with Boundary-value Problems
Brooks/Cole Publishing Company, 1997 - Boundary Value Problems - 582 pages
This Fourth Edition of the expanded version of Zill's best-selling A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS places an even greater emphasis on modeling and the use of technology in problem solving and now features more everyday applications. Both Zill texts are identical through the first nine chapters, but this version includes six additional chapters that provide in-depth coverage of boundary-value problem-solving and partial differential equations, subjects just introduced in the shorter text. Previous editions of these two texts have enjoyed such great success in part because the authors pique students' interest with special features and in-text aids. Pre-publication reviewers also praise the authors' accessible writing style and the text's organization, which makes it easy to teach from and easy for students to understand and use. Understandable, step-by-step solutions are provided for every example. And this edition makes an even greater effort to show students how the mathematical concepts have relevant, everyday applications. Among the boundary-value related topics covered in this expanded text are: plane autonomous systems and stability; orthogonal functions; Fourier series; the Laplace transform; and elliptic, parabolic, and hyperparabolic partial differential equations, and their applications.
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Introduction to Differential Equations
FirstOrder Differential Equations
Modeling with F irstOrder
13 other sections not shown
Answers to odd-numbered approximate assume auxiliary equation boundary conditions boundary-value problem capacitor Cauchy-Euler equation converges cosh critical point damping deﬁned Deﬁnition deﬂection determine differential operator eigenvalues eigenvectors equation of motion equilibrium position Euler example EXERCISES Answers family of solutions ﬁnd ﬁnite ﬁrst ﬁrst-order differential equation force Fourier series gal/min given differential equation graph homogeneous inﬁnite initial conditions initial-value problem integral interval Laplace transform last equation linear equation linearly independent mass mathematical model matrix method nonhomogeneous nonlinear nth-order obtain odd function odd-numbered problems begin ODE solver orthogonal particular solution polynomial population power series regular singular point roots Runge-Kutta method satisﬁes Section separation of variables series circuit series solution shown in Figure sinh solution curve solve the given spring steady-state substitution superposition principle tank temperature Theorem tion variables weight zero