Differential equations: a modeling approach
This text takes a strong mathematical modeling approach. By integrating modeling throughout the text, the authors provide a better intuitive understanding of the concepts presented. They also take what students learned in calculus and apply it to real-world problems. The text is loaded with relevant applications, many of which are engineering-oriented. The text includes coverage of phase-plane analysis and control systems.
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DIFFERENTIAL EQUATIONS AND MODELS
FIRSTORDER DIFFERENTIAL EQUATIONS
10 other sections not shown
algebraic approximation arbitrary constants assume boundary conditions calculate capacitor characteristic equation circuit coefficients coeﬂicients continuous function damping deﬁned deﬁnition derivative determine displacement eigenvalues eigenvector equa equilibrium position estimate Euler’s method EXAMPLE exponential ﬁeld FIGURE ﬁnd ﬁnding ﬁrst ﬁrst-order equation ﬁxed ﬂow ﬂuid forcing function Fourier Fourier series function f fundamental set given graph heat equation homogeneous linear independent variable initial conditions initial value problem integral interval krill Laplace transform Legendre polynomials linear equations linear system linearly independent linearly independent solutions mass matrix motion nonhomogeneous obtain partial differential equation particular solution phase plane piecewise continuous polynomial population power series rest point roots satisﬁes second-order equation Section side of Eq slope solution curve solution to Eq solve speciﬁed spring Step Substitution temperature Theorem tion trajectory vector velocity voltage Wronskian yields zero