A Course in Ordinary Differential Equations
The first contemporary textbook on ordinary differential equations (ODEs) to include instructions on MATLAB®, Mathematica®, and MapleTM, A Course in Ordinary Differential Equations focuses on applications and methods of analytical and numerical solutions, emphasizing approaches used in the typical engineering, physics, or mathematics student's field of study.
Stressing applications wherever possible, the authors have written this text with the applied math, engineer, or science major in mind. It includes a number of modern topics that are not commonly found in a traditional sophomore-level text. For example, Chapter 2 covers direction fields, phase line techniques, and the Runge-Kutta method; another chapter discusses linear algebraic topics, such as transformations and eigenvalues. Chapter 6 considers linear and nonlinear systems of equations from a dynamical systems viewpoint and uses the linear algebra insights from the previous chapter; it also includes modern applications like epidemiological models. With sufficient problems at the end of each chapter, even the pure math major will be fully challenged.
Although traditional in its coverage of basic topics of ODEs, A Course in Ordinary Differential Equations is one of the first texts to provide relevant computer code and instruction in MATLAB, Mathematica, and Maple that will prepare students for further study in their fields.
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Geometrical and Numerical Methods for FirstOrder
Elements of HigherOrder Linear Equations
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A Course in Ordinary Differential Equations, Second Edition
Stephen A. Wirkus,Randall J. Swift
Limited preview - 2014
analytic antiderivative approximate behavior bifurcation calculate characteristic equation coefﬁcients column commands Computer Code consider constant coefficients converges corresponding curve deﬁned deﬁnition derivative determine direction ﬁeld eigenvalues eigenvectors equilibrium solution Euler’s method Example Existence and Uniqueness exponential Figure ﬁnd ﬁnding ﬁrst ﬁrst-order equations ﬁt function f fundamental set Gauss-Jordan elimination given gives graph homogeneous equation indicial equation initial condition initial-value problem inverse Laplace transform linear algebra linear combination linearly independent m-ﬁle Maple Mathematica Matlab matrix matrix exponential multiplication nonhomogeneous equation Note nth order nullclines nullspace numerical solution obtain original vector parameters particular solution phase line plane plot polynomial population power series reﬂection regular singular point roots Runge-Kutta method satisﬁes Section set of solutions Show sketch the original solve speciﬁc stability subspace substitution tion unique solution unstable variables vector ﬁeld vector space zero