Advanced Engineering Mathematics
Through four editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. ADVANCED ENGINEERING MATHEMATICS featuries a greater number of examples and problems and is fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts. And problem sets incorporate the use of such leading software packages as MAPLE. Computational assistance, exercises and projects have been included to encourage students to make use of these computational tools. The content is organized into eight-parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, Special Functions, Partial Differential Equations, Complex Analysis, and Historical Notes.
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PART ONE ORDINARY DIFFERENTIAL EQUATIONS
Chapter Two Second Order Differential Equations
Chapter Three The Laplace Transform
21 other sections not shown
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approximation Assume boundary conditions boundary value problem calculate called choose circle closed path coefficients column complex numbers component compute Consider constant cos(x critical point defined Definition denoted determine diagonal discrete Fourier transform dot product eigenfunction eigenvalues eigenvectors element Euler Euler's method evaluate example finite formula Fourier series Fourier sine function given graph heat equation Hint homogeneous initial condition initial value problem interval inverse Laplace transform limit point line integral linear combination linear system linearly independent linearly independent solutions method motion multiple nonzero obtain open disk order differential equation origin orthogonal partial derivatives phase portrait piecewise continuous plane polynomial positive integer positive number power series Proof Prove radius real numbers result roots satisfies scalar second order series converges shown in Figure sin(x solve Sturm-Liouville problem surface temperature theorem trajectories variables vector field vector space velocity write