Advanced Engineering MathematicsAdvanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) that reinforce ideas and provide insight into more advanced problems. A Student Solutions Manual is also available. * Comprehensive coverage of frequently used integrals, functions and fundamental mathematical results * Contents selected and organized to suit the needs of students, scientists, and engineers * Contains tables of Laplace and Fourier transform pairs * New section on numerical approximation * New section on the ztransform * Easy reference system 
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Contents
53  
Ordinary Differential Equations  225 
Fourier series Integrals and The Fourier Transform  543 
Vector Calculus  623 
Complex Analysis  709 
Partial Differential Equations  925 
Numerical Mathematics  1043 
Answers  1109 
1143  
1147  
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Common terms and phrases
analytic function applied arbitrary constants Bessel functions boundary conditions boundary value problem called Cauchy characteristic circle coefficients column complex numbers complex plane contour convergence coordinates corresponding cosine curve deﬁned deﬁnition derivatives detA determinant diagonal differential equation eigenvalues eigenvectors elements equilibrium point example Exercises expression ﬁnd ﬁrst follows Fourier series Fourier series representation Fourier transform function f given gives grad homogeneous improper integral initial conditions initial value problem integrand interval inverse involving Laplace transform Laurent series line integral linear linearly independent mapping matrix matrix exponential multiplicity nonhomogeneous obtained odd function order equation orthogonal parameter point x0 polynomial power series proof properties radius real axis real number region result satisfies scalar second order Section series expansion shown in Fig shows sinx solve Sturm–Liouville substituting surface theorem unit vector variable wave zplane zero