Analytical and Computational Methods of Advanced Engineering Mathematics
 List Price: $119.99
 Binding: Hardcover
 Publisher: Springer Verlag
 Publish date: 11/01/1998
Description:
1 Numerical Analysis. 1.1 The Nature of Numerical Analysis. 1.2 Polynomial Interpolation. 1.3 Numerical Integration and Differentiation. 1.4 Solution of Equations. 1.5 Inverse Functions. 1.6 Implicit Functions. 1.7 Numerical Summation of Infinite Series. 2 Ordinary Differential Equations of First Order. 2.1 The Nature of Differential Equations. 2.2 Separable Equations. 2.3 Linear FirstOrder Equations. 2.4 Exact Equations. 2.5 Applications to Some SecondOrder Equations. 2.6 The Initial Value Problem. 2.7 Numerical Methods for the Initial Value Problem. 3 Ordinary Differential Equations of Higher Order. 3.1 Examples from Engineering and Physics. 3.2 Linear SecondOrder Equations  Structure of Solutions. 3.3 Linear SecondOrder Equations with Constant Coefficients. 3.4 Linear SecondOrder Equations with Analytic Coefficients. 3.5 Numerical Methods for SecondOrder Equations. 3.6 Linear Equations of Order n > 2. 4 The Laplace Transform. 4.1 The Nature of the Laplace Transform. 4.2 The Laplace Transforms of Some Elementary Functions. 4.3 Operational Rules for the Laplace Transform. 4.4 Applications to Differential Equations. 4.5 Applications to Systems of Differential Equations. 5 Linear Algebra. 5.1 Systems of Linear Equations. 5.2 The Gauss Elimination Method. 5.3 Vector Spaces. 5.4 Matrices and Matrix Algebra. 5.5 The Fundamental Theorem of Linear Algebra. 5.6 Determinants and Cramer's Rule. 5.7 Eigenvalues and Eigenvectors. 6 Vector Analysis. 6.1 Vector Algebra. 6.2 Vector Calculus of Curves in Space. 6.3 Vector Calculus of Surfaces in Space. 6.4 Calculus of Scalar and Vector Fields. 6.5 Integral Theorems of Vector Calculus. 6.6 XRay Diffraction and Crystal Structure. 7 Partial Differential Equations of Mathematical Physics. 7.1 Vibrating Strings: D'Alembert's Wave Equation. 7.2 Heat Diffusion in Rods: Fourier's Heat Equation. 7.3 Heat Diffusion in Plates. 7.4 SteadyState Heat Diffusion in Plates: The Laplace Equation. 7.5 Vibrations of Drums. 7.6 Heat Diffusion in Solids. 7.7 SteadyState Heat Diffusion in Solids. 8 Fourier Analysis and SturmLiouville Theory. 1 Fourier Series. 8.1 Dirichlet Boundary Conditions and Fourier Sine Series. 8.2 Orthogonality and Fourier Coefficients. 8.3 Convergence of Fourier Sine Series. 8.4 Neumann Boundary Conditions and Fourier Cosine Series. 8.5 Periodic Boundary Conditions and the Complete Fourier Series. 8.6 Proofs of the Convergence Theorems (Optional). II Fourier Integrals. 8.7 Heat Diffusion in an Infinite Rod. 8.8 Orthogonality Calculation. 8.9 The Fourier Integral. 8.10 Fourier Sine and Cosine Integrals. III SturmLiouville Theory. 8.11 Heat Diffusion in Nonhomogeneous Rods. 8.12 SturmLiouville Problems: Basic Theory. 8.13 Construction of Eigenvalues and Eigenfunctions. 8.14 Singular SturmLiouville Problems. 9 Boundary Value Problems of Mathematical Physics. 9.1 Heat Diffusion in One Dimension. 9.2 Vibration of Strings and Traveling Waves. 9.3 SteadyState Diffusion of Heat in Plates. 9.4 Transient Diffusion of Heat in Plates. 9.5 Vibrations of Drums. 9.6 SteadyState Diffusion of Heat in Solids. 9.7 The Laplace Transform Method. Appendix: Answers and Hints to Selected Exercises. References.
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