Author | Gustafson, Grant B. author |
---|---|
Title | Analytical and Computational Methods of Advanced Engineering Mathematics [electronic resource] / by Grant B. Gustafson, Calvin H. Wilcox |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0633-0 |
Descript | XXIV, 733 p. online resource |
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 First-Order Equations -- 2.4 Exact Equations -- 2.5 Applications to Some Second-Order 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 Second-Order Equations โ Structure of Solutions -- 3.3 Linear Second-Order Equations with Constant Coefficients -- 3.4 Linear Second-Order Equations with Analytic Coefficients -- 3.5 Numerical Methods for Second-Order 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 Cramerโs 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 X-Ray Diffraction and Crystal Structure -- 7 Partial Differential Equations of Mathematical Physics -- 7.1 Vibrating Strings: DโAlembertโs Wave Equation -- 7.2 Heat Diffusion in Rods: Fourierโs Heat Equation -- 7.3 Heat Diffusion in Plates -- 7.4 Steady-State Heat Diffusion in Plates: The Laplace Equation -- 7.5 Vibrations of Drums -- 7.6 Heat Diffusion in Solids -- 7.7 Steady-State Heat Diffusion in Solids -- 8 Fourier Analysis and Sturm-Liouville Theory -- 1 Fourier Series -- II Fourier Integrals -- III Sturm-Liouville Theory -- 9 Boundary Value Problems of Mathematical Physics -- 9.1 Heat Diffusion in One Dimension -- 9.2 Vibration of Strings and Traveling Waves -- 9.3 Steady-State Diffusion of Heat in Plates -- 9.4 Transient Diffusion of Heat in Plates -- 9.5 Vibrations of Drums -- 9.6 Steady-State Diffusion of Heat in Solids -- 9.7 The Laplace Transform Method -- Appendix: Answers and Hints to Selected Exercises -- References