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Essentials of applied mathematics for engineers and scientists /

The second edition of this popular book on practical mathematics for engineers includes new and expanded chapters on perturbation methods and theory. This is a book about linear partial differential equations that are common in engineering and the physical sciences. It will be useful to graduate stu...

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Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autor principal:	Watts, Robert G.
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	Cham, Switzerland : Springer, ©2012.
Edición:	2nd ed.
Colección:	Synthesis lectures on mathematics and statistics ; #12.
Temas:	Engineering mathematics. Differential equations, Partial > Numerical solutions. Differential equations, Linear > Numerical solutions. Fourier analysis. Laplace transformation. Mathématiques de l'ingénieur. Équations aux dérivées partielles > Solutions numériques. Équations différentielles linéaires > Solutions numériques. Analyse de Fourier. Transformation de Laplace. TECHNOLOGY & ENGINEERING > Engineering (General) TECHNOLOGY & ENGINEERING > Reference. Differential equations, Linear > Numerical solutions Differential equations, Partial > Numerical solutions Engineering mathematics Fourier analysis Laplace transformation separation of variables orthogonal functions Laplace transforms complex variables and Sturm-Liouville transforms differential equations perturbation methods perturbation theory
Acceso en línea:	Texto completo

Tabla de Contenidos:

1. Partial differential equations in engineering
1.1 Introductory comments
1.2 Fundamental concepts
Problems
1.3 The heat conduction (or diffusion) equation
1.3.1 Rectangular Cartesian coordinates
1.3.2 Cylindrical coordinates
1.3.3 Spherical coordinates
The Laplacian operator
1.3.4 Boundary conditions
1.4 The vibrating string
1.4.1 Boundary conditions
1.5 Vibrating membrane
1.6 Longitudinal displacements of an elastic bar
Further reading.
2. The Fourier method: separation of variables
2.1 Heat conduction
2.1.1 Scales and dimensionless variables
2.1.2 Separation of variables
2.1.3 Superposition
2.1.4 Orthogonality
2.1.5 Lessons
Problems
2.1.6 Scales and dimensionless variables
2.1.7 Separation of variables
2.1.8 Choosing the sign of the separation constant
2.1.9 Superposition
2.1.10 Orthogonality
2.1.11 Lessons
2.1.12 Scales and dimensionless variables
2.1.13 Getting to one nonhomogeneous condition
2.1.14 Separation of variables
2.1.15 Choosing the sign of the separation constant
2.1.16 Superposition
2.1.17 Orthogonality
2.1.18 Lessons
2.1.19 Scales and dimensionless variables
2.1.20 Relocating the nonhomogeneity
2.1.21 Separating variables
2.1.22 Superposition
2.1.23 Orthogonality
2.1.24 Lessons
Problems
2.2 Vibrations
2.2.1 Scales and dimensionless variables
2.2.2 Separation of variables
2.2.3 Orthogonality
2.2.4 Lessons
Problems
Further reading.
3. Orthogonal sets of functions
3.1 Vectors
3.1.1 Orthogonality of vectors
3.1.2 Orthonormal sets of vectors
3.2 Functions
3.2.1 Orthonormal sets of functions and Fourier series
3.2.2 Best approximation
3.2.3 Convergence of Fourier series
3.2.4 Examples of Fourier series
Problems
3.3 Sturm-Liouville problems: orthogonal functions
3.3.1 Orthogonality of eigenfunctions
Problems
Further reading.
4. Series solutions of ordinary differential equations
4.1 General series solutions
4.1.1 Definitions
4.1.2 Ordinary points and series solutions
4.1.3 Lessons: finding series solutions for differential equations with ordinary points
Problems
4.1.4 Regular singular points and the method of frobenius
4.1.5 Lessons: finding series solution for differential equations with regular singular points
4.1.6 Logarithms and second solutions
Problems
4.2 Bessel functions
4.2.1 Solutions of Bessel's equation
Here are the rules
4.2.2 Fourier-Bessel series
Problems
4.3 Legendre functions
4.4 Associated Legendre functions
Problems
Further reading.
5. Solutions using Fourier series and integrals
5.1 Conduction (or diffusion) problems
5.1.1 Time-dependent boundary conditions
5.2 Vibrations problems
Problems
5.3 Fourier integrals
Problem
Further reading.
6. Integral transforms: the Laplace transform
6.1 The Laplace transform
6.2 Some important transforms
6.2.1 Exponentials
6.2.2 Shifting in the s -domain
6.2.3 Shifting in the time domain
6.2.4 Sine and cosine
6.2.5 Hyperbolic functions
6.2.6 Powers of t: tm
6.2.7 Heaviside step
6.2.8 The Dirac Delta function
6.2.9 Transforms of derivatives
6.2.10 Laplace transforms of integrals
6.2.11 Derivatives of transforms
6.3 Linear ordinary differential equations with constant coefficients
6.4 Some important theorems
6.4.1 Initial value theorem
6.4.2 Final value theorem
6.4.3 Convolution
6.5 Partial fractions
6.5.1 Nonrepeating roots
6.5.2 Repeated roots
6.5.3 Quadratic factors: complex roots
Problems
Further reading.
7. Complex variables and the Laplace inversion integral
7.1 Basic properties
7.1.1 Limits and differentiation of complex variables: 7.1.1
Analytic functions
Integrals
7.1.2 The Cauchy integral formula
Problems.
8. Solutions with Laplace transforms
8.1 Mechanical vibrations
Problems
8.2 Diffusion or conduction problems
Problems
8.3 Duhamel's theorem
Problems
Further reading.
9. Sturm-Liouville transforms
9.1 A preliminary example: Fourier sine transform
9.2 Generalization: the Sturm-Liouville transform: theory
9.3 The inverse transform
Problems
Further reading.
10. Introduction to perturbation methods
10.1 Examples from algebra
10.1.1 Regular perturbation
10.1.2 Singular perturbation.
11. Singular perturbation theory of differential equations.
Appendix A. The roots of certain transcendental equations
Appendix B.
Author's biography.

Essentials of applied mathematics for engineers and scientists /

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