Applied engineering mathematics /

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Annotation This book strives to provide a concise and yet comprehensive cover-age of all major mathematical methods in engineering. Topics in-clude advanced calculus, ordinary and partial differential equations, complex variables, vector and tensor analysis, calculus of variations, integral transfor...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Yang, Xin-She
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, UK : Cambridge International Science Publishing, 2007.
Temas:
Engineering mathematics.
Mathematical analysis.
Mathématiques de l'ingénieur.
Analyse mathématique.
TECHNOLOGY & ENGINEERING > Material Science.
Engineering mathematics
Mathematical analysis
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Preface
  • Acknowledgements
  • About the Author
  • Contents
  • 1. Calculus
  • 1.1 Differentiations
  • 1.2 Integrations
  • 1.3 Partial Differentiation
  • 1.4 Multiple Integrals
  • 1.5 Some Special Integrals
  • 2. Vector Analysis
  • 2.1 Vectors
  • 2.1.1 Dot Product and Norm
  • 2.2 Vector Algebra
  • 2.3 Applications
  • 3. Matrix Algebra
  • 3.1 Matrix
  • 3.2 Determinant
  • 3.3 Inverse
  • 3.4 Matrix Exponential
  • 3.5 Hermitian and Quadratic Forms
  • 3.6 Solution of linear systems
  • 4. Complex Variables
  • 4.1 Complex Numbers and Functions
  • 4.2 Hyperbolic Functions
  • 4.3 Analytic Functions
  • 4.4 Complex Integrals
  • 5. Ordinary Differential Equations
  • 5.1 Introduction
  • 5.2 First Order ODEs
  • 5.3 Higher Order ODEs
  • 5.4 Linear System
  • 5.5 Sturm-Liouville Equation
  • 5.5.1 Bessel Equation
  • 6. Recurrence Equations
  • 6.1 Linear Difference Equations
  • 6.2 Chaos and Dynamical Systems
  • 6.3 Self-similarity and Fractals
  • 7. Vibration and Harmonic Motion
  • 7.1 Undamped Forced Oscillations
  • 7.2 Damped Forced Oscillations
  • 7.3 Normal Modes
  • 7.4 Small Amplitude Oscillations
  • 8. Integral Transforms
  • 8.1 Fourier Transform
  • 8.2 Laplace Transforms
  • 8.3 Wavelet
  • 9. Partial Differential Equations
  • 9.1 First Order PDE
  • 9.2 Classification
  • 9.3 Classic PDEs
  • 10. Techniques for Solving PDEs
  • 10.1 Separation of Variables
  • 10.2 Transform Methods
  • 10.3 Similarity Solution
  • 10.4 Travelling Wave Solution
  • 10.5 Green's Function
  • 10.6 Hybrid Method
  • 11. Integral Equations
  • 11.1 Calculus of Variations
  • 11.2 Integral Equations
  • 11.3 Solution of Integral Equations
  • 12. Tensor Analysis
  • 12.1 Notations
  • 12.2 Tensors
  • 12.3 Tensor Analysis
  • 13. Elasticity
  • 13.1 Hooke's Law and Elasticity
  • 13.2 Maxwell's Reciprocal Theorem
  • 13.3 Equations of Motion
  • 13.4 Airy Stress Functions.
  • 13.5 Euler-Bernoulli Beam Theory
  • 14. Mathematical Models
  • 14.1 Classic Models
  • 14.2 Other PDEs
  • 15. Finite Difference Method
  • 15.1 Integration of ODEs
  • 15.2 Hyperbolic Equations
  • 15.3 Parabolic Equation
  • 15.4 Elliptical Equation
  • 16. Finite Volume Method
  • 16.1 Introduction
  • 16.2 Elliptic Equations
  • 16.3 Parabolic Equations
  • 16.4 Hyperbolic Equations
  • 17. Finite Element Method
  • 17.1 Concept of Elements
  • 17.2 Finite Element Formulation
  • 17.3 Elasticity
  • 17.4 Heat Conduction
  • 17.5 Time-Dependent Problems
  • 18. Reaction Diffusion System
  • 18.1 Heat Conduction Equation
  • 18.2 Nonlinear Equations
  • 18.3 Reaction-Diffusion System
  • 19. Probability and Statistics
  • 19.1 Probability
  • 19.2 Statistics
  • References
  • Appendix A Mathematical Formulas
  • A.1 Differentiations and Integrations
  • A.2 Vectors and Matrices
  • A.3 Asymptotics
  • A.4 Special Integrals
  • Index.

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