Applied engineering mathematics / / Xin-She Yang

• Autore: Yang Xin-She
• Pubblicazione: Cambridge, UK, : Cambridge International Science Publishing, c2007
• Descrizione fisica: 1 online resource (333 p.)
• Soggetto topico: Engineering mathematics; Mathematical analysis
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: This book endeavours to strike a balance between mathematical and numerical coverage of a wide range of mathematical methods and numerical techniques. It strives to provide an introduction, especially for undergraduates and graduates, to engineering mathematics and its applications. Topics include advanced calculus, ordinary differential equations, partial differential equations, vector and tensor analysis, calculus of variations, integral equations, the finit difference method, reaction-diffusion system, and probability and statistics. The book also emphasizes the application of important mathematical methods with dozens of worked examples. The applied topics include elasticity, harmonic motion, chaos, kinematics, pattern formation and hypothesis testing. The book can serve as a textbook in engineering mathematics, mathematical modelling and scientific computing.
• Titolo autorizzato: Applied engineering mathematics
• ISBN: 1-907343-65-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910958953503321
• Lo trovi qui: Univ. Federico II