Advanced Mathematical Methods in Science and EngineeringCRC Press, 13. 10. 2000 - Počet stran: 752 Gathering an extensive range of mathematical topics into a plenary reference/text for solving science and engineering problems, Advanced Mathematical Models in Science and Engineering elucidates integral methods, field equation derivations, and operations applicable to modern science systems. Applying academic skills to practical problems in science and engineering, the author reviews basic methods of integration and series solutions for ordinary differential equations; introduces derivations and solution methods for linear boundary value problems in one dimension, covering eigenfunctions and eigenfunction expansions, orthogonality, and adjoint and self-adjoint systems; discusses complex variables, calculus, and integrals as well as application of residues and the integration of multivalued functions; considers linear partial differential equations in classical physics and engineering with derivations for the topics of wave equations, heat flow, vibration, and strength of materials; clarifies the calculus for integral transforms; explains Green's functions for ordinary and partial differential equations for unbounded and bounded media; examines asymptotic methods; presents methods for asymptotic solutions of ordinary differential equations; and more. |
Obsah
ORDINARY DIFFERENTIAL EQUATIONS | 1 |
SERIES SOLUTIONS OF ORDINARY | 19 |
8 | 29 |
SPECIAL FUNCTIONS | 43 |
9 | 56 |
11 | 62 |
15 | 68 |
17 | 75 |
6 | 548 |
APPENDIX A INFINITE SERIES | 585 |
INFINITE SERIES OF FUNCTIONS OF ONE VARIABLE | 591 |
APPENDIX B SPECIAL FUNCTIONS | 599 |
FRESNEL FUNCTIONS Cx Sx AND Fx | 606 |
TCHEBYSHEV POLYNOMIALS Tnx AND Unx | 612 |
CONFLUENT HYPERGEOMETRIC FUNCTIONS Macs | 618 |
ORTHOGONAL COORDINATE SYSTEMS | 625 |
22 | 89 |
25 | 95 |
EIGENVALUE PROBLEMS | 107 |
3 | 113 |
WAVES IN ACOUSTIC HORNS | 124 |
7 | 130 |
FUNCTIONS OF A COMPLEX VARIABLE | 185 |
PARTIAL DIFFERENTIAL EQUATIONS | 293 |
INTEGRAL TRANSFORMS | 383 |
GREENS FUNCTIONS | 453 |
19 | 460 |
20 | 479 |
24 | 485 |
28 | 493 |
29 | 500 |
32 | 507 |
34 | 515 |
3 | 538 |
DIRAC DELTA FUNCTIONS | 635 |
APPENDIX E PLOTS OF SPECIAL FUNCTIONS | 651 |
MODIFIED BESSEL FUNCTION OF THE FIRST AND SECOND KIND OF ORDER 0 1 2 | 653 |
BESSEL FUNCTION OF THE FIRST AND SECOND KIND OF ORDER 12 | 654 |
| 655 | |
ANSWERS | 663 |
CHAPTER 2 | 665 |
CHAPTER 3 | 669 |
CHAPTER 4 | 670 |
CHAPTER 5 | 683 |
CHAPTER 6 | 690 |
CHAPTER 7 | 705 |
CHAPTER 8 | 710 |
CHAPTER 9 | 719 |
APPENDIX A | 722 |
| 723 | |
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Advanced Mathematical Methods in Science and Engineering, Second Edition S.I. Hayek Náhled není k dispozici. - 2010 |
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