5 Solution of linear equations containing a square matrix

Kapitel in diesem Buch

1. Frontmatter I
2. Preface V
3. Introduction VII
4. Contents XI
5. Part I Applied matrix algebra
6. 1 Matrices and linear algebraic equations 3
7. 2 Determinants 45
8. 3 Vectors and vector expansions 66
9. 4 Solution of linear equations by eigenvector expansions 83
10. 5 Solution of linear equations containing a square matrix 123
11. 6 Generalized eigenvectors and canonical forms 161
12. 7 Quadratic forms, positive definite matrices and other applications 180
13. Part II
14. Abstract vector space concepts 206
15. 8 Vector space over a field 209
16. 9 Linear transformations 216
17. 10 Normed and inner product vector spaces 231
18. 11 Applications of finite-dimensional linear algebra 255
19. Part III Linear ordinary differential equations-initial value problems, complex variables and Laplace transform
20. 12 The linear initial value problem 279
21. 13 Linear systems with periodic coefficients 294
22. 14 Analytic solutions, adjoints and integrating factors 304
23. 15 Introduction to the theory of functions of a complex variable 320
24. 16 Series solutions and special functions 346
25. 17 Laplace transforms 363
26. Part IV Linear ordinary differential equations-boundary value problems
27. 18 Two-point boundary value problems 425
28. 19 The nonhomogeneous BVP and Green’s function 447
29. 20 Eigenvalue problems for differential operators 480
30. 21 Sturm–Liouville theory and eigenfunction expansions 498
31. 22 Introduction to the solution of linear integral equations 522
32. Part V Fourier transforms and solution of boundary and initial-boundary value problems
33. 23 Finite Fourier Transforms 553
34. 24 Fourier transforms on infinite intervals 600
35. 25 Fourier transforms in cylindrical and spherical geometries 645
36. Part VI
37. Formulation and solution of some classical chemical engineering problems 684
38. 26 The classical Graetz–Nusselt problem 687
39. 27 Friction factors for steady-state laminar flow in ducts 699
40. 28 Multicomponent diffusion and reaction 708
41. 29 Packed-bed chromatography 726
42. 30 Stability of transport and reaction processes 745
43. Bibliography
44. Index 765