2 Determinants

Chapters in this book

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 1
7. 2 Determinants 44
8. 3 Vectors and vector expansions 65
9. 4 Solution of linear equations by eigenvector expansions 82
10. 5 Solution of linear equations containing a square matrix 122
11. 6 Generalized eigenvectors and canonical forms 160
12. 7 Quadratic forms, positive definite matrices and other applications 179
13. Part II: Abstract vector space concepts
14. Introduction 205
15. 8 Vector space over a field 207
16. 9 Linear transformations 214
17. 10 Normed and inner product vector spaces 229
18. 11 Applications of finite-dimensional linear algebra 253
19. Part III: Linear ordinary differential equations-initial value problems, complex variables and laplace transform
20. 12 The linear initial value problem 277
21. 13 Linear systems with periodic coefficients 292
22. 14 Analytic solutions, adjoints and integrating factors 302
23. 15 Introduction to the theory of functions of a complex variable 318
24. 16 Series solutions and special functions 344
25. 17 Laplace transforms 361
26. Part IV: Linear ordinary differential equations-boundary value problems
27. 18 Two-point boundary value problems 423
28. 19 The nonhomogeneous BVP and Green’s function 445
29. 20 Eigenvalue problems for differential operators 478
30. 21 Sturm–Liouville theory and eigenfunction expansions 496
31. 22 Introduction to the solution of linear integral equations 520
32. Part V: Fourier transforms and solution of boundary and initial-boundary value problems
33. 23 Finite Fourier transforms 551
34. 24 Fourier transforms on infinite intervals 598
35. 25 Fourier transforms in cylindrical and spherical geometries 642
36. Part VI: Formulation and solution of some classical chemical engineering problems
37. Introduction 681
38. 26 The classical Graetz–Nusselt problem 683
39. 27 Friction factors for steady-state laminar flow in ducts 695
40. 28 Multicomponent diffusion and reaction 704
41. 29 Packed-bed chromatography 721
42. 30 Stability of transport and reaction processes 740
43. Bibliography 759
44. Index 761