B Fréchet and Gâteaux derivatives

Chapters in this book

1. Frontmatter I
2. Preface V
3. Contents VII
4. 1 Polynomial interpolation 1
5. 2 Numerical integration 44
6. 3 Piecewise polynomial approximation 89
7. 4 The Euler method 122
8. 5 The order 2 Taylor series method – TS(2) 149
9. 6 The order p Taylor series method – TS (p) 168
10. 7 Linear multistep methods – LMMs 188
11. 8 Runge–Kutta methods – RKMs 204
12. 9 The series solution method – SSM 227
13. 10 The Adomian polynomials method 249
14. 11 Weak solutions and variational methods for some classes of linear first-order dynamic systems 266
15. 12 Variational methods for nonlinear dynamic equations 281
16. A Rolle’s theorem 303
17. B Fréchet and Gâteaux derivatives 309
18. C Pötzsche’s chain rules 319
19. D Lebesgue integration. L^p-spaces. Sobolev spaces 329
20. E Mazur’s theorem 377
21. Bibliography 379
22. Index 381