9 Phase plane analysis

Chapters in this book

1. Frontmatter I
2. Memorial Dedicated to Professor Antonio Ambrosetti V
3. Preface VII
4. Contents XI
5. 1 A brief survey of some topics in calculus 1
6. 2 First order linear differential equations 8
7. 3 Analytical study of first order differential equations 23
8. 4 Solving and analyzing some nonlinear first order equations 45
9. 5 Exact differential equations 63
10. 6 Second order linear differential equations 79
11. 7 Higher order linear equations 103
12. 8 Systems of first order equations 115
13. 9 Phase plane analysis 143
14. 10 Introduction to stability 167
15. 11 Series solutions for linear differential equations 190
16. 12 Laplace transform 207
17. 13 A primer on equations of Sturm–Liouville type 221
18. 14 A primer on linear PDE in 2D. I: first order equations 241
19. 15 A primer on linear PDE in 2D. II: second order equations 256
20. 16 The Euler–Lagrange equations in the Calculus of Variations: an introduction 288
21. Solutions 311
22. Bibliography 357
23. Index 359