4. Solving and analyzing some nonlinear first order equations

Kapitel in diesem Buch

1. Frontmatter I
2. Preface V
3. Acknowledgment IX
4. Contents XI
5. 1. A brief survey of some topics in calculus 1
6. 2. First order linear differential equations 7
7. 3. Analytical study of first order differential equations 21
8. 4. Solving and analyzing some nonlinear first order equations 43
9. 5. Exact differential equations 59
10. 6. Second order linear differential equations 73
11. 7. Higher order linear equations 95
12. 8. Systems of first order equations 105
13. 9. Phase plane analysis 125
14. 10. Introduction to stability 149
15. 11. Series solutions for linear differential equations 173
16. 12. Laplace transform 187
17. 13. A primer on equations of Sturm–Liouville type 201
18. 14. A primer on linear PDE in 2D I: first order equations 221
19. 15. A primer on linear PDE in 2D II: second order equations 237
20. 16. The Euler–Lagrange equations in the Calculus of Variations: an introduction 267
21. Bibliography 289
22. Index 291