By James C. Robinson
Publisher: Cambridge University Press
Print Publication Year:2004
Online Publication Date:September 2012
Online ISBN:9780511801204
Hardback ISBN:9780521826501
Paperback ISBN:9780521533911
Book DOI: http://dx.doi.org/10.1017/CBO9780511801204
Subjects: Differential and integral equations, dynamical systems and control theory
This introduction to ordinary differential and difference equations is suited not only for mathematicians but for scientists and engineers as well. Exact solutions methods and qualitative approaches are covered, and many illustrative examples are included. Matlab is used to generate graphical representations of solutions. Numerous exercises are featured and proved solutions are available for teachers.
Reviews:
pp. i-vi
pp. vii-xii
pp. xiii-xiv
pp. 1-2
Part I - First order differential equations: Read PDF
pp. 3-4
1 - Radioactive decay and carbon dating: Read PDF
pp. 5-8
2 - Integration variables: Read PDF
pp. 9-10
3 - Classification of differential equations: Read PDF
pp. 11-17
4 - *Graphical representation of solutions using MATLAB: Read PDF
pp. 18-21
5 - ‘Trivial’ differential equations: Read PDF
pp. 22-37
6 - Existence and uniqueness of solutions: Read PDF
pp. 38-45
7 - Scalar autonomous ODEs: Read PDF
pp. 46-58
8 - Separable equations: Read PDF
pp. 59-74
9 - First order linear equations and the integrating factor: Read PDF
pp. 75-88
10 - Two ‘tricks’ for nonlinear equations: Read PDF
pp. 89-98
Part II - Second order linear equations with constant coefficients: Read PDF
pp. 99-100
11 - Second order linear equations: general theory: Read PDF
pp. 101-110
12 - Homogeneous second order linear equations: Read PDF
pp. 111-119
pp. 120-130
14 - Inhomogeneous second order linear equations: Read PDF
pp. 131-140
pp. 141-149
16 - Higher order linear equations: Read PDF
pp. 150-156
Part III - Linear second order equations with variable coefficients: Read PDF
pp. 157-158
17 - Reduction of order: Read PDF
pp. 159-163
18 - *The variation of constants formula: Read PDF
pp. 164-169
19 - *Cauchy–Euler equations: Read PDF
pp. 170-175
20 - *Series solutions of second order linear equations: Read PDF
pp. 176-198
Part IV - Numerical methods and difference equations: Read PDF
pp. 199-200
pp. 201-212
22 - Difference equations: Read PDF
pp. 213-223
23 - Nonlinear first order difference equations: Read PDF
pp. 224-232
24 - The logistic map: Read PDF
pp. 233-246
Part V - Coupled linear equations: Read PDF
pp. 247-248
25 - *Vector first order equations and higher order equations: Read PDF
pp. 249-252
26 - Explicit solutions of coupled linear systems: Read PDF
pp. 253-258
27 - Eigenvalues and eigenvectors: Read PDF
pp. 259-268
28 - Distinct real eigenvalues: Read PDF
pp. 269-284
29 - Complex eigenvalues: Read PDF
pp. 285-294
30 - A repeated real eigenvalue: Read PDF
pp. 295-300
31 - Summary of phase portraits for linear equations: Read PDF
pp. 301-306
Part VI - Coupled nonlinear equations: Read PDF
pp. 307-308
32 - Coupled nonlinear equations: Read PDF
pp. 309-322
33 - Ecological models: Read PDF
pp. 323-340
34 - Newtonian dynamics: Read PDF
pp. 341-351
35 - The ‘real’ pendulum: Read PDF
pp. 352-359
36 - *Periodic orbits: Read PDF
pp. 360-363
37 - *The Lorenz equations: Read PDF
pp. 364-372
pp. 373-378
Appendix A - Real and complex numbers: Read PDF
pp. 379-381
Appendix B - Matrices, eigenvalues, and eigenvectors: Read PDF
pp. 382-386
Appendix C - Derivatives and partial derivatives: Read PDF
pp. 387-394
pp. 395-399
No references available.