Modelling with Differential and Difference Equations

Any student wishing to solve problems via mathematical modelling will find that this book provides an excellent introduction to the subject.

Preface; Introduction to the student; Part I. Simple Models In Mechanics: 1. Newtonian mechanics; 2. Kinematics on a line; 3. Ropes and pulleys; 4. Friction; 5. Differential equations: linearity and SHM; 6. Springs and oscillations; Part II. Models with Difference Equations: 7. Difference equations; 8. Linear difference equations in finance and economics; 9. Non-linear difference equations and population growth; 10. Models for population genetics; Part III. Models with Differential Equations: 11. Continuous growth and decay models; 12. Modelling heat flow; 13. Compartment models of mixing; Part IV. Further Mechanics: 14. Motion in a fluid medium; 15. Damped and forced oscillations; 16. Motion in a plane; 17. Motion in a circle; Part V. Coupled Models: 18. Models with linear interactions; 19. Non-linear coupled models; References; Index.