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Viser: Differential and Difference Equations Through Computer Experiments - With Diskettes Containing PHASER: an Animator/Simulator for Dynamical Systems for IBM Personal Computers
Differential and Difference Equations Through Computer Experiments
With Diskettes Containing PHASER: an Animator/Simulator for Dynamical Systems for IBM Personal Computers
Hüseyin Kocak
(2012)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- Paperback
- Udgiver: Springer New York (Februar 2012)
- ISBN: 9781468402735
1. What is a Differential Equation'.-
1.1. Systems of Differential Equations.-
1.2. Geometrical Interpretation.-
1.3. Higher Order Equations.-
1.4. Non-autonomous Equations.-
2. Numerical Methods.-
2.1. Overview of Numerics.-
2.2. A Comparison of Algorithms.-
2.3. Practical Guidelines.-
3. What is a Difference Equation'.-
3.1. One-dimensional Difference Equations.-
3.2. Application: Calculating $$\sqrt 2$$.-
3.3. Systems of Difference Equations.-
3.4. Planar Poincare Maps.- II: Handbook of PHASER.-
4. Learning to Use PHASER.-
4.1. The Startup Screen Layout.-
4.2. Interacting with PHASER.-
5. Lessons with PHASER.- Lesson
1. In and out of PHASER.- Lesson
2. Changing menus.- Lesson
3. Direction field.- Lesson
4. Changing views.- Lesson
5. Graphing variables.- Lesson
6. Initial conditions and parameters.- Lesson
7. Making transcripts for demonstrations.- Lesson
8. Browsing through the library.- Lesson
9. Entering your equations.- Lesson
10. Euler vs. Runge-Kutta.- Lesson
11. Stair step diagrams.- Lesson
12. Three-dimensional graphics.- Lesson
13. Advanced graphics: A 4D example.- Lesson
14. Planar sections and Poincare maps.- Lesson
15. Grand finale: Demo.-
6. Reference Guide to Menus.-
6.1. The NUMERICS Menu.-
6.2. The UTILITIES Menu.-
6.3. The VISUALAID Menu.-
6.4. The Graphical VIEWS.- III: Library of Equations.-
7. Differential Equations.-
7.1. One-dimensional Equations cubicld.-
7.2. Two-dimensional Equations linear2d, pendulum, vanderpol, predprey, saddlenod, pitchfork, transcrit, hopf, dzerol, dzero2, dzero3, hilbert2, hilbert4, averfvdp, gradient.-
7.3. Three-dimensional Equations lorenz, linear3d, vibration, bessel, euler, laguerre, legendre, forcevdp, forcepen, mathieu, forceduf, rossler, zeroim, silnikov, silnikov2.-
7.4. Four-dimensional Equations harmoscil, kepler, r3body, henheile, coplvdpl, coplvdp2, couplosc, reson21.-
8. Difference Equations.-
8.1. One-dimensional Equations logistic, dislinld, discubic, newton, tent, singer, mod, arnold.-
8.2. Two-dimensional Equations dislin2d, gauss, quad1, quad2, henon, lozi, dellogis, dispprey, bounball, anosov, cremona, icremona, gingerman.-
8.3. Three-dimensional Equations dislm3d, act.- What remains to be done'.- Appendix A: PHASER Quick Reference.- Appendix B: Library of Equations.- References.