An Introduction to Differential Equations; Order and Chaos

by Florin Diacu, University of Victoria

• ISBN13: 9780716732969
• ISBN10: 0716732963
• Format: Trade Book
• Copyright: 2000-08-15
• Publisher: W. H. Freeman

Summary

In the past ten years, the teaching of calculus--and consequently that of differential-equations--has seen a split between the traditional approach and a more intuitive one, commonly known as "reform." An Introduction to Differential Equations reconciles these two directions. It keeps what is good and efficient from the classical style while eliminating the non-essential and heavy-going. And it includes the newer, more qualitative methods involving modeling and computers, but without over-emphasizing technology. By combining the most valuable aspects of the two approaches, An Introduction to Differential Equations provides students with a global and realistic view of the methods used today in differential equations.

Table of Contents

Preface	ix
Introduction	1	(12)
First-Order Equations	13	(70)
Equations and Solutions	13	(8)
Separable Equations	21	(11)
Linear Equations	32	(9)
Qualitative Methods	41	(9)
Existence and Uniqueness	50	(10)
Numerical Methods	60	(8)
Computer Applications	68	(12)
Modeling Experiments	80	(3)
Second-Order Equations	83	(76)
Homogeneous Equations	83	(9)
Integrable Cases	92	(10)
Nonhomogeneous Equations	102	(8)
Harmonic Oscillators	110	(11)
Qualitative Methods	121	(13)
Numerical Methods	134	(8)
Computer Applications	142	(14)
Modeling Experiments	156	(3)
Linear Systems	159	(66)
Linear Algebra	159	(10)
Fundamental Results	169	(10)
Equations with Constant Coefficients	179	(10)
Qualitative Methods	189	(11)
Numerical Methods	200	(8)
Computer Applications	208	(14)
Modeling Experiments	222	(3)
Nonlinear Systems	225	(44)
Linearization	225	(10)
Periodic Solutions	235	(6)
Gradient and Hamiltonian Systems	241	(10)
Stability	251	(8)
Chaos	259	(7)
Modeling Experiments	266	(3)
The Laplace Transform	269	(40)
Fundamental Properties	269	(8)
Step Functions	277	(11)
Initial Value Problems	288	(9)
Computer Applications	297	(9)
Modeling Experiments	306	(3)
Power Series Solutions	309	(36)
The Power Series Method	309	(7)
Approximations	316	(7)
Regular Singular Points	323	(8)
Computer Applications	331	(12)
Modeling Experiments	343	(2)
Solutions to Odd Numbered Problems	345	(44)
Bibliography	389	(2)
Sources of Photographs	391	(2)
Index	393