Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as weil as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high Ievel of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. T AM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Seiences ( AMS) series, which will focus on advanced textbooks and research Ievel monographs. Preface to the Fourth Edition There are two major changes in the Fourth Edition of Differential Equations and Their Applications. The first concerns the computer programs in this text. In keeping with recent trends in computer science, we have replaced all the APL programs with Pascal and C programs. The Pascal programs appear in the text in place ofthe APL programs, where they are followed by the Fortran programs, while the C programs appear in Appendix C.
Firstorder differential equations
12 Firstorder linear differential equations
13 The Van Meegeren art forgeries
14 Separable equations
15 Population models
16 The spread of technological innovations
17 An atomic waste disposal problem
18 The dynamics of tumor growth mixing problems and orthogonal trajectories
33 Dimension of a vector space
34 Applications of linear algebra to differential equations
35 The theory of determinants
36 Solutions of simultaneous linear equations
37 Linear transformations
38 The eigenvalueeigenvector method of finding solutions
39 Complex roots
310 Equal roots
19 Exact equations and why we cannot solve very many differential equations
110 The existenceuniqueness theorem Picard iteration
111 Finding roots of equations by iteration
1111 Newtons method
112 Difference equations and how to compute the interest due on your student loans
113 Numerical approximations Eulers method
1131 Error analysis for Eulers method
114 The three term Taylor series method
115 An improved Euler method
116 The RungeKutta method
117 What to do in practice
Secondorder linear differential equations
22 Linear equations with constant coefficients
221 Complex roots
222 Equal roots reduction of order
23 The nonhomogeneous equation
24 The method of variation of parameters
25 The method of judicious guessing
26 Mechanical vibrations
261 The Tacoma Bridge disaster
262 Electrical networks
27 A model for the detection of diabetes
28 Series solutions
257 Singular points Euler equations
282 Regular singular points the method of Frobenius
283 Equal roots and roots differing by an integer
29 The method of Laplace transforms
210 Some useful properties of Laplace transforms
211 Differential equations with discontinuous righthand sides
212 The Dirac delta function
213 The convolution integral Consider the initialvalue problem
214 The method of elimination for systems
215 Higherorder equations
Systems of differential equations