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Field name	Details
Dewey Class	515
Title	Differential Equations and Their Applications ([EBook] :) : Short Version / / by Martin Braun.
Author	Braun, Martin
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer US, , 1978.
Physical Details	VIII, 319 p. : online resource.
ISBN	9781468400533
Summary Note	This textbook is a unique blend of the theory of differential equations and their exciting application to ··real world" problems. First, and foremost, it is a rigorous study of ordinary differential equations and can be fully understood by anyone who has completed one year of calculus. However, in addition to the traditional applications, it also contains many exciting '·real life" problems. These applications are completely self contained. First, the problem to be solved is outlined clearly, and one or more differential equations are derived as a model for this problem. These equations are then solved, and the results are compared with real world data. The following applications are covered in this text. I. In Section 1.3 we prove that the beautiful painting ··Disciples at Emmaus" which was bought by the Rembrandt Society of Belgium for $170,000 was a modern forgery. 2. In Section 1.5 we derive differential equations which govern the population growth of various species, and compare the results predicted by our models with the known values of the populations. 3. In Section 1.6 we try to determine whether tightly sealed drums filled with concentrated waste material will crack upon impact with the ocean floor. In this section we also describe several tricks for obtaining informa tion about solutions of a differential equation that cannot be solved explicitly.:
Contents note	1 First-order differential equations -- 1.1 Introduction -- 1.2 First-order linear differential equations -- 1.3 The van Meegeren art forgeries -- 1.4 Separable equations -- 1.5 Population models -- 1.6 An atomic waste disposal problem -- 1.7 The dynamics of tumor growth, mixing problems, and orthogonal trajectories -- 1.8 Exact equations, and why we cannot solve very many differential equations -- 1.9 The existence-uniqueness theorem; Picard iteration -- 1.10 Difference equations, and how to compute the interest due on your student loans -- 2 Second-order linear differential equations -- 2.1 Algebraic properties of solutions -- 2.2 Linear equations with constant coefficients -- 2.3 The nonhomogeneous equation -- 2.4 The method of variation of parameters -- 2.5 The method of judicious guessing -- 2.6 Mechanical vibrations -- 2.7 A model for the detection of diabetes -- 2.8 Series solutions -- 2.9 The method of Laplace transforms -- 2.10 Some useful properties of Laplace transforms -- 2.11 Differential equations with discontinuous right-hand sides -- 2.12 The Dirac delta function -- 2.13 The convolution integral -- 2.14 The method of elimination for systems -- 2.15 A few words about higher-order equations -- 3 Systems of differential equations -- 3.1 Algebraic properties of solutions of linear systems -- 3.2 Vector spaces -- 3.3 Dimension of a vector space -- 3.4 Applications of linear algebra to differential equations -- 3.5 The theory of determinants -- 3.6 The eigenvalue-eigenvector method of finding solutions -- 3.7 Complex roots -- 3.8 Equal roots -- 3.9 Fundamental matrix solutions; eAt -- 3.10 The nonhomogeneous equation; variation of parameters -- 3.11 Solving systems by Laplace transforms -- 4 Qualitative theory of differential equations -- 4.1 Introduction -- 4.2 The phase-plane -- 4.3 Lanchester’s combat models and the battle of Iwo Jima -- Appendix A -- Some simple facts concerning functions of several variables -- Appendix B -- Sequences and series -- Answers to odd-numbered exercises.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4684-0053-3
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Braun, Martin . Corporate Authors: SpringerLink (Online service) . Classification: 515 .

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Differential Equations and Their Applications: Short Version /

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