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AuthorBraun, Martin. author
TitleDifferential Equations and Their Applications [electronic resource] / by Martin Braun
ImprintNew York, NY : Springer US, 1983
Edition (Third Edition) Short Version
Connect tohttp://dx.doi.org/10.1007/978-1-4684-0173-8
Descript X, 341 p. online resource

SUMMARY

There are two major changes in the Third Edition of Differential Equations and Their Applications. First, we have completely rewritten the section on singular solutions of differential equations. A new section, 2.8.1, dealing with Euler equations has been added, and this section is used to motivate a greatly expanded treatment of singular equations in sections 2.8.2 and 2.8.3. Our second major change is in Section 2.6, where we have switched to the metric system of units. This change was requested by many of our readers. In addition to the above changes, we have updated the material on population models, and have revised the exercises in this section. Minor editorial changes have also been made throughout the text. New York City March,1983 Martin Braun vi Preface to the First Edition 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


CONTENT

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 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 Lanchesterโ{128}{153}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


Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis



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