Author | Braun, Martin. author |
---|---|
Title | Differential Equations and Their Applications [electronic resource] : Short Version / by Martin Braun |
Imprint | New York, NY : Springer US, 1978 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0053-3 |
Descript | VIII, 319 p. online resource |
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 Lanchesterโs 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