Scientific computing with ordinary differential equations: By Peter Deuflhard and Folkmar Bornemann. Translated by Werner C. Rheinboldt. Springer, New York. (2002). 485 pages. $59.95. (CD-Rom included.)

BOOK REPORTS 515 Scientific Comuutinq with Ordinatw Differential Equations. By Peter Deuflhard and Folkmar Bornemann. Trans- lated by Werner C. Rheinboldt. Springer, New York. (2902). 485 pages. $59.95. (CD-Rom included.) Contents: Preface. Outline. 1. Tim-dependent processes in science and engineering. 1.1. Newton’s celestial mechanics. 1.2. Classical molecular dynamics. 1.3. Chemical reaction kinetics. 1.4. Electrical circuits. Exercises. 2. Exis- tence and uniqueness for initial value problems. 2.1. Global existence and uniqueness. 2.2. Examples of maximal continuation. 2.3. Structure of nonunique solutions. 2.4. Weakly singular initial value problems. 2.5. Singu- lar perturbation problems. 2.6. Quasilinear differential-algebraic problems. Exercises. 3. Condition of initial value problems. 3.1. Sensitivity under perturbations. 3.1.1. Propagation matrices. 3.1.2. Condition numbers. 3.1.3. Perturbation index of DAE problems. 3.2. Stability of ODES. 3.2.1. Stability concept. 3.2.2. Linear au- tonomous ODES. 3.2.3. Stability of fixed points. 3.3. Stability of recursive mappings. 3.3.1. Linear autonomous recursions. 3.3.2. Stability of fixed points. Exercises. 4. One-step methods for nonstiff IVPs. 4.1. Conver- gence theory. 4.1.1. Consistency. 4.1.2. Convergence. 4.1.3. Concept of stiffness. 4.2. Explicit Runge-Kutta methods. 4.2.1. Concept of Runge-Kutta methods. 4.2.2. Classical Runge-Kutta methods. 4.2.3. Higher-order Runge-Kutta methods. 4.2.4. Discrete condition numbers. 4.3. Explicit extrapolation methods. 4.3.1. Concept of extrapolation. 4.3.2. Asymptotic expansion of discretiaation error. 4.3.3. Extrapolation of explicit midpoint rule. 4.3.4. Extrapolation of StGrmer/Verlet discretization. Exercises. 5. Adaptive control of one-step methods. 5.1. Local accuracy control. 5.2. Control-theoretic analysis. 5.2.1. Excursion to PID controllers. 5.2.2. Step-size selection as controller. 5.3. Error estimation. 5.4. Embedded Runge-Kutta methods. 5.5. Local versus achieved accuracy. Exercises. 6. One-step methods for stiff ODE and DAE IVPs. 6.1. Inheritance of asymptotic sta- bility. 6.1.1. Rational approximation of matrix exponential. 6.1.2. Stability domains. 6.1.3. Stability concepts. 6.1.4. Reversibility and discrete isometrics. 6.1.5. Extension to nonlinear problems. 6.2. Implicit RungeKutta methods. 6.2.1. Stability functions. 6.2.2. Solution of nonlinear systems. 6.3. Collocation methods. 6.3.1. Basic idea of collocation. 6.3.2. Gauss and Radau methods. 6.3.3. Dissipative ODES. 6.3.4. Conservation of quadratic first integrals. 6.4. Linearly implicit one-step methods. 6.4.1. Linearly implicit Runge-Kutta methods. 6.4.2. Lin- early implicit extrapolation methods. 6.4.3. Dynamic elimination of fast modes. Exercises. 7. Multistep methods for ODE and DAE IVPs. 7.1. Multistep methods on equidistant meshes. 7.1.1. Consistency. 7.1.2. Stability. 7.1.3. Convergence. 7.1.4. Discrete condition numbers. 7.2. Inheritance of asymptotic stability. 7.2.1. Weak instability in multistep methods. 7.2.2. Linear stability in stiff problems. 7.3. Direct construction of efficient mul- tistep methods. 7.3.1. Adams methods for nonstiff ODE problems. 7.3.2. BDF methods for stiff ODE and DAE problems. 7.4. Adaptive control of order and step size. 7.4.1. Adams methods on variable meshes. 7.4.2. BDF methods on variable meshes. 7.4.3. Nordsieck representation. Exercises. 8. Boundary value problems for ODES. 8.1. Sensitivity for two-point BVPs. 8.1.1. Local uniqueness. 8.1.2. Condition numbers. 8.2. Initial value meth- ods for timelike BVPs. 8.2.1. Shooting method. 8.2.2. Multiple shooting method. 8.3. Cyclic systems of linear equations. 8.3.1. Discrete condition numbers. 8.3.2. Algorithms. 8.4. Global discretization methods for spacelike BVPs. 8.4.1. Elementary finite difference methods. 8.4.2. Adaptive collocation methods. 8.5. More general types of BVPs. 8.5.1. Computation of periodic orbits. 8.52. Parameter identification in ODES. 8.6. Variational prob- lems 8.6.1. Classical variational problems. 8.6.2. Optimal control problems. Exercises. References. Software. Index. The Dvnamic Neuron. By John Smythies. The MIT Press, Cambridge, MA. (2002). 150 pages. $35. Contents: Preface. Acknowledgments. 1. Synaptic biochemistry. 1.1. Introduction. 1.2. Evidence for synaptic plasticity. 1.3. An introduction to the glutamate synapse and its redox-related biochemical features. 1.4. Biochemical fac- tors in synaptic plasticity. 1.5. The biochemical basis of the Hebbian synapse. 1.6. More redox reactions at the synapse. 2. Endocytosis and exocytosis. 2.1. The role of endocytosis. 2.2. Some enzymes involved in endocytosis. 2.3. Exocytosis. 2.4. Ubiquitation. 2.5. The special case of endocytosis in neurons. 2.6. The functional significance of membrane and receptor endocytosis. 3. Special proteins. 3.1. The role of cell adhesion molecules. 3.2. Scaf- folding proteins. 3.3. Axon growth-directing proteins. 3.4. Role of neurotropins. 3.5. Role of actin. 3.6. Role of local protein synthesis. 4. Miscellaneous items. 4.1. Volume transmission and spillover. 4.2. Other neurtransmit- ters. 4.3. Arachidonic acid signaling. 4.4. Hormonal modulation of synaptic plasticity. 4.5. Psychological stress. 4.6. Energy. 4.7. The role of astrocytes. 5. Pharmacological implications and clinical applications. 6. Conclusions. Appendix A. mRNAs whose level is altered following glutamate receptor stimulation. Appendix B. Receptors that are endocytosed. Notes. Abbreviations and acronyms. References. Index. Finite Elements Usins Made: A Sumbolic Proarammina Avvroach. By A. Portela and A. Charafi. Springer, New York. (2002). 325 pages. $49.95. (CD-Rom included.) Contents: Preface. 1. Introduction to Maple. 1.1. Basics. 1.2. Entering commands. 1.3. Fundamental data types. 1.5. Names. 1.6. Basic types of Maple objects. 1.6.1. Sequences. 1.6.2. Lists. 1.6.3. Sets. 1.6.4. Arrays. 1.6.5. Ta- bles. 1.6.6. Strings. 1.7. Evaluation rules. 1.7.1. Levels of evaluation. 1.7.2. Last-name evaluation. 1.7.3. One-level evaluation. 1.7.4. Special evaluation rules. 1.7.5. Delayed evaluation. 1.8. Algebraic equations. 1.9. Differentiation1 and integration. 1.10. Solving differential equations. 1.11. Expression manipulation. 1.12. Basic programming constructs. 1.13. Functions, procedures and modules. 1.14. Maple’s organization. 1.15. Linear algebra compu- tations. 1.16. Graphics. 1.17. Plotter: Package for finite element graphics. 1.17.1. Example. 1.17.2. Example.