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140122  eng 
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a 9789400954922

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1 

a Cherruault, Y.

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a Mathematical Modelling in Biomedicine
h Elektronische Ressource
b Optimal Control of Biomedical Systems
c by Y. Cherruault

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a 1st ed. 1986

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a Dordrecht
b Springer Netherlands
c 1986, 1986

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a XVIII, 258 p
b online resource

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0 

a 0 Introduction  1 General Remarks on Modelling  1.1 Definitions  1. 2 The main techniques for modeling  1.3 Difficulties in modeling  2 Identification and Control in Linear Compartmental Analysis  2.1 The identification problem  2.2 The uniqueness problem  2.3 Numerical methods for identification  2.4 About the nonlinear case  2.5 Optimization techniques  3 Optimal Control in Compartmental Analysis  3.1 General considerations  3.2 A first explicit approach  3.3 The general solution  3.4 Numerical method  3.5 Optimal control in nonlinear cases  4 Relations Between dose and Effect  4.1 General considerations  4.2 The nonlinear approach  4.3 Simple functional model  4.4 Optimal therapeutics  4.5 Numerical results  4.6 Nonlinear compartment approach  4.7 Optimal therapeutics using a linear approach  4.8 Optimal control in a compartmental model with time lag  5 General Modelling in Medicine 

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a 5.1 The problem and the corresponding model  5.2 The identification problem  5.3 A simple method for defining optimal therapeutics  5.4 The Pontryagin method  5.5 A simplified technique giving a suboptimum  5.6 A naive but useful method  6 Blood Glucose Regulation  6.1 Identification of parameters in dogs  6.2 The human case  6.3 Optimal control for optimal therapeutics  6.4 Optimal control problem involving several criteria  7 Integral Equations in Biomedicine  7.1 Compartmental analysis  7.2 Integral equations from biomechanics  7.3 Other applications of integral equations  8 Numerical Solution of Integral Equations  8.1 Linear integral equations  8.2 Numerical techniques for nonlinear integral equations  8.3 Identification and optimal control using integral equations  8.4 Optimal control and nonlinear integral equations  9 ProblemsRelated to Partial Differential Equations  9.1 General remarks 

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a 9.2 Numerical resolution of partial differential equations  9.3 Identification in partial differential equations  9.4 Optimal control with partial differential equations  9.5 Other approaches for optimal control  9.6 Other partial differential equations  10 Optimality in Human Physiology  10.1 General remarks  10.2 A mathematical model for thermoregulation  10.3 Optimization of pulmonary mechanics  10.4 Conclusions  11 Errors in Modelling  11.1 Compartmental modeling  11.2 Sensitivity analysis  12 Open Problems in Biomathematics  12.1 Biological systems with internal delay  12.2 Biological systems involving retroaction  12.3 Action of two (or more) drugs in the human organism  12.4 Numerical techniques for global optimization  12.5 Biofeedback and systems theory  12.6 Optimization of industrial processes  12.7 Optimality in physiology  13 CONCLUSIONS  Appendix — The Alienor program  References

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a Mathematical Modeling and Industrial Mathematics

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a Mathematical models

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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a Mathematics and Its Applications

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a 10.1007/9789400954922

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u https://doi.org/10.1007/9789400954922?nosfx=y
x Verlag
3 Volltext

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a 003.3

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a Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton. The Scandal of Father Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (nontrivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, cod ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces
