Mathematical Modelling In Biomedicine: Optimal Control Of Biomedical Systems (mathematics And Its Applications)

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 (non-trivially) 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. 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 (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, codƯ ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical proƯ gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces Front Matter....Pages i-xviii Introduction....Pages 1-2 General Remarks on Modelling....Pages 3-14 Identification and Control in Linear Compartmental Analysis....Pages 15-52 Optimal Control in Compartmental Analysis....Pages 53-95 Relations Between Dose and Effect....Pages 96-121 General Modelling in Medicine....Pages 122-136 Blood Glucose Regulation....Pages 137-151 Integral Equations in Biomedicine....Pages 152-161 Numerical Solution of Integral Equations....Pages 162-172 Problems Related to Partial Differential Equations....Pages 173-192 Optimality in Human Physiology....Pages 193-208 Errors in Modelling....Pages 209-216 Open Problems in Biomathematics....Pages 217-237 Conclusions....Pages 238-239 Back Matter....Pages 240-258