Mathematical Tools for Telemedicine

This book is intended for professionals who must deal with telemedicine having little or no knowledge of matrix algebra and matrix calculus, and little or no knowledge of higher mathematics with special reference to differential equations: no other books cover these topics starting from scratch. It would therefore fill the gap existing between very simple and elementary textbooks and much more complicated ones, mainly adopting mathematical and on engineering approaches.

Aims and objectives of this volume are to provide non-mathematicians and non-physicists with an almost complete coverage of the topic, from calculus and linear algebra to matrix derivatives, hat matrices, and regression models, as well as to give basic information about the description of a system by means of differential equations, which will be useful for a deeper understanding of telemedicine.

The book is mainly addressing postgraduate students in medicine, biology, biostatistics, but it would also be a very useful tool researchers in other fields of a medical/biomedical curriculum.

Focus on applications to medicine Education approach to the subject Fills a literature gap as the book is positioned between the most elementary and the complicated ones on this subject

Contenu

Part 1 General introduction.- Chapter 1 A preamble: what is, and what telemedicine is for.- Chapter 2 How the brain works.- Chapter 3 Some examples of logic reasoning in humans.- Chapter 4 Working with data.- Chapter 5 A note on Bayesian probability.- Chapter 6 Neural networks.- Chapter 7 Machine learning and deep learning.- Chapter 8 Arti.cial intelligence.- Part 2 Telemedicine.- Chapter 9 Systems.- Chapter 10 Telemedicine, e-health, telehealth.- Chapter 11 Computer networks.- Chapter 12 Communications.- Chapter 13 Wearable sensors.- Chapter 14 Medical imaging.- Chapter 15 Some areas of telemedicine.- Chapter 16 Telesurgery.- Part 3 Math insights.- Chapter 17 Calculus in one and more variables.- Chapter 18 Integral transforms.- Chapter 19 A primer of fractional calculus.- Chapter 20 Vectors.- Chapter 21 Matrices.- Chapter 22 Matrix differentiation.- Chapter 23 Differential equations.- Chapter 24 Introduction to partial differential equations.- Chapter 25 Some mathematics for neural networks.