About The BookWhile compiling this book, I have developed chapter 1 on 'Partial Differential Equations, Stochastic Generalization and Coordinate Systems Orthogonality for Modeling Cancer', Chapter 2 on 'Hilbert Space and Orthogonal Basis for Precise Understanding of Cancer Prognosis and Treatments via orthogonal Therapies, ' Chapter 3 on 'Adomian Decomposition, Laguerre Polynomials and Series Solution for Cancer Modeling, ' Chapter 4 on 'Partial Fraction Decomposition: Decomposing Cancer Anomalies via Nonlinear Fractional PDEs, ' Chapter 5 on 'The Harmonics: Cancer Prognosis and Treatments Using Resonant Frequencies and Harmonic Generation Imaging, ' Chapter 6 on 'The Laplace Transforms: Applications of CNT's In Cancer Prognosis and Treatments, ' Chapter 7 on 'Applications of Random Initial Values Generation in Cancer Initiation and Progression, ', Chapter 8 on 'Mathematical Models and Cancer Research, ' Chapter 9 on 'Genetic Algorithms in Cancer Research, ' Chapter 10 on 'Somatic Evolution: Harnessing Evolution in Therapeutics, ' Chapter 11 'Power Law Applications in Modeling Cancer Tumor and Metastatic Growth, ' Chapter 12 on 'Models Integration in Cancer Systems Biology and Fuzzy Imaging', Chapter 13 on 'Evolutionary Dynamics for Precise Understanding of Tumor Growth via Exponential Growth Model, ' Chapter 14 on 'Quantitative Computer Simulation for Modeling Cancer Anomalous Behavior via Nonlinear Fractional PDEs, ' Chapter 15 on 'Statistical Testing of Hypotheses in Cancer Research, ' Chapter 16 on 'Optimal Control Problems in clinical trials and Cancer Prognosis and Treatments', ' Chapter 17 on Applications of Boundary-Value Analysis of Non Fractional PDEs in Modeling Anomalous Behavior in Cancer' and Chapter 18 on 'Spectral Clustering Applications in Cancer Prognosis and Treatments via Nonlinear Stochastic PDEs'. Partial differential equation is known to be the basis of all physical problems and real world problems like CANCER can be formulated as initial-boundary value partial differential equation. It was in the year 2016, that I wrote a book entitled "Exact Solutions for Partial Differential Equations," Published in Germany. The book presents a novel and robust initial-boundary value analysis framework for partial differential equations. The EXACT analytical solutions are generated from the initial conditions and satisfied the boundary conditions of the fractional nonlinear partial differential equations.In this book, which has been written completely new, I have explored the evolutionary dynamics of cancer and the use of evolutionary and genetic PDEs equations with random initial values in cancer development and response to therapies. Cancer emerges due to an evolutionary process in the SOMATIC tissue. The fundamental laws of evolution can best be formulated as EXACT mathematical equations. Therefore, the process of cancer initiation, progression and treatment is amenable to mathematical investigation. Thus, cancer as a random biodynamical system with anomalous behavior can be modeled with exact mathematical formulation.The subject matter has been so arranged that even a layman can understand how to apply the "exact mathematical solutions" to the problems of CANCER! This book is strongly and widely recommended for in-depth references in all matter of cancer research.
