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Introduction to Mathematics for Computational Biology
ISBN-13: 9783031365652 / Twarda / 2023 / 266 str.
Introduction to Mathematics for Computational Biology
ISBN-13: 9783031365652 / Twarda / 2023 / 266 str.
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(netto: 537,98 VAT: 5%)
Najniższa cena z 30 dni: 501,19 zł
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Kategorie:
Kategorie BISAC:
Wydawca:
Springer International Publishing AG
Seria wydawnicza:
ISBN-13:
9783031365652
Rok wydania:
2023
Ilość stron:
266
Wymiary:
23.5 x 15.5
Oprawa:
Twarda
Dodatkowe informacje:
Wydanie ilustrowane
4.2 Examples of derivatives
4.3 Geometric interpretation of the derivative
4.4 The algebra of derivatives
4.5 Definition of integral
4.6 Relation between integral and derivative
4.7 Methods of integration
4.7.1 Integration by parts4.7.2 Integration by substitution
4.7.3 Integration by partial fraction decomposition
4.7.4 The reverse chain rule
4.7.5 Using combinations of methods
4.8 Ordinary differential equations
4.8.1 First-order linear equations
4.8.2 Initial value problems4.9 Partial differential equations
4.10 Discretization of differential equations
4.10.1 The Implicit or Backward Euler Method
4.10.2 The Runge-Kutta Method
4.11 Systems of differential equations
5.1 Modelling in systems biology
5.2 The different types of mathematical models
5.3 Chemical kinetics: From diagrams to mathematical equations
5.4 Kinetics of chemical reactions
5.4.1 The law of mass action
5.4.2 Example 1: The Lotka-Volterra System
5.4.3 Example 2: The Michaelis-Mentin Reactions
5.5 Conservation laws
5.6 Markov passes
5.7 The master equation
5.7.1 The chemical master equation
5.8 Molecular approach to chemical kinetics
5.8.1 Reactions are collisions
5.8.2 Reaction rate5.8.3 Zeroth-, first, and second order reactions
5.8.4 Higher-order reactions
5.9 Fundamental hypothesis of stochastic chemical kinetics
5.10 The reaction probability density function
5.11 The stochastic simulation algorithms
5.11.1 Direct method
5.11.2 First Reaction Method
5.11.3 Next Reaction Method
5.12 Spatio-temporal simulation algorithms
5.13 Ordinary differential equation stochastic models: the Langevin equation
5.14 Hybrid algorithms
6. Reaction-diffusion systems
6.1 The physics of reaction-diffusion systems6.2 Diffusion of non-charged molecules
6.2.1 Intrinsic viscosity and frictional coefficient
6.2.2. Calculated second virial coefficient
6.3 Algorithm and data structures
6.4 Drug release
6.4.1 The Higuchi model
6.4.2 Systems with different geometries6.4.3 The power-law model
6.5 What drug dissolution is
6.6 The diffusion layer model (Noyes and Whitney)
6.7 The Weibull function in dissolution
6.7.1 Inhomogeneous conditions
6.7.2 Drug dissolution is a stochastic process
6.7.3 The inter-facial barrier model
6.7.4 Compartmental model
Part III
7. Linear Algebra Background
7.1 Matrices
7.1.1 Introduction
7.1.2 Special matrices
7.1.3 Operation on matrices
7.1.4 Transposition and symmetries
7.2 Linear systems
7.2.1 Introduction
7.2.2 Special linear systems
7.2.3 General linear systems
7.2.4 The Gaussian Elimination method
7.2.5 Gaussian elimination for rectangular systems7.2.6 Consistency of linear systems
7.2.7 Homogeneous linear systems
7.2.8 Nonhomogeneous linear systems
7.3 Least-squares problems
7.4 Permutations and determinants
7.5 Eigenvalue problems
7.5.1 Introduction
