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Mathematics for Enzyme Reaction Kinetics and Reactor Performance is the first set in a unique 11 volume-collection on Enzyme Reactor Engineering. This two volume-set relates specifically to the wide mathematical background required for systematic and rational simulation of both reaction kinetics and reactor performance and to fully understand and capitalize on the modelling concepts developed. It accordingly reviews basic and useful concepts of Algebra (first volume), and Calculus and Statistics (second volume). A brief overview of such native algebraic entities as scalars, vectors, matrices and determinants constitutes the starting point of the first volume the major features of germane functions are then addressed. Vector operations ensue, followed by calculation of determinants. Finally, exact methods for solution of selected algebraic equations – including sets of linear equations, are considered, as well as numerical methods for utilization at large.The second volume begins with an introduction to basic concepts in calculus, i.e. limits, derivatives, integrals and differential equations limits, along with continuity, are further expanded afterwards, covering uni- and multivariate cases, as well as classical theorems. After recovering the concept of differential and applying it to generate (regular and partial) derivatives, the most important rules of differentiation of functions, in explicit, implicit and parametric form, are retrieved – together with the nuclear theorems supporting simpler manipulation thereof. The book then tackles strategies to optimize uni- and multivariate functions, before addressing integrals in both indefinite and definite forms. Next, the book touches on the methods of solution of differential equations for practical applications, followed by analytical geometry and vector calculus. Brief coverage of statistics–including continuous probability functions, statistical descriptors and statistical hypothesis testing, brings the second volume to a close.
Volume 1
Basic Concepts of Algebra
Scalars, Vectors, Matrices, and Determinants
Function Features
Vector Operations
Matrix Operations
5ensor Operations
Determinants
Solution of Algebraic Equations
Volume 2
Basic Concepts of Calculus
Limits, Derivatives, Integrals, and Differential Equations
Limits and Continuity
Differentials, Derivatives, and Partial Derivatives
Integrals
Infinite Series and Integrals
Analytical Geometry
Transforms
Solution of Differential Equations
Vector Calculus
Numerical Approaches to Integration
Continuous Probability Functions
Statistical Hypothesis Testing
Linear Regression